MATHEMATICS QUESTIONNAIRE – X CLASS 1. REAL NUMBERS
2 MARK QUESTIONS: 9. Find the LCM and HCF of (i) 12, 18
PRIORITY-I
(ii) 12,15,21 (iii) 23 x 32 and 24 x 3 by 1 MARK QUESTIONS:
1. State Euclid’s division algorithm
prime factorization method 10. Use Euclid’s algorithm to find the HCF of (i) 900,270 (ii) 96,72
2. Expand (i) log 15 (ii) (iii) logx2y3z4 (iv) log (vi) log
11. Find the HCF and LCM of 75 and 160 by
(v) log
fundamental theorem of Arithmetic and verify LCM x HCF =product of two
(vii) log
numbers
3. Explain why i. 17x11x2+17x11x5 ii. 7x11x13+13 iii.7x6x5x4x3x2x1+5 is a
13. Show that i. 7
composite number 4. Determine i. iii.
12. Solve i. 3x=5x-2 ii. 2x+1=31-x iii. 3x=5x+2
iv. 5-
ii. iv. vii.
ix.
x.
+
iv. 2log3-1/2log16+log12
+
as a single logarithm
-
15. Show that i. 4n
ii. 6n iii.12n ,n N can
never end with the digit 0
xiv. log(a2xb3)-log(a3/b2 )
16. State whether the following are
xv. logba.logcb.logac2/3
terminating or non- terminating repeating
5. Write the following in exponential form =x
is irrational
iii. 2logx+3log4+log2
xiii. log1218+log128
i.
vi.
ii. log10+2log3-log2
viii.
xi. 2log3+3log2+log5-log12 xii.
iii. 3+2
14. Write i. 2log3+3log5-5log
v.
vi.
v.
ii. 3
decimal without actual division
ii. log5625=y
iii. log101000=z
iv. log7
=-a
v. log100.001=-4
vi.log5125=3
i.
ii.
iii.
v.
vi.
vii.
iv. iii.
6. Find the HCF of the smallest composite
17. Find the value of a+b+c+d if product of
number and the smallest prime number?
first ten natural numbers is written as 2ax3bx5cx7d
7. If HCF (306,657)=9,find LCM 8. Write the condition to be satisfied by ‘q’
18. If the prime factorization of natural
so that a rational number p/q has a
number (n) is 23x32x52x7. How many
terminating decimal expansion?
consecutive zeroes will it have at the end of it justify your answer? 19. If log2(x2-4x+7)=2 find the value of ’x’ PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 4 MARK QUESTIONS:
6. Write any rational number between 2/3 &
1. Use Euclid’s division lemma to show that
3/5?
any positive odd integer is of the form
7. Find the value of log108 when log2=0.3010
6q+1 or 6q+3 or 6q+5 where q is integer
8. Can you find the HCF of 7 and 9 without
2. Use Euclid’s lemma to show that square of
using prime factorization method? Justify
any positive integer is of form 3p,3p+1
your answer? 9. If x=9,y=log32 then find xy
3. Show that i. are irrationals.
10. What can you say about the LCM and HCF of any two consecutive numbers and
4. If log(x+y/3) =1/2(logx+logy) then find
prime numbers?
the value of x/y+y/x.
2 MARK QUESTIONS:
5. If i.x2+y2=25xy then show that
11. Write any four laws of logarithms?
2log(x+y)=3log3+logx+logy
12. Is i. log2 ii. log3
ii.x2+y2=6xy then show that
iii. log100
iv.
a rational or irrational? justify your answer
2log(x+y)=3log2+logx+logy
13. Do you think that sum of two irrational
6. (2.3)x=(0.23)y = 1000
and product of two irrational is again an
then find the value of 1/x-1/y
irrational? Justify your answer
7. Show that a positive odd integer is of the
14. Find ‘x’ if i.2
form 4q+1 or 4q+3 where q is integer 8. Show that If x2+y2 =3xy then
ii. 2
2log(x-y)=logx+logy
2
ii.x +y =10xy,
iii.
2log(x+y)=logx+logy+2log2+log3
log9-log3=logx
= -3 +
iv.
9. If a2+b2=7ab then
=0
15. Why 6n+5n always end with 1? Explain
log(a+b/3)=1/2(loga+logb)
16. Prove that logaa=1
10. Use Euclid’s division lemma to show that
17. What is the difference between rational
the cube of any positive integer is of the
and irrational number expressed in decimal
form 9m,9m+1,9m+8
form?
PRIORITY-II
18. Show that
1 MARK QUESTIONS: 1. Sate fundamental theorem of arithmetic
log27540=2log2+4log3+log5+log17 19. Insert 4 rational numbers between ¾ and 1
2. If LCM of two numbers ’a’ and ‘b’ is 24 and their HCF is ‘1’ then find the numbers 3. If log10x=a, write 10
2a-3
without using a+b/2 formula 20. A number when divided by 61 gives 21 as
value in terms of x
4. Define logarithm of a natural number?
quotient and 32 as remainder find the number
5. Is log110 defined? Why? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 21. Check whether (2
is
3. Write Roaster form of i. A={x:x is a natural number greater than
rational or irrational? Justify your answer 22. Write
on simplification gives a
rational or an irrational number?
50
but
smaller
ii.
B={x:x
is
an
than
100}
integer,
x2=4}
iii. C={x:x is a letter in the word
4 MARK QUESTIONS:
‘LOYAL’}
1. Show that one and one out of n,n+2 or n+4
iv D={x:x is prime which is divisor of 60}
is divisible by 3 where ‘n’ is any positive
v. E={x:x is a letter of ‘RAMANUJAN’}
integer
vi.F={x:x=n2-1,n
}
2. Show that every positive even integer is of the form 2q and that every positive odd
4. A={Rectangles}, B={Rhombuses} guess
integer is of the form 2q+1 where ‘q’ is some integer 3. Plot
A 5. Is an empty set is finite? why?
on number line
6. The intersection of any two disjoint sets is
4. Prove that logaxy=logax+logay
a null set why?
5. Use Euclid’s division lemma to show that the cube of any positive integer is of the
7. Is Q={x:x+6=6} is not an empty set why? 8. Write any two examples of sets from your
form 7m or 7m+1 or 7m+6
daily life?
2. SETS
9. Express all colors of rainbow as a set 10. Construct two sets A and B such that
PRIORITY-I
A 1 MARK QUESTIONS:
11. If n(AUB)=51,n(A)=20, n(B)=44 then find
1. Define i. set ii. Empty set iii. Finite set iv. Infinite set v. sub set vi. Equal sets vii. Disjoint sets viii. Cardinal numbers of
n(A B) 12. Is
Justify your answer
13. Write two sets of your choice involving
a set and give an example
geometrical ideas?
2. Write the set builders form of
14. If A={0,1,2}, B={2,4} find n(AUB)
i.AU
A
15. If A is the set of all names of workers in a
v. A-B vi. {2,4,8,16,32}
factory. State whether A is finite of infinite
vii. {5,25,125,625}
16. P ={set of factors of 5} Q={set of factors
viii. {1,4,9,16-----,100}
of 25} R={set of factors 125} which is
ix. A={1,1/2,1/3,1/4}
false.
x. A={1,2,3,4} xi. B={1,8,27,64,125}
i. P Q, ii.Q R, iii.R P, iv.P R
xii.{a,e,i,o,u} xiii. Set of rational numbers
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MATHEMATICS QUESTIONNAIRE – X CLASS 2 MARK QUESTIONS:
4 MARK QUESTIONS:
17. Represent AUB, A B,A-B,B-A, A B ,
1. A={x:x is prime 20}, B={x=2n+1,
B A , A B C as Venn Diagrams
n W,n 9} find i. AUB ii A what do you observe?
18. If A={1,2,3,4}, B={1,2,3,5,6} then find A
2. If A={x:x is a natural number}, B={x:x is
are they equal?
an even natural number}, c={x:x is odd
19. If A={2,4,6,8,10}, B={3,6,9,12,15} find
natural numbers} D={x: x is a prime} find
A-B and B-A comment
AUB,AUC, AUD,A B,A C, A D, B C,
20. IfA={0,2,4} then find A
B D,C D,A-B,B-A,A-C,B-C,C-D, A-D,B-D
21. If i. A={1,2,3},B={3,4,5}
3. If A={3,6,9,12,15,18,21},
ii. A={3,4,5,6,7}, B={1,6,7,8,9} then verify n(A
B={4,8,12,16,20}
)=n(A)+n(B)-n(A-B)
C={2,4,6,8,10,12,14,16}, D={5,10,15,20}
22. List all subsets of i. A={},
ii. B={p,q},
then find A-B,A-C,A-D,B-A,C-A,D-A,
iii. C={x,y,z}
iv.D={1,4,9,16}
B-C,B-D,C-B,D-B
23. If A={2,4,6,8,10}, B={3,6,9,12,15} find
4. Prove that if ,A B, B A then A=B 5. For any two sets A,B verify A-B,A
A B,A B,A-B,B-A through venn
A are mutually disjoint with an example
diagram
6. State whether true or false justify your
24. Let A={5,6,7,8}, B={7,8,9,10} find i. A
answer i. {2,3,4,5},
ii. AUB iii. A-B iv. B-A
{a,e,i,o,u},
25. Write roster and set builder form of “ the
A-B={3,4,5},
B-A={1,8,9}
{3,6} disjoint ii.
{a,b,c,d} disjoint
iii.{2,6,10,14},{3,7,11,15} disjoint
set of natural numbers which divides 42” 26. If
,B-
iv.{2,6,10},{3,7,11} disjoint
and
7. State A=B or not
A B={6,7} then find AUB 27. Write an example to propose that A B then AUB=B 28. A={x:x factors of 32}, B={1,2,4,8,16,32} then A=B or not justify? 29. If A={3,4,5}, B={1,6,7,8} verify whether
i. A={a,b,c,d}
B={d,c,a,b}
ii. A={4,8,12,16},
B={8,4,16,18} iii.
A={2,4,6,8,10},
B={x:2 is positive
integer andx<10}
iv. A={x:x is a
multiple of 10} B={10,15,20,25,30----} v. A={x:x is a letter of
n(AUB)=n(A)+n(B) or not 30. If A is the set of all primes below 5 and B is the set of all prime factors of 30 then
‘ASSASSINATION’} B={x:x is letter of “STATION”}
verify A-B=B-A? or not? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS PRIORITY-II 1 MARK QUESTIONS: 1. If A={quadrilaterals}, B={ point, line,
13. If A={x:x N and x
} and
B={x:x N and x
} then write the
set A-B in the set Builder form
triangle} state whether A B OR
14. Write two pairs of disjoint sets out of
B A Or any answer
A, B, A-B, A
2. If n(A)= 10, n(B)=7, n(A B)=5 then
,B-A
15. From the figure write the sets A, B,
find n(AUB)
A-B, B-A, A B, A B
3. Is the empty set is subset to every set. Justify you answer? 4. If
n(P)=8,n(Q)=5
then
find
the
minimum and maximum number of elements in PUQ
16. Establish the relation among the sets of
5. N W Z R Is this true?
real numbers, rational, irrational,
6. B is the set of all months in a year
integers, whole numbers and natural
having 30 days write the above set in
numbers using Venn diagrams
the roster form
17. Answer the following questions and justify your answer i. P={x:x2=4 and
7. If B={A,C,L,S} then write this set in set builder form
3x-9} is it a empty set or singleton set?
8. Raju said that if A,B are non empty
Ii. Q={x=x is a natural number,
sets then either, A B or B A do you
x<2017} it is a finite set or infinite set
agree justify your answer
iii. R={set of all triangles in a plane having the sum of their three angles is
9. Write the formula of n(AUB)if A,B are
less than 180} is an empty set
disjoint
18. A={a,b,c,d}, B={b,d,e}, C={c,d,e,f}
2 MARK QUESTIONS:
then find A (B C)
10. If A={a,e,i,o,u}, B={a,i,u} check
19. A={x:x N ,x<8}, B={x:x N,
i. A iii. A
2
iv. B
4 MARK QUESTIONS:
v. B A vi. (A-B) (B-A)=(A B)-(A B)
1. State finite or infinite give reason 11. If A={2,3,5}then find A
,A
i. A={x N and x<100}
comment
ii. B={x: x N and x 5}
12. let A={2,4,6,8,10},B={3,6,9,12,15} then find (AUB)-(A
iii. C={12, 22 ,32----} v. D={1, 2, 3, 4}
)
v. E={x: x is a day of week} PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 2. Which of the following are sets? Justify
7. Find the number of zeroes of
i. the collection of all months of a year beginning with “j”
(ii) x2 – 1
(i) 2x+1
(iii)
x3
8. Find the sum of the zeroes and product of zeroes of ax2 + bx + c?
ii. The collection of ten most talented
2 MARK QUESTIONS:
writers of India. iii. A team of eleven best cricket batsmen
9. If p(x) = x2 – 5x – 6 the value of find
of the world. iv. The collection of all boys
p(0), p(1), p(2), p(3),p(-1),p(-2),p(-3)?
In your class v. the collection of all even
10. If p(m) = m2 – 3m + 1 find the value of
integers
p(1) and p(-1)?
3. Which are empty sets? Justify
11. Check whether -3 and 3 are the zeroes of the polynomial x2 – 9?
i. set of integers lie between 2 and 3 ii. Set of natural numbers that are smaller
12. Check whether -2 and 3 are the zeroes of the polynomial p(x) = x2 -x– 6?
than 1 iii. Set of odd numbers that leave
13. Find the zeroes of the polynomial
remainder zero when divided by 2
i) p(x) = x2 +5x +6 ii) p(x) = (x+2)(x-3)
iv. Set of lines passing through a point
iii) p(x) = x4 – 16 14. Why are ¼ and –1 zeroes of the
3. POLYNOMIALS
polynomials p(x) = 4x2 + 3x – 1?
PRIORITY-I
15. Find the zeroes of the polynomial 1 MARK QUESTIONS:
p(x) = x2 +7x +10 and verify the relationship between the zeroes and
1. Give an example for i) linear polynomial
coefficients?
ii) quadratic polynomial
16. Draw the rough sketch of y=x3
iii) Cubic polynomial 2. Write the general form of a first degree
17. Find the zeroes of the polynomial p(x) = x2 - 3 and verify the relationship
polynomial in one variable x?
between the zeroes and coefficients?
3. Define zeroes of polynomial? 4. If p(x) = 5x7 – 6x5 + 7x – 6 then find
18. Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2
i) coefficient of x5? ii) degree of p(x)?
respectively?
iii. constant term. 5. Write the polynomial that has i)1 zero ? ii) 2 zeroes?
it are 2 and -1/3 respectively?
iii) no zero
6. How will you verify if polynomial has only one zero?
19. Find quadratic polynomial if the zeroes of 20. Divide 2x2 + 3x + 1 by x + 2? 21. Divide 3x3 + x2 + 2x + 5 by 1+ 2x + x2?
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MATHEMATICS QUESTIONNAIRE – X CLASS 4 MARK QUESTIONS:
11. Write a general polynomial of degree ‘n’
1. Draw the graphs of the given polynomial and find the zeroes. Justify the answers.
with coefficients that are a0,a1----an 12. If
(i) p(x) = x2 – x – 12 (ii) p(x) = x2 – 6x + 9
2x2+7x+5, find the value of
(iii) p(x) = x2 – 4x + 5 (iv) p(x) = x2 + 3x-4 2
(v) p(x) = x – 1
2
(vi) x – 3x – 4
2. Draw the graphs of (i) y = x2 – x – 6 (ii) y = 6 – x – x2 and find zeroes in each
2 MARK QUESTIONS: 1. Find the value of ‘k’ so that x3-3x2+4x+k is exactly divisible by x-2 2. If are the zeros of p(x)=x3+x2+
case. What do you notice? 3. Verify that 1, –1 and –3 are the zeroes of
3. If
the cubic polynomial x3 + 3x2 – x – 3 and check the relationship between zeroes and the coefficients 4. Find all the zeroes of 2x4 – 3x3 – 3x2 + 6x – 2, if you know that two of its zeroes are
2 and - 2 PRIORITY-II 1 MARK QUESTIONS: 1. Write the division algorithm?
are the zeros of 2x2+x-1 then
find the value of 4. If p(x)=3x2+5x-6 then find p(1) and p(2) 5. Find a quadratic polynomial with the sum ¼ and product -1 of its zeros 6. Find the value of ‘m’ in order that x42x3+3x2-mx+6 may be divisible by x-3 7. If are the zeroes of a polynomial of degree 3, then give the relations between the zeroes and the coeffients of the polynomial 4 MARKS QUESTIONS:
2. If R(x)=x -10x+40 then find R(1)+R(0)
zero of y = x3 - 4x?
2
3. Write the condition for ax +bx+c is not to
2. Verify that 3, –1, -1/3 are the zeroes of the
be a quadratic polynomial
cubic polynomial p(x) = 3x3 – 5x2 – 11x –
2
4. Write the degree of i. x +7x +1
3, and then verify the relationship between
ii. x-x7+3 5. Is
+1 then find the
1. Draw the graph of y = x3 - 4x, find the
2
3
are zeroes of the polynomial
the zeroes and the coefficients
a polynomial? Justify your answer?
3. On dividing x3 – 3x2 + x + 2 by a
6. What is the degree of a zero polynomial?
polynomial g(x), the quotient and
2
7. Find the product of zeros of 2017 x -1
remainder were x – 2 and – 2x + 4,
8. Find the sum and product of the zeroes of
respectively. Find g(x)
2
4. Divide 3x2 – x3 – 3x + 5 by x – 1 – x2, and
p(x)=6x -7x+3 9. What is the shape of graph of quadratic polynomial and linear polynomial?
verify the division algorithm? 5. Obtain all other zeroes of 3x4 + 6x3 – 2x2 –
10. When the upward parabola forms a
10x – 5, if two of its zeroes are
quadratic polynomial graph?
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MATHEMATICS QUESTIONNAIRE – X CLASS 4. LINEAR EQUATIONS IN TWO
10. Find the value of k, the equations 2x-ky+3=0
VARIABLES
and
4x+6y-5=0
represent
parallel lines?
PRIORITY-I
11. For what value of k, the equations 1 MARK QUESTIONS:
3x+4y+2=0 and 9x+12y+k=0 represent
1. Write the general form of linear equation
coincident lines? 12. 5pencils and 7pens together cost
in two variables and write condition?
2. Solve 2(x+3) = 18?
Rs.50, where as 7pencils and 5pens
3. Find ‘x’ which satisfies the equation
together cost Rs.46. write pair of linear equations to find the cost of 1
2x-(4-x) = 5-x?
pencil and that 1 pen?
4. Check whether the pair of linear equations 2x+y-5 = 0 and 3x-2y-4 = 0
13. The larger of two supplementary angles exceeds the smaller by 18°. Find the
interesting, parallel, or coincident lines?
angles?
5. Check whether the pair of linear equations 3x+4y = 2 and 6x+8y = 5
14. Two angles are complementary. The
interesting, parallel, or coincident lines?
larger angle is 3° less than twice the
6. Check whether the pair of linear equations
measure of the smaller angle. Find the measure of each angle.
2x-3y = 5 and 4x-6y =15 are consistent?
7. Represent the following situations as linear
15. Solve
i)
3x+2y=11
and
2x+3y=4
equations form :
ii) 3x + 4y = 25, 5x - 6y = -9 by
i) The number of skirts is two less than
elimination method?
twice the number of pants purchased. Also
16. Half the perimeter of a rectangular garden,
the number of skirts is four less than four
whose length is 4m more than its width, is
times the number of pants purchased.
36m.Find the dimensions of the garden
ii) The number of girls is 4 more than the
17. Solve i)0.2x + 0.3y = 13, 0.4x + 0.5y = 2.3 ii) 3x - 5y = -1, x - y = - 1by substitution
number of boys
method
2 MARKS QUESTIONS
4 MARKS QUESTIONS 7. For what value of p, the equations
1. In a garden there are some bees and
2x+py = -5 and 3x+3y = -6 have a unique
flowers. If one bee sits on each flower,
solution?
one bee will be left. If two bees sit on
8. Check the equation i. x+2y=5, 3x+4y=20 ii. x+y=2, 2x+2y=4 are consistent or not
each flower, one flower will be left. Find the number of bees and flowers?
9. If px+3y-(p-3)=0, 12x+py-p=0 has infinite solutions then find ‘p’? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 2. Solve
4. Mary told her daughter, “seven years ago,
2 3 4 9 2 and 1 x y x y
I was seven times as old as you were
3. The perimeter of rectangular plot is
be three times as old as you will be.” Find
32m.If the length is increased by 2m
the present age of Mary and her daughter.
then. Also, three years from now, I shall
and the breadth is decreased by 1m, the
5. A fraction becomes 4/5, if 1 is added to
area of plot remains same. Find the
both numerator and denominator. If,
length and breadth of plot?
however, 5 is subtracted from both numerator and denominator, the
4. The sum of a two digit number and the number obtained by reversing the digit
fraction becomes 1/2. What is the
is 66. If the digits of the number differ
fraction?
by 2, find the number. How many such
6. A man travels 370 km partly by train and partly by car. If he covers 250 km by
numbers are there? 5. A boat goes 30km upstream and 44km
train and the rest by car, it takes him 4
downstream in 10hrs in 13hrs it can go
hours. But if he travels 130 km by train
40km upstream and 55km downstream.
and the rest by car, it takes 18 minutes
Determine the speed of the stream and
more. Find the speed of the train and that
that of the boat in still water.
of the car.? of
7. 2 women and 5 men can together finish
hydrochloric acid in stock. One is 50%
an embroidery work in 4 days while 3
solution and the other is 80% solution
women and 6 men can finish it in 3 days.
how much of each should be used to
Find the time taken by 1 woman alone
obtained 100ml of a 68% solutions
and 1 man alone to finish the work.
6. A
chemist
has
two solutions
7. The ratio of incomes of two persons is
8. The area of a rectangle gets reduced by
9:7 and the ratio of their expenditures is
80 sq units if its length is reduced by 5
4:3 if each of them manages to save
units and breadth is increased by 2 units.
2000 per month find their monthly
If we increase the length by 10 units and
income?
decrease the breadth by 5 units, the area will increase by 50 sq units. Find the
8. Tabita went to a bank to withdraw
length and breadth of the rectangle.
Rs.2000. she asked the cashier to give the cash in Rs.50 and Rs.100 notes
9. Solve
only. She got 25 notes in all. How
2 3 5 4 13 and 2 ? x y x y
many notes each of Rs.50 and Rs.100 she received? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 10. Solve 5 2 15 7 1 and 10? x y x y x y x y 11.
9. If two supplementary angles are in the ratio 1:3, then find the angles 10. 2 tables and 3 chairs together cost Rs 2000/- whereas 3 tables and 2 chairs
Solve
5 1 6 3 2 and 1? x 1 y 2 x 1 y 2
together
x y x y 2 and 6? 12. solve xy xy 13. Solve 6x+3y=6xy and 2x+4y=5xy 14. Solve 2x+3y = 1 and 3x-y = 7
Rs
3000/-.
Form
the
appropriate pair of linear equations for this situation. 11. The coach of a cricket team bus 3 bats and 6 balls for Rs 3900/-. Later he buys another bat and 3 more balls for Rs 1300/-
graphically?
of same kind. Represent this situation
15. Solve 3x+2y = 5 and 2x-2y = 7
algebraically
graphically? 16. Solve 2x-3y = 8 and 4x-6y = 9
12. In a class of 40 students, number of girls is 10 greater than number of boys. Connect
graphically?
this situation algebraically by linear
PRIORITY-II 1 MARK QUESTIONS:
equation.
1. What is the value of ‘a’ for which (3, a)
13. Write two linear equations such that they form parallel and intersecting lines with
lies on 2x-3y=5?
line representing 2x+3y-8=0.
2. Write the number of solutions of the following
cost
pair
of
linear
2 MARKS QUESTIONS
equations
14. For what value of ‘k’, the system of
x+3y-4=0, 2x+6y=7?
equations 2x + ky = 10, 3x+ (k+3) y=12
3. If a pair of linear equations in two
are parallel.
variables is consistent, then which lines are
15. Write the value of ‘k’ for which the system
represented by two equations?
of equations x+y-4=0 and 2x+ky-3=0 has
4. Comment on the solution of dependent
no solution.
pair of linear equations. 5. Write the possible situations when two
16. If the system of equations 3x+y=1, (2k-1)x+(k-1)y=2k+1 is inconsistent, then
lines are drawn in the same plane?
find ‘k’.
6. What is the solution set of inconsistent
17. Check whether the pair of linear equations
equations?
2x+y-5=0 and 3x-2y-4=0 are intersecting,
7. The larger of two complementary angles is
parallel or coincident lines?
double the smaller. Find the angles 8. Is a dependent pair of linear equations
18. For what value of ‘k’, the system of equations x-ky=2, 3x+2y=-5 has a unique
always consistent? Why or why not?
solution. PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 4 MARKS QUESTIONS
5. QUADRATIC EQUATIONS
1. Solve
PRIORITY-I
10 2 15 5 4 and 2 x y x y x y x y 2. Solve
3 2 9 4 2 and 1 x y x y x y x y
1 MARK QUESTIONS: 1. Raju and Rajendar together have 45 marbles. Both of them lost 5 marbles each and the product of the number of marbles
3. Solve 1 1 3 ; 3x y 3x y 4
now they have is 124. Represent the situation in the form of quadratic equation to find out how many marbles they have
1 1 1 2(3x y) 2(3x y) 8
previously?
4. Solve x+y=a+b, ax-by=a2-b2 using method
2. The sum of the reciprocals of Rehman’s
of elimination.
ages (in years) 3 year ago and 5 years from
5. Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours
now is 1/3 find his present age. 3. Verify
the
following
equations
are
if he travels 120 km by train and rest by
quadratic or not? Explain?
car. He takes 20 minutes more if he travels
i.(x+ )2 =3.(x+ )+4; ii. (2x+1)(3x+2)=6
200 km by train and rest by car. Find the
(x-1)(x-2); iii. x2+2
speed of the train and the car
4. Determine
6. In a competitive exam, 3 marks are to be
the
x+3=0
nature
of
roots
of
i) x2+x+1=0,ii. 2x2+x-1=0 iii. 4x2-4x+1=0
awarded for every correct answer and for every wrong answer, 1 mark will be
5. The hypotenuse of a right triangle is 25cm.
deducted. Madhu scored 40 marks in this
we know that the difference in the lengths
exam. Had 4 marks been awarded for each
of the other two sides is 5cm. Represent
correct answer and 2 marks deducted for
the situation in the form of quadratic
each incorrect answer, Madhu would have
equation to find out the lengths of two
scored 50 marks. How many questions were there in the test? (Madhu attempted
sides? 6. The product of two consecutive positive
all the questions)
integers is 306. Represent the situation in the form of quadratic equation to find the integers? 7. Verify that 1 and 3/2 are roots of 2x2-5x+3=0?
PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 8. Find the roots of 2x2-5x+3=0
by
21. Sum of the area of two squares is 468m2 if
factorization method ?
the difference of their perimeters is 24m
9. Find the discriminant of 2x2-4x+3=0√and hence find the nature of the roots?
then find the sides of the two squares. 22. Write any two uses of quadratic equations?
10. Find the value of k for 2x2-kx+3=0,so that
23. Find roots of
it has two equal roots ?
24. Find two consecutive odd positive integers, sum of whose square is 290?
2 MARKS QUESTIONS 11. Find two numbers whose sum is 27 and
25. Find the roots 2 x2 2 2 x 1 0 if they exist, using quadratic formula?
product is 182? 12. The root of the following equations has real and equal roots, find the value k.
26. Find the roots of
i. x -2x(1+3k)+7(3+2k)=0 ii.(k+1)x2-2(k-1)x+1=0
and find the nature of its roots find them if they are real?
- +2=0 by factorization method.
4 MARKS QUESTIONS:
14. Find the quadratic equation whose roots are 2+
=3
1 27. Find the discriminant of 3x 2 2 x 0 3
2
13. Solve
2 x2 7 x 5 2 0
1.
and 2-
whose perimeter is 28m, and whose area is
15. Check (x-2) is a factor of x3-4x2-x+1=0
40m2
16. Explain the benefits of evaluating the discriminant of a quadratic equation before
Find the dimensions of the rectangle
2. The base of a triangle is 4cm longer than its altitude. If the area of triangle is 48cm2,
attempting to solve it. What does it value
then find its base and altitude?
signifies. 17. Find two consecutive positive integers,
3. It is possible to design a rectangular park of perimeter 80m and area 400m2? If so
sum of whose square is 613?
find its length and breadth 18. Find the roots of i)
= x -4,7 ii) 4. If a polygon of ‘n’ sides has
=3 x 0,2
n(n-3)
19. find the roots of the equation i. 5x2-6x-2=0
diagonals. How many sides will a polygon
by the method of completing the square
having 65 diagonals? Is there a polygon
ii.x2+7x-6=0, iii. x2-10x+9=0
with 50 diagonals?.
20. the difference of squares of two numbers is
5. Two water taps together can fill a tank in
180 the square of the smaller number is 8
9 hours. The tap of larger diameter takes
times the larger number find the two
10 hours less than the smaller one to fill
numbers
the tank separately find the time in which watch tap can separately fill the tank. PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 6. If The diagonal of a rectangular field is
PRIORITY – II:
60meters more than the shorter side. If the longer side is 30 metre more than the shorter side, find the sides of the field.
1 MARK QUESTIONS: 1. If the root of the equation x 2 7 x k 0 is -1 then find the value of ‘k’ and other
7. A ball is thrown vertically upward from
root?
the top of a building 96m tall with an initial velocity 80m/sec the distance ‘s’ of
2. The product of two consecutive odd integers is 63 represent this in the form of
the ball from the ground after t seconds is
a quadratic equation
S=96+80t-4.9t2 after how many seconds
3. Give two examples for a quadratic
does the ball strike the ground.
equation which has no real roots
8. A motor boat whose speed is 18km/h in
x
xx ?
still water. It takes 1 hour more to go
4. Find the roots of x
24km upstream than to return downstream
5. Draw the rough sketch of the graph of
to the same spot. Find the speed of the
quadratic equation touching x-axis at one
stream?
point?
9. The altitude of a right triangle is 7m less
6. If b2-4ac 0, then write the roots of quadratic equation ax2+bx+c=0?
than its base. If the hypotenuse is 13cm.
7. Find sum and product of the roots of the
find the other two sides?
equation x2-4x+3=0
10. A motor boat heads upstream a distance
8. Why do we take ‘a’ common while
of 24km on a river whose current is running at 3 km per hour. The trip up and
making a quadratic equation ax2+bx+c=0
back takes 6 hours. Assuming that the
to complete a square
motor boat maintained a constant speed,
9. Find ‘x’ if i. 3+32x=4x3x ii. ax(x-1)=1/a-6
what was its speed?
10. Find the value of ‘k’ for which the equation x2-4x+k=0 has distinct real roots.
11. Is it possible to design a rectangular
2 MARKS QUESTIONS:
mango grove whose length is twice its breadth, and the area is 800m2? If so, find
1. Find the roots of the equation
its length and breadth?
x
1 1 4 ,x 0? x 4
2. Divide 51 into two parts such that their product is 378? 3. Find ‘K’ so that (k-12)x2+2(k-12)x+2=0 has equal roots. 4. Sum of two numbers is 15, if sum of their reciprocal is 3/10 find the numbers PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 5. Solve the equation a2x2+(a2-b2)x-b2=0 6. If x=2 and x=3 are roots of the equation
6.PROGRESSIONS PRIORITY-I
2
3x -2k+2m=0 find the value of k and m.
1 MARK QUESTIONS:
7. Krishna told “every quadratic equation will have real roots” Raghav told 7x=9x2
1. Write first three terms of the AP when a=4 and d=-3?
is a quadratic equation who is correct?
2. Find d of the AP ¼,-1/4,-3/4,-5/4………?
Justify your answer. 8. Find the value of ‘k’ if x2+x-k=2 and x210x+(2k-3)=0 have 3 has a common root. 9.
3. Find d of the AP
2, 8, 18, 32 ,….?
4. Find the 10th term of the AP 5, 1, -3, 7,…………..?
Find the quadratic equation whose roots
5. Which term of the AP
are 2+3i and 2-3i
21, 18, 15,
……………………… is -81 ?
10. Find the value of k for the quadratic equation 9x2-kx+4=0 so that this has two
6. Find the sum of first 100 natural numbers?
equal roots.
7. Write the GP, if a=3, and r=2 ? 8. Check weather 301 is a term of the list of
11. If the roots of the quadratic equation
number 5,11,27,23,……
kx(x-2)+6=0 are equal then find the value of ‘k’
9. Find the sum of -1,1/4,3/2..(10 terms) 10. Which term of the G.P; 2, 2
12. If one root of the quadratic equation 2x2+kx-6=0 is 2, find the value of k also
128? 11. In an A.P the sum of n terms is always not
find the other root 13. Solve the quadratic equation x2-2ax+a2-
equal to zero say your opinion on this
b2=0 by factorization method.
statement?
14. Determine whether the quadratic equation
12. If x,x+2,x+3 are consecutive terms of a G.P. then find x.
3x2+2 5 -5=0 have real roots and if so,
13. Find the common ratio of the GP 25,-5, 1,
find the roots
-1/5, …………………?
15. Find the roots of 9x2+7x-2=0 by using
14. Find x so that x,x+2, x+6 are consecutive
quadratic formula.
terms of GP ?
16. What are the methods to solve a quadratic equation?
,4…..is
15. Find the 10th term of the GP 5,25,125….? 2 MARK QUESTIONS: 13. Determine the AP whose 3rd term is 5 and the 7th term is 9. ? 14. How many two digits numbers are divisible by 3? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 15. Find the 11th term from the last of the A.P
28. In a GP the 3rd term is 24 and 6th term is 192. Find the 10th term ?
series 10,7,4……62 16. How many multiples of 4 lie between 10
29. Deduce sum to n terms in an A.P. by
and 250?
Gauss? 4 MARKS QUESTIONS
17. Find the sum of the first 40 positive integers divisible by 6?
1. A sum of Rs.1000 is invested at 8%
18. If 3rd and 9th terms of a n A.P are 4 and -8
simple interest per year. Calculate the
respectively which term of the A.P is zero
interest at the end of each year. Do these
19. The first term and the last terms of an A.P
interests form an AP? If so, find the
are 17 and 350 respectively if the common difference is 9 how many terms are there
interest at the end of 30 years? 2. In a flower bed, there are 23 rose plants
and what is their sum?
in the first row, 21 in the second row, 19
20. Which term of AP 3, 8, 13, 18,
in the third row and so on. There are 5
…………………..78?
rose plants in the last row. How many
21. Find the 31st term of an AP whose 11th term is 38 and 16th term is 73. ?
rows are there in the flower bed.? 3. A manufacture of TV sets produced
th
22. Find the 20 term from the end of the AP
600sets in the third year and 700 sets in
3,8, 13,……………….., 253?
the seventh year. Assuming that the
23. Subbarao started work in 1995 at annual
salary
of
Rs.5000
production increases uniformly by a fixed
and
number every year, find
received an increment of Rs.200
(i) the production in the 1st year?
each year. In which year did his
(ii) the production in the 10th year?
income reach Rs.7000?
(iii)the total production in 7 years?
24. If the sum of the first 14 terms of an AP is
4. The sum of the 4th and 8th terms of an
1050 and its first term is 10. Find the 20th
AP is 24 and the sum of the 6th and 10th
term. ?
terms is 44. Find the first three terms of
25. How many terms of the AP
the AP.
24,21,18,……..must be taken so that their
5. A sum of 700/- is to be used to give seven
sum is 78 .?
cash prizes to students of a school for their
26. Find the sum of first 24 terms of the list of
overall academic performance if each prize
numbers whose nth term is given by
is 20/- less than its preceding prize find the
an = 3+2n .?
value of each of the prizes.
27. Find the 20th term and nth term of the GP
6. The 4th term of a GP is 2/3 and the 7th term is 16/81. Find the GP?
5 5 5 , , ………? 2 4 8
PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 7. If the geometric progressions 162,54,18….
5. If the sum of first 7 terms of an AP is 49
…………….have their nth
and that of 17 terms is 289, find the sum of
And
first n terms
term find the value of ‘n’
6. Show that a1,a2,----an from an AP where an=9-5n PRIORITY-II
7.
2 MARK QUESTIONS:
The 24th term of an AP is twice its 10th term show that its 72nd terms is 4 times the
1. Which term of the GP 2,8,32,---is 512? 2. Is 84 is a term of the sequence 3,7,11----?
15th term 8. Parking fee for a two wheeler is Rs 10/-
3. In 56,63,70,---497 series how many terms
per day for first day and then after Rs 2/-
are there?
for every day. So what will be the amount
4 MARKS QUESTIONS:
to be paid for 15 days
1. A Contractor constriction job specifies a
9. In a chemical atomic fusion, neutrons are
penalty for delay of completion beyond a
got tripled after every reaction. If 30
certain date as follows Rs. 200 for the first
numbers of neutrons were present at the
day. The penalty for each succeeding day
beginning of the reaction find after how
being Rs 50 more than the preceding day.
man reactions the number of neutrons be
How much money does the contractor pay
17,71,470
as penalty if he has delayed the work by 30
10. If
days
in
a
series
Sn=an2+bn+c
where
Sn denotes the sum of ‘n’ terms then prove
2. A spiral is made up of successive
that the series is arithmetic from the
semicircles, with centers alternately at A and B, starting with centre at A, of radius
second term onwards. 11. If 1/b+c, 1/c+a, 1/a+b are in A.P. , then
0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . What
show that a2, b2, c2 are in A.P.?
is the total length of such a spiral made up of thirteen consecutive semicircles? 3. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row? 4. For what values of n are the nth terms of two AP’s 63,65,67,---- and 3,10,17---equal? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 10.MENSURATION
9. The lateral surface area of a cylinder is equal to the curved surface area of a cone.
PRIORITY-I
If the radius be the same , find the ratio of
2 MARK QUESTIONS:
the height of the cylinder and slant height
1. The radius of conical tent is 7m and its
of the cone?
height is 10m. Calculate the length of
10. A joker cap is in the form of right circular
canvas used in the making the tent if width
cone whose base radius is 7cm and height
of canvas is 2m?
is 24cm. find the area of the sheet required
2. An oil drum is in the shape of a cylinder having
the
following
to make 10 such caps?
dimensions.
11. A cylinder and a cone have bases of equal
Diameter is 2m, and height is 7m. The
radii and are equal heights. Show that their
2
painter charges Rs 3 per m to paint the drum. Find the total charges to be paid to
volumes are in the ratio 3:1? 12. A heap of rice is in the form of a cone of
the painter for 10 drums?
diameter 12m, and height is 8m. Find its
3. A sphere, a cylinder and a cone are of the
volume? How much canvas cloth is
same radius and same height. Find the ratio of their curved surface areas?
required to cover the heap? 13. Find the volume of the largest right
4. A company wanted to manufacture 1000
circular cone that can be cut out of a cube
hemi spherical basins from a thin steel
whose edge is 7cm?
sheet. The radius of the hemi spherical
14. A metallic sphere of radius 4.2cm. is
basin is 21cm. Find the required area of
melted and recast into the shape of a
steel sheet to manufacture the above hemi
cylinder of radius 6cm. find the height of
spherical basins?
the cylinder?
5. A right circular cylinder has base radius
15. Metallic spheres of radius 6cm,8cm, and
14cm, and height 21cm. find i. area of base
10cm respectively are melted to form a
or area of each end ii. Curved surface area
single solid sphere. Find the radius of the
iii. Total surface area and iv. Volume of
resulting sphere? 4 MARKS QUESTIONS
the right circular cylinder? 6. Find the volume and surface area of a
1. A medicine capsule in the shape of a
sphere of radius 2.1cm?
cylinder with two hemi spheres stuck to
7. Find the volume and total surface area of a hemi sphere of radius 3.5cm?
each of its ends. The length of the capsule is 14mm and the width is 5mm. find its
8. Find the volume of right circular cone with
surface area?
radius 6cm and height 7cm? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 2. A toy is in the form of a cone mounted on
of the cylindrical and conical portions are
a hemisphere the diameter of the base and
12cm and 7cm respectively. Find the
the height of the cone are 6 cm and 4 cm
volume of the solid toy?
respectively. Determine the surface area of
8. A women self help group (DWACRA) is
the joy
supplied to a rectangular solid of wax with 3
3. Two cubes each of volume 64cm are
diameters 66cm,42cm, 21cm to prepare
joined end to end together. Find the
cylindrical candles each 4.2cm in diameter
surface area of the resulting cuboid?
and 2.8cm of height. Find the number of
4. A cylindrical container is filled with ice
candles?
cream whose diameter is 12cm and height
9. A hemispherical bowl of internal radius 15
is 15cm the whole ice cream is distributed
cm. contains a liquid. The liquid is to be
to 10 children in equal cones having
filled into cylindrical bottles of diameter 5
hemispherical tops. If the height of the
cm. and height 6 cm. How many bottles
conical portion is twice the diameter of its
are necessary to empty the bowl?
base find the diameter of the ice cream
10. A 20m deep well with diameter 7m. is dug
cone
and the earth from digging is evenly
5. A solid metallic sphere of diameter 28cm
spread out to form a platform 22m. by
is melted and recast into a number of smaller cones each of diameter 4 cm and
14m. Find the height of the platform. 11. An iron pillar consists of cylindrical portion of 2.8 m height and 20cm in
height 3cm. find the number of cones so
diameter and a cone of 42cm height
formed
surmounting it. Find the we3ight of the
6. A solid consisting of a right circular cone
pillar if 1 cm3 of iron weights 7.5g
standing on a hemisphere is placed upright in a right circular cylinder full of water
PRIORITY II: 2 MARK QUESTIONS:
and touches the bottom find the volume of water left in the cylinder given that the
1. A cone of height 24cm and radius of base 6cm is made up of modeling clay. A child
radius of the cylinder is 3cm and its
moulds it in the form of a sphere find the
heights in 6cm. the radius of the
radius of the sphere.
hemisphere is 2cm and the height of the
2. The diameters of the internal and external
cone is 4cm 7. A solid toy is in the form of a right circular cylinder with hemi spherical shape at one end and a cone at the other end. Their common diameter is 4.2cm and the height
surface of a hollow hemispherical shell are 6cm and 10cm respectively. It is melted and recast into a cylinder of diameter 14cm find the height of the cylinder. PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 3. The diameter of a metallic sphere is 6cm it
13. Write the principle of T.S.A of cuboid and
is melted and drawn into a long wire having a circular cross section of diameter
write nomenclature 14. If the ratio of volumes of two sphere is
as 0.2cm find the length of the wire.
64:27 find the ration of their radii
4. How many silver coins 1.75 cm in
15. A cone is on a hemisphere whose
diameter and thickness 2mm need to be
combined diameter is 14cm if height of the
melted to form a cuboid of dimensions
cone is 7cm then find total surface area?
5.5 cm x10cm x3.5cm?
16. The volume and surface area of combined
5. The curved surface area of a cone is
object is given as [
] draw the
2
4070cm and its diameter is 70cm what is its slant height?
suitable figure to it. 17. The radius of two cones are equal and the
6. A cubical box has each edge 10cm and another
cuboid
box
has
ratio of their slant heights are in the ration
dimensions
3:2 then find the ratio of their curved
12.5cm x 10cm x 8cm which box has grater surface area and how much?
surface area 18. If one liter of water to fill in a cube shape
7. A sphere is inscribed in a cylinder such
tin what are measurements requires of
that diameter of the sphere is equal to the height of the cylinder is the surface area of
cube (in cms) explain 19. T.S.A of sphere is 4
the sphere equal to the curved surface area
hemisphere is 3
of the cylinder? If yes explain how?
but T.S.A of
insted of 2
how do
you justify write the LSA formula of cone
8. Express the volume of a sphere in terms of diameter‘d’?
and define the terms in it 20. The diameter of a metallic sphere is 6cm it
9. In what ratio are the volumes of a cylinder
is melted and drawn a wire having
a cone and a sphere if each has the same
diameter of the cross section as 0.2 cm
diameter and the same height?
find the length of the wire.
10. By which multiplying the surface area of a sphere of radius ‘r’ the volume of sphere
21. A rectangular solid of wax with diameters 66cm, 42cm, 21cm is used to prepare 75
can be obtained?
cylindrical candles having diameter 2.1cm
11. Draw a solid shape combining more than
height 2.8cm it is true? Support your
two solid objects
answer?
12. If the dimensions of a cuboid are l, b and h
22. A tap is hemisphere over a cone the
respectively then express the length of the longest pole can be placed inside of it in terms of l, b and h?
common radius is 7cm height of the conical part is 24cm find the TSA and volume of the top. PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 7. COORDINATE GEOMETRY
15. Find the centroid of the triangle formed by the line 4x+5y-20=0 with co – ordinate
PRIORITY-I
axis?
1 MARK QUESTIONS
16. In what ratio does the point (-4,6) divide3s
1. What is the distance between A (4, 0) and
the line segment joining the points
B (8, 0)?
A(-6,10) and B(3,-8)
2. Find the slope of the line passing through
17. Find the point on x-axis which is
the points A(0,4) and B(4,0)
equidistant from (2,-5) and (-2, 9)?
3. What is the distance between A (8, 3) and
18. If the distance between two points (x, 7)
B (-4, 3)?
and (1, 15) is 10. Find x?
4. Find the distance between the points origin
19. Find the radius of the circle whose Centre
and A (7, 4)?
is (3, 2) and passes through (-5,6)?
5. Find the distance between A (2, 0) and
20. Find the coordinates of the point which
B (0, 4)?
divides the line segment joining the points
6. Find the distance between A (4, 2) and B (8, 6)?
(4,-3) and (8, 5) in the ratio 3:1 internally? 21. In what ratio does the point (-4,6) divide
7. Find the midpoint of line segment joining
the line segment joining the points
the points (3, 0) and (1, -4)?
A(-6,10) and B(3,-8)?
8. Find the centroid of the triangle whose
22. Find the ratio in which the y-axis divide
vertices are (3, -5), (-7, 4) and (10, -2)?
the line segment joining the points (5,-6)
9. The points (2, 3), (x, y) and (3,-2) are
and (1,-4). Also find the point of
vertices of a triangle. If the centroid of this triangle is again(x, y), find (x, y)?
intersection? 23. Find the area of triangle whose vertices are
10. The end points of line are (2, 3) and (4, 5). Find the slope of the line?
(1,-1), (-4, 6) and (-3,-5)? 24. Find the area of triangle formed by the
11. Find the slope of the line AB with A (4, -6) and B (7, 2)?
points A (5, 2), B (4, 7) and C (7, -4)? 25. The points (3,-2), (-2,8) and (0,4) are three
2 MARKS QUESTIONS
points in a plane. Show that these points
12. Find the distance between A (2, 3) and
are collinear?
B(4,1)?
26. Find the value of b for the points (1, 2)
13. If the distance between (2,-3) and (10,y) is 10 units then find y
(-1, b) and (-3, -4) are collinear? 27. Determine the x so that 2 is the slope of
14. Name the type of quadrilateral formed by
the line through P (2, 5) and Q (x, 3)?
the points(-1,-2),(1,0), (-1,2), (-3,0) and give reasons for your answer PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 4 MARKS QUESTIONS:
41. Find the area of a triangle whose lengths of sides are 15m, 17m, 21m, use Heron’s
28. Show that the points A (4, 2), B (7, 5), C (9, 7) are lie on a same plane?
formula and verify your answer by using
29. Find the coordinates of points which divide the line segment joining A(-4,0) and
the formula A= ½ bh? 42. Find the area of a triangle formed by the points (0,0),(4,0),(4,3) by using Heron’s
B(0,6) into four equal 30. Show that the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are vertices of square?
formula? 43. Find the area of a triangle formed by
31. Find a relation between x and y such that
joining midpoints of the sides of the
the point (x, y) is equidistant from the
triangle whose vertices are (0,-1), (2,1),and
points (7, 1) and (3, 5)?
(0,3). Find the ratio of this area to the area
32. Find a point on the y-axis which is equidistant from the points A (6, 5) and
of the given triangle? 44. Find the area of quadrilateral whose
B (-4, 3)?
vertices are (-4,-2),(-3,-5),(3,-2) and (2,3)?
33. Verify the points (1, 5), (2, 3) and (-2, -1)
45. Find the area of a triangle formed by the points (2,3),(-1,3),(2,-1) by using Heron’s
are collinear or not? 34. Show that the points A (a, o), B (-a, o), C (0, a) are form an equilateral triangle?
formula? PRIORITY II: 1 MARK QUESTIONS:
35. Show that the points (-4, -7), (-1, 2), (8, 5) and (5,-4) are vertices of rhombus?
1. Find the slope of line joining (2,3) and
36. Find the coordinates of the points of trisection of the line segment joining the
(2,6) 2. If the line 2x+3y=k passes through origin, find ‘k’
points A (2, -2) and B (-7, 4)? 37. Find the coordinates of the points of trisection of the line segment joining the
3. Find midpoint of points(2,7) and (12,-7) 4. Write the co-ordinates of p which divides
points A (2, 6) and B (-4, 8)?
the line segment joining A(x1,y1) and
38. Show that the points (7, 3), (6, 1), (8, 2) and (9, 4) are vertices of parallelogram.?
B(x2,y2) in the ratio m1:m2 5. Find the slope of line perpendicular to
39. If the points A( 6,1),B (8,2), C(9,4) and
2x+3y+5=0
D(p,3) are the vertices of a parallelogram,
6. Which points are called collinear points?
find p?
7. Write area of triangle using heron’s
40. If A(-5,7), B(-4,-5),C(-1,-6) and D(4,5) are the vertices of a quadrilateral ,then find the
formulae 8. What do you meant by trisectional points
area of quadrilateral ABCD?
of a line? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 9. A,B and C are any three points such that
23. In what ratio is segment joining the points
AB+BC=AC what can you say about the points
(-3,2) and(6,1) divide by y-axis 24. If p(b+c,c+a) and Q(c+a,a+b) find PQ
10. Name quadrant to which the following
25. An ant is at (4,5) on graph sheet mounted
points belongs (-3,7),(8,1)
of a wall. If it moves to a point (5,2) and
11. Write the angle made by bisector of first
turns to reach another point (3,6) find the
quadrant
distance travelled by the ant.
12. Find perpendicular distance of A(5,12)
26. Find the coordinates of the centroid of the
from y-axis
triangle, whose vertices are(-4,4), (-2,2)
13. If C(2,p) is a point on the line segment
and(6,12)
joining the points A(6,5) and B(2,11)
27. Find the coordinates of the centre of circle
explain condition for the point ‘C’ to
having the points (9,3) and (1,-1) as the
become the midpoint of AB
end points of the diameter
14. Which of the points Q(3,5) and R(-1,1) are
28. If you plot the points (0,0), (2,0), (2,2),
nearer to the point p(4,4) 15. Write
the
distance
(0,2) and join them in order. Name the between
quadrilateral so obtained based on your
A(a+b,a-b),B(a-b, a+b)
observations
16. Write the formulae to find distance between two points on the same horizontal
4 MARKS QUESTIONS: 1. Vertices of a triangle ABC are A(3,5),
line and vertical line
B(7,4) and C(10,8). The midpoints of the
17. Mention the coordinate axis on which the
sides BC,CA and AB are D,E and F
points (0,6),(0,-2),(0, 2 )
respectively are the centroid of
18. Find the distance between the point p(cos
and Q(-cos
are same or not 2. If the distances of p(x,y) from A(a+b,b-a)
19. (3,-4) is a point on a circle whose center is
and B(a-b,a+b) are equal, then prove that
origin. Guess the radius of the circle.
a x b y
2MARKS QUESTIONS: 20. If p=(2,5), Q=(x,-7) find the possible value
3. If p(x,y) is any point on the line joining the
of x so that PQ=13
points A(a,0) and B(0,b) then show that
21. Find the distance between points(acosx,0)
x y 1 a b
and (0,asinx) 22. Find are area of triangle formed by
and
4.
Prove that the area of triangle whose3 vertices are(t,t-2),(t+2,t+2) and (t+3,t) is
vertices(3,0), (0,4), (0,0)
independent of t PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 5. Prove that the midpoint of the hypotenuse
13. If the sides of a triangle are 3 cm, 4 cm
of a right angled triangle is equidistant
and 6 cm long, determine whether the
from its vertices.
triangle is a right-angled triangle.?
6. The line joining points A(6,9) and B(-6,-9) are given i. in which ratio does origin
2MARKS QUESTIONS:
divide AB ? And what it is called for AB ?
AD 3 ,AC DB 4
ii.in which ratio does the point P(2,3)
14. In ∆ABC,DE // BC and
divide AB ? iii.in which ratio does the
= 5.6 . Find AE
point q(-2,-3) divide AB iv. In how many
15. In ∆ABC,LM //AB, AL = x-3, AC=
equal parts is AB divided by P and Q v.
2x, BM = x-2, BC = 2x+3 find the value of x?
what do we call P and Q for AB ?
16. The perimeters of two similar triangles
8. SIMILAR TRIANGLES
are 30cm and 20cm respectively. If one PRIORITY-I
side of the first triangle is 12cm determine the corresponding side of the second
1 MARK QUESTION
triangle?
1. What are similar triangles?
17. In
2. What are similar polygons?
if DE || AB, AD=8x+9,
CD=x+3, BE=3x+4 and CE=x then find
3. State THALES theorem? 4. Write properties of similar triangles 5. Is similarity of triangles different from
the value of ‘x’. 18. Give
two
different
examples
of
i. similar figures ii. non similar figures iii.
similarity of polygons? Why? 6. Seethe said that “square and rhombus are similar figures” do you accept her
Congruent figures 19. In a trapezium ABCD, AB|| DC, Eand F are points on non parallel sides AD and
statement? Justify your answer? 7. State the converse of the Basic
BC respectively such EF||AB, then show that
proportionality theorem? 8. State AAA similarity criterion ?
20. Prove that a line drawn through the
9. State SSS similarity criterion ?
midpoint of one side of a triangle, parallel
10. State SAS similarity criterion ?
to another side bisects third side?
11. State Pythagoras theorem?
21. Prove that a line joining the midpoints
12. State Converse of Pythagoras
of any two sides of a triangle is parallel to the third side?
Theorem?
PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 22. A person 1.65m tall casts 1,8m
30. A ladder 25m long reaches a window
shadow. At the same instance, a lamp-post
of the building 20m above the ground.
casts a shadow of 5.4m. Find the height of
Determine the distance of the foot of the
the lamp-post?
ladder from the building?
23. A man sees the top of a tower in a
31. A ladder 15m long reaches a window
mirror which is at a distance of 87.6m
of the building 9m above the ground on
from the tower. The mirror is on the
one side of a street . Keeping is foot at the
ground facing upwards. The man is away
same point , the ladder is turned to other
from the mirror and his height is 1.5m.
side of the street to reach a window 12m
How tall is the tower?
high. Find the width of the street?
24. A girl of height 90cm is walking away
32. Hypotenuse of a right triangle is 6m
from the base of a lamppost at a speed of
more than twice of it’s the shortest side. If
1.2m/sec. If the lamp post is 3.6m above
the third side is 2m less than the
the ground, find the length of her shadow
hypotenuse, find the sides of triangle?
after 4 seconds?
33. ABC is an isosceles right triangle
25. A flag pole 4m tall casts a 6m shadow.
right angled at C. Prove that AB2 = 2AC2
At the same time, a nearby building casts
34. A wire attached to vertical pole of
shadow of 24m, how tall is the building?
height 18m is 24m long and has a stake
26. ∆ABC ∆DEF and their areas are
attached to the other end. How far from
64cm2
the base of the pole should the stake be
and
121cm2
respectively.
If
EF = 15.4cm, then find BC?
driven so that the wire will be taut.?
27. Prove that the ratio of if the areas of
35. Two poles of heights 6m and 11m
two similar triangles are equal to the
stand on a plane ground. If the distance
square of the ratio of their corresponding
between the feet of the poles is 12m , find
medians?
the distance between their tops.?
28. ∆ABC
4 MARKS QUESTIONS:
∆DEF.BC = 3cm, EF = 4cm,
and area of ∆ABC = 54cm2 , determine
1.
State and prove THALES theorem?
the area of ∆DEF
2.
State and prove converse of
29. The areas of two similar triangles are
THALES theorem.
81cm2 and 49cm2 respectively. If the
3.
altitude of the bigger triangle is 4.5cm.
the three sides of right angled triangle
find the corresponding altitude of the
show that the area of the triangle on the
smaller triangle?
hypotenuse is equal to the sum of the areas
Equilateral triangles are drawn on
of triangles on the other two sides. PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 4. Draw a line segment of length
PRIORITY II: 1 MARK QUESTIONS:
7.2cm, and divide it in the ratio 5:3. Measure the two parts 5.
1. If the attitude of two similar triangles are
Construct a triangle shadow similar
in the ratio 2:3 what is ration of their areas
to the given triangle ∆ABC, with its sides
2. If ABC and DEF are two triangles such
equal to 5/3 of corresponding sides of
that
∆ABC? 6.
ar(
Construct a triangle of sides 4cm,
5cm, 6cm. Then Construct a triangle
AB BC CA 3 DE EF FD 4
then
write
):ar( DEF)
3. Write two examples for similar figures from your daily life
similar to it, whose sides are 2/3 of
4. What mathematical concept is observed
corresponding sides of first triangle.
when your photo is enlarged
7. Construct an isosceles triangle whose base is 8cm, and altitude is 4cm. Then
5. If
C =900 if AC=6cm then find AB
draw another triangle whose sides are of corresponding sides of isosceles
ABC is a isosceles triangle in which
6. If I
DEF are similar such that
2AB=DE and BC=8 Then find EF
triangle? Prove that the ratios of the areas of
7. When do we say two triangles are similar?
two similar triangles is equal to the ratios
8. In what way similarity of triangles is
8.
different from similarity of polygons
of the squares of their corresponding sides 9.
State and prove PYTHAGORAS
10. Give an example from your daily life
theorem? 10.
where scale factor is used
State and prove converse of
11. Is a square similar to rectangle? Justify
PYTHAGORAS theorem? 11.
9. Define regular polygon
your answer
ABC is a right triangle right angle
at C. Let BC = a, CA = b, AB = c and p be
12. Give an example of Pythagorean triplet
the length of perpendicular from C on AB.
13. If the ratio of perimeters of two similar
Prove that (i) pc = ab ii. 12.
1 1 1 2 2? 2 p a b
triangles is 4:25 find the ratio of their area 14. Write the relation between the areas and
Prove that the sum of the squares
the sides of similar triangles
of the sides of a rhombus is equal to the sum of the squares of its diagonals? 13.
O’ is any point inside a rectangle
ABCD. Prove that OB2 + OD2 = OA2 + OC2? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 2 MARKS QUESTIONS:
9.TANGENTS AND SECANTS TO
1. The area of two similar triangles are 2
A CIRCLE
2
160cm and 121cm respectively if the
PRIORITY-I
longest sides of larger triangle is 26cm what is the length of corresponding similar
1 MARK QUESTIONS:
triangle
1. Define a tangent and a secant to a circle
2. If
ABC is equilateral triangle such that
2. Find the length of a tangent to a circle with centre O and radius 6cm from a point such
AD BC then find the value of AD2 3. InPQR and XYZ it is given PQR
that OP = 10cm?
XYZ ,
and y z 900 XY:XZ=3:4 then find the
3. Draw a circle and two lines parallel to given line such that one is a tangent and
ratio of sides in PQR
the other a secant to the circle?
4. Verify 4cm, 6cm and 8cm from a
4. Calculate the length of a tangent from a
Pythagoras triplet or not
point 15cm away from the centre of circle
5. Write the relation between the sides and diagonals of a rhombus?
of radius 9cm? 5. Find the area of sector whose radius is
4 MARKS QUESTIONS:
7cm, with the given angle 600?
1. AB,CD,PQ are perpendicular to BD,
6. The length of the minute hand of a clock is
AB=x, CD=y and PQ=z prove that
14cm. Find the area of swept by minute hand in 10minutes?
2. In an equilateral triangle ABC, D is a point on side BC such that BD=1/3BC prove
2 MARKS QUESTIONS 7. Prove that the tangent at any point of a
that 9AD2=7AB2
circle is perpendicular to radius through the point of contact?
3. BL and CM are medians of ∆ABC right
8. A tangent PQ at a point P of a circle of
angle at A. prove that 4(BL2 + CM2 ) = 5BC2?
radius 5cm meets a line through the centre O at a point Q so that OQ= 12cm. find the
4. Prove that three times the square of any
length of PQ?
side of an equilateral triangle is equal to four times the square of the altitude?
9. Prove that the tangents to a circle at the end points of a diameter are parallel? 10. Prove that the lengths of tangents drawn from an external point to a circle are equal?
PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 11. If a circle touches all four sides of a
20. . Find the area of the segment AYB
quadrilateral ABCD at points PQRS, then
showing in the adjacent figure. If radius of
prove that AB+CD= BC+DA?
the circle is 21 cm and AOB = 1200?
12. Two concentric circles are radii 5cm, 3cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle? 13. Prove that the parallelogram
21. Find the area of the segments shaded in
circumscribing a circle is a rhombus?
figure, if PQ = 24 CM., PR = 7 CM. and
14. A chord of circle of a radius 10cm
QR is the diameter of the circle with centre O (Take π=22/7)?
subtends a right angle at the centre. Find the area of the corresponding minor segment and major segment? 15. A chord of circle of a radius 12cm subtends an angle of 1200 at the centre. Find the area of the corresponding minor segment of the circle?
PRIORITY II:
4 MARKS QUESTIONS 16. Draw a pair of tangents to a circle of radius 5cm which are inclined to each
MARK QUESTIONS: 1. ON SIDE3 AB as diameter of right angled
other at an angle 600?
triangle ABC is a circle is drawn intersecting hypotenuse AC in p prove
17. Draw a circle of radius 6cm. from a point
PB=PC
10cm away from its centre, construct the pair of tangents to the circle and measure
2. Write the formulae for segment area in a
their lengths. Verify by using Pythagoras
circle radius ‘r’ given that the sector angle
theorem?
is ‘ ’
18. Construct a tangent to a circle 4cm from a
3. What is the angle subtended is a circle is
point on the concentric circle of radius
centre radius 6cm by an arc of length
6cm and measure its length. Also verify
3 cm
the measurement by actual calculation?
4. Find the length of tangent drawn from a
19. Draw a circle with the help of a bangle.
point 8cm away flows the center of a circle
Take a point outside the circle construct the pair of tangents from this point to the
of radius 6cm 5. How many parallel tangents can a circle
circle measure them write conclusion.
have? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 6. Two concentric circles have center at ‘o’
18. A line through the centre o of a circle of
OP=4cm an OB=5cm AB is a chord of
radius 7cm cuts the tangent at a point p on
outer circle and a tangent to inner circle at
the circle at Q such that PQ=24cm find
p find length of p
OQ
7. AP and AQ are two tangents of a circle with center ‘o’ and OQP =450 then find
2 MARKS QUESTAIONS: 1. AB and AC are two tangents to a circle with centre ‘o’ . if OAB =x then find the
POQ
value of ‘x’
8. What can you say about the tangents
2. If area of a regular hexagon is 24
drawn at ends of diameter of a circle?
sq.cm
find its side
9. Draw rough sketch of tangent drawn from
3. Find area of quadrant of circle whose
external point
radius is 7cm
10. The circumference of a circle exceeds the diameter by 16.8cm find the circumference
4. A chord AB of 8cm is drawn is a circle with centre ‘o’ of radius 5cm find the
of the circle
length of tangents from external point p to
11. What is the difference between a tangent
A and B
and secant 12. Write the formula for the area of a sector
5. The length of tangent to a circle of radius 2.5cm from an external point ‘p’ is 6cm
and explain the variables used in the
find distance of p from nearest point to a
formula
circle
13. How can you mark the centre of a circle if
6. The area of circle is 220cm2 then find area
the centre of a circle is unknown?
of square inscribed in it
14. How can you find the area of major circle
7. If radius of two concentric circles is 8cm
segment using area of minor circle
and 10cm then find length of chord of
segment?
larger circle which is tangent to other
15. The tangents to a circle at the end points of
8. A sector is cut from a circle of radius 7cm
diameter are parallel represent the
if the angle of sector is 720 find area
statement diagrammatically
9. If two tangents to a circle of radius 5cm
16. Define the segment of a circle? Draw different types of segments of a circle? 17. A point is 13cm away from the center of
are inscribed to each other at angle of 600 then find the length of each tangents
the circle the length of the tangent drawn from A to the circle is 12cm find the radius of the circle
PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 4 MARKS QUESTIONS:
11. TRIGNOMETRY
1. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm. sweeping through an angle of 115°.
PRIORITY-I 1 MARK QUESTIONS:
Find the total area cleaned at each sweep
1. Define all trigonometric ratios?
of the blades.?
2. The value of sinA and cosA is always less
2. Find the area of the shaded region in
than 1. Why?
figure, where ABCD is a square of
3. Evaluate sin450 +cos450?
side 10cm. and semicircles are
4.
Evaluate 2tan245+cos230-sin260?
drawn with each side of the square as diameter (use π = 3.14)
5. Evaluate
2 tan 30 1 tan 2 45
6. Evaluate
sec35 ? cos ec35
7. If sin A = sin B then prove that A+B = 900? 8. Express sin81 + tan81 in terms of 3. Find the area of the shaded region in
trigonometric ratios of angles between 00
figure, if ABCD is a square of side 7cm. and APD and BPC are semicircles.
and 450?
9. Express sin75 + cos75 in terms of trigonometric ratios of angles between 00 and 450?
10.Evaluate tan48 tan16 tan42 tan74? 11.Evaluate cos36cos54 – sin36 sin54? 4. AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm 0
12.If tanx =5/12 then find secx? 13.If sinA =15/17 then find cosA?
with centre O. if AOB =30 then find the
14.If cosecx =25/7 then find cotx?
area of the shaded region(use = )
15.If secx+tanx= p then find secx-tanx?
5. A round table top has six equal designs, if the radius of the table top is 14cm then
2 MARKS QUESTIONS
16.If tanA = ¾ then find other trigonometric ratios of A ?
find the cost of making the designs with paint at the rate of 5/- per cm2
17.If 3tanA = 4 then find sinA and cosA
6. Calculate the area of the designed region,
18.If cosA= 12/13 then find sinA and tan A
common between the two quadrants of the circles of radius 10cm each PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 19.A chord of circle of radius 6cm is making an angle 600 at the centre. Find the length
PRIORITY II: 1. IF A B the find sin A B is it true? Why
of the chord?
explain
20.If sin(A-B)= ½ and cos(A+B) = ½ find A and B.
2. If tan
then find the value of sin
3. If cos 7A=sin(A-60) where A is an acute
21.Evaluate sin60 cos30 + sin30cos60. What is the value of sin(60+30). What can you
angle find the value of A. 4. What can you say about cot 00=
is it
conclude? defined? Why?
22. Show that cot
tan
sec cosec
23.Show that tan2
tan 4
sec4 -sec2 ?
1 cos 24.Show that (cosec -cot )2= ? 1 cos
25.Show that
5. Is it right to say that sin(A+B)= sinA+sinB? Justify your answer? 6. If the angles A,B,C of a ABC are A.P then find the value of cosB
1 tan 2 A tan 2 A 2 cot A 1
7. If cot
4 MARKS QUESTIONS
8. If cos x =
26.If A, B, C are interior angles of ∆ABC, then show that sin
A B C = COS ? 2 2 A B C =Cot ? 2 2
then find the value of
log(sinx)+log(tan x) 9. Evaluate
27.If A, B, C are interior angles of ∆ABC, then show that tan
= then
.
10. In ABC if C =900 BC+CA=23 cm and
BC-CA=7 cm then find sin A and tan B? 11. Raju says “sin2200+sin2700=1”. Do you
28.Prove that
1 cos A cos ecA cot A 1 cos A
29.Prove that
1 sin A sec A tan A ? 1 sin A
agree with his statement? Give reason?
30.Prove that (sinA+ cosecA)2 + (cosA+ secA)2 = 7+ tan2A + cot2A?
31.If cos ec cot k then prove that k 2 1 cos 2 ? k 1
PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 12. APPLICATIONS OF TRIGONOMETRY
7. A tower stands vertically on the ground. From a point which is 15meter away from the foot if the tower, the angle of elevation
PRIORITY-I
of the top of tower is 450 .what is the
1 MARK AND 2 MARK QUESTIONS: 1. The top of a clock tower is observed at angle of 0 and the foot of the tower is at the distance of d meters from the observer . Draw the diagram for this data? 2. Rinky observes a flower on the ground
8. What is the difference that you observed in
from the balcony of the first floor of a
9. A person put a 10m ladder in 600 angle
height of the tower
between an elevation and angle of depression.
the
with the ground to paste a cinema poster
height of the first floor of the building is x
on a wall. Draw a figure for the given data.
building at the angle of depression
10. A ladder 25m long reaches a window of
meters. Draw the diagram for this data?
building
3. A large balloon has been tied with a rope
20m,
above
the
ground.
and it is floating in the air. A person has
Determine the distance of the foot of the
observed the balloon from the top of the
ladder from the building.
building at angle of elevation
1
and foot
11. Suppose you are shooting an arrow from
.
the top of a building at an height of 6m to
The height of the building is h feet. Draw
a target on the ground at an angle of
the diagram for this data?
depression of 600 what is the distance
of the rope at an angle of depression of
between you and the object?
4. A person is flying a kite at angle of elevation
0
and the length of thread from
12. A ladder of length x metre is leaning against a wall making angle
his hand to kite is l.Draw the diagram for
with the
ground which trigonometric ratio would
this data? 5. A boy observed the top of an electric pole
you like to consider to find height of the
at an angle of elevation of 600 when the
point on the wall at which the ladder is
observation point is 8 meters away from
touching?
the foot of the tower. Find the height of the
13. When a ladder kept 450 angle made with the round raju said that “the distance
pole? 6. Rajender observes a person standing on
between the boot of the ladder and the wall
the ground from a helicopter at an angle of
is equal to the height of the wall which the
depression 450 . If the helicopter flies at
ladder top was touch”. In his statement
height of 50meters from the ground . what
true. Justify your answer?
is the distance of the person from
14. Length of the shadow of a 15m high pole is 5
Rajender?
at 70 clock in the morning. Then, PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS what is the angle of elevation of the sun
top of the tower is 300. Find the height of
rays with the ground at the time?
the tower and width of the road?
15. An observer of height 1.8m is 13.2m away
20. A tree breaks due storm and broken part
from a palm tree. The angle of elevation of
bends so that the top of the tree touches the
the top of the tree from his eyes is
ground by making 300 angle with the
450.what is the height of the palm tree?
ground. The distance between the foot of
4 MARK QUESTIONS:
the tree and the top of the tree on the
16. Two men on either side of a temple of 30m
ground is 6m. find the height of the tree
height observe its top at the angles of elevation300 and 600 respectively. find the
before falling down.? 21. A boat has to cross the river. it crosses the river by making an angle of 600 with the
distance between the two men? 17. A straight high way leads to the foot of the
bank of the river due to the stream of the
tower. Ramaiah standing at the top of the
river and travels a distance of 600m to
tower observes a car at angle of depression
reach the another side of the river. What is
300. The car is approaching the foot of the
the width of the river?
tower with a uniform speed. Six seconds
22. The angles of elevation of the top of a
later, the angle of depression of the cars is
tower from two points are at a distance of
0
found to be 60 . Find the time taken by a
4m and 9m find the height of the tower
car to reach the foot of the tower from this
from the base of the tower and in the same
point?
straight line with it are complementary.
18. The angle of elevation of the top of a
23. An electrician wants to repair an electric
building from the foot of the tower is 30º
connection on a pole of height 9m. he
and the angle of elevation of the top of the
needs to reach 1.8m below the top of the
tower from the foot of the building is 60º.
pole to do repair work. What should be the
If the tower is 30 m high, find the height of
length of the ladder which he should use
the building?
when he climbs it an angle of 600 with the ground? What will be the distance between
19. A TV tower stands vertically on the side of
foot of the ladder and foot of the pole?
a road. From a point on the other side
24. A 1.5m tall boy is looking at the top of the
directly opposite to the tower, the angle of
temple which is 30m in height from a
elevation of the top of the tower is 600.
point at a certain distance. The angle of
From another point 10m away from this
elevation from his eye to the top of the
point , on the joining this point to the foot
crown of the temple increases from 300 to
of the tower, the angle of elevation of the
600 as he walks towards the temple. Find PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS the distance he walked towards the temple?
13.PROBABILITY PRIORITY-I
25. Two poles of equal heights are standing
1 MARK AND 2 MARK QUESTIONS:
opposite to each other side of the road,
1. A die is thrown twice. What is the
which is 120feet wide. From a point
probability that (i) 5 will not come up
between them on the road, the angles of
either time? II. 5 will come up at least
elevation of the top of the poles are 600
once
and 300 respectively. Find the height of the
2. A bag contains 4 red and 6 black balls. A
poles and the distances the point from the
ball is taken out of the bag at random. Find
poles?
the probability of getting a black ball? 3. If P(E) = 0.05, what is the probability of
26. A statue stands on the top of a 2m tall
‘not E’?
pedestal. From a point on the ground, the
4. A bag contains a red ball, a blue ball and a
angle of elevation of the top of the statue is
yellow ball, all the balls being of the same
60º and from the same point, the angle of
size. Raju takes out a ball from the bag
elevation of the top of the pedestal is 45º.
without looking into it. What is the
Find the height of the statue?
probability that he takes out the (i) yellow
27. From the top of a building, the angle of
ball? (ii) red ball? (iii) blue ball?
elevation of the top of a cell tower is 60º
5. Suppose we throw a die once. (i) What is
and the angle of depression to its foot is
the probability of getting a number greater
45º. If distance of the building from the
than 4 ? II. What is the probability of
tower is 7m, then find the height of the
getting a number less than or equal to 4?
tower?
6. One card is drawn from a well-shuffled
28. A wire of length 18 m had been tied with
deck of 52 cards. Calculate the probability
electric pole at an angle of elevation 30º
that the card will (i) be an ace, (ii) not be
with the ground. Because it was converting
an ace?
a long distance, it was cut and tied at an
7. A bag contains lemon flavoured candies
angle of elevation 60º with the ground.
only. Malini takes out one candy without
How much length of the wire was cut?
looking into the bag. What is the probability that she takes out (i) an orange flavored candy? (ii) a lemon flavored candy?
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MATHEMATICS QUESTIONNAIRE – X CLASS 8. It is given that in a group of 3 students, the
17. Two dice one red and one white, are
probability of 2 students not having the
thrown at the same time. Write down all
same birthday is 0.992. What is the
the possible outcomes. What is the
probability that the 2 students have the
probability that the sum of the two
same birthday?
numbers appearing on the top of the dice is
9. Find the probability of getting a head when a coin is tossed once. Also find the
i) 8
ii) 13 iii) less than or equal to 12?
18. Rahim removes all the hearts from the
probability of getting a tail?
cards what is the probability? i) getting an
10. Write a situation with equally likely event
ace from the remaining pack ii) getting a
and find the sample space?
diamonds iii) getting a card that is not a
11. Is getting a tail complementary to getting a head? Give reason?
heart iv) getting the ace of hearts 19. Natural numbers 1 to 25 are written on
12. Can 7/2 be the probability of an event?
cards and kept in a bag. A card is
Explain?
randomly picked up find the probability of
13. A box contains 3blue, 2 white and 4 red
the following events i) the number is prime
marble. If a marble is drawn at random
ii) the number is composite iii) the number
from the box what is the probability that it
is neither prime nor composite iv)verify
will be i) white?
whether the sum of the probabilities of
ii)not blue?
iii) red?
14. 12 defective pens are accidentally mixed
above three events is 1.
with 132 good ones. It is not possible to
20. A kiddy bank contains hundred 50p coins,
just look at a pen and tell whether it is
fifty 1rupee coins, twenty 2 rupee coins
good or not it is defective. One pen is
and ten 5 rupee coins. If it is equally likely
taken out at random from this lot.
that one of the coins will fall out when the
Determine the probability that the pen
bank is turned upside down, what is the
taken out is a good one
probability that the coin (i) will be a 50p
15. Sarada and hamida are friends. What is the3 probability that both will have i)
coin? (ii) will not be a 5 rupee coin 21. A box contain 5 red marbles, 8 white
different birthdays? ii)the same birthday?
marbles and 4 green marbles. One marble
4 MARK QUE3STIONS:
is taken out of the box at random. What is
16. A bag contains 3 red balls and 5 black
the probability that the marble taken out
balls. A ball is drawn at random from the
will be (i) red? (ii) white? (iii) green (iv)
bag. What is the probability that the ball
not green?
drawn is (i) red? (ii) not red?
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MATHEMATICS QUESTIONNAIRE – X CLASS 22. A die is thrown once. Find the probability
28. One card is drawn from a well
of getting : (i) A prime number ii. a
shuffled deck of 52 cards. Find the
number lying between 2 and 6 iii. an odd
probability of Getting (i) a king of
number?
red color (ii) a face card (iii) a red
23. A box contains 90 discs which are
face card (iv) the jack of hearts (V)
numbered from 1 to 90. If one disc is
a spade (vi) the queen of diamonds?
drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5? 24. A game consists of tossing a one rupee coin 3 times and noting its outcome each
14.STATISTICS PRIORITY-I 1 MARK QUESTIONS: 1. Define the mean for ungrouped data?
time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and
loses
otherwise.
Calculate
2. Find the mean of first “n” natural numbers?
the
probability that Hanif will lose the game?
3. Find the mean of 5,6,9,10,6,12,3,6,11,10?
25. A bag contains 4 red, 5 black and 3 yellow balls. A ball is taken out of the bag at
4. What is mode?
random. Find the probability that the ball
5. Find the mode of 5,6,9,10,6,12,3,6,11,10,4,6,7.?
taken out is of (i) yellow colour (ii) not of
6. Can “ mode “ be calculated for
red colour.?
grouped data with un equal class
26. Gopi buys a fish from a shop for his
sizes?
aquarium. The shopkeeper takes out one fish at random from a tank containing 5
7. Write the formula for mode for
male fish and 8 female fish. What is the
grouped data?
probability that the fish taken out is a male
8. What is median?
fish?
9. Find the median of 2, 3, 6, 0, 1, 4, 8, 2,5?
27. A game of chance consists of spinning an arrow which comes to rest pointing at one
10. Find the median of the data 5,3, 1,4,6,7,0?
of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is
11. Will the median class and modal
the probability that it will point at (i) 8?
class of a grouped data always be
(ii) an odd number? (iii) a number greater
different? Justify your answer?
than 2? (iv) a number less than 9?
12. Find the mean of X, X + 1, X + 2, X + 3, X + 4, X + 5 and X + 6? PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 2 MARK QUESTIONS: 13. Write the formula for mean by
3. The following distribution shows the daily pocket allowance of children of a
direct method? Explain each term in
locality. The mean pocket allowance is Rs
it?
18. Find the missing frequency f?
14. Write the formula for mean by assumed method? Explain each term in it? 15. Write the formula for mean by step
4. Find the mode of the following data?
deviation method? Explain each term in it? 16. Write the formula for mode for
5. Find the median of the following data?
grouped data? Explain each term in it? 17. Write the formula for median for grouped data? Explain each term in it?
6. If the median of 60 observations is 28.5 find the values of x and y?
18. Find ‘X’ if the median of the observations in ascending order 24, 25, 26, X + 2, X + 3, 30, 31, 34 is 27.5? 4 MARKS QUESTIONS: 1. Find the mean of the following frequency
7. The following distribution gives the daily income of 50 workers of a factory.
table?
2. Find the mean of the following frequency
Convert the distribution above to a less than
table?
cumulative frequency distribution, and draw its ogive?
PREPARED BY SANKAR GUTTA
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MATHEMATICS QUESTIONNAIRE – X CLASS 8.The following table gives production yield per hectare of wheat of 100 farmers of a village
Convert the distribution above to a more than cumulative frequency distribution, and draw its ogive? 9.Draw both ogives for the following data. Find the median of the data?
PREPARED BY SANKAR GUTTA
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