Math-Quiz-15 MATH-QUIZ Preliminary Test Paper Sets and Functions & Aptitude Dur: 60 minutes

23.08.2015

Max: 100 marks

Instructions: 1. All the Questions are Compulsory. 2. Each question carries 4 marks. 3. Each wrong answer carries −1 mark. 4. Not answering to a question will credit or debit Nothing. 5. Don’t afraid of your neighbour’s expression, he also don’t know the answer. Answer all the Questions: 1. A tree has broken by wind and the brokened portion is touching the ground with an 45◦

(4)

with the ground at 10 m away from the foot of the tree. The entire length of the tree was (a) 15 m

p (c) 10( 2 + 1) m

(b) 20 m

2. The value of cos2 (108◦ ) + cos2 (144◦ ) (a)

3 4

(b)

5 4

p (d) 5( 3 + 2) m

. (c)

5 2

(4) (d)

4 5

3. If the roots of the quadratic equation x2 + px + q = 0 are tan 30◦ and tan 15◦ , then the

(4)

value of 2 + q − p is (a) 1

(b) 2

(c) 3

(d) 0

4. If f ( x) = 2 x2 + 2, then what is the value of f ( x + 4)? (a) 2 x2 + 4 5. If f ( x) = (a) 6

p 3

(b) 2 x2 + 16 x + 32

x3 − 2 x + 6 and g( x) = (b) 8

(c) 2 x2 + 16 x + 34

(4) (d) 2 x2 + x + 6

136 , then the value of g( f (2)) is x + 17 (c) 8.2

(4)

(d) none of these

6. A regular hexagon is inscribed in the circle with center O. If the

(4)

circle has a radius of 2, what is the area of the shaded region? p p p (d) 4π − 4 (a) 2π − 3 3 (b) 2(2π − 3 3)(c) 36 3 7. The number of solutions of (a) 0

(b) 1

p 3 x2 + x + 5 = x − 3 is

(c) 2

(4) (d) 4

q

8. The value of x = (a) 3

6+

p

p 6 + 6 + . . . ∞ is

(b) 2

(4) (c) 1

(d) none of these

9. A train covers a distance in 50 min ,if it runs at a speed of 48kmph on an average.The

(4)

speed at which the train must run to reduce the time of journey to 40min will be. (a) 50kmph

(b) 60kmph

(c) 65kmph

(d) 70kmph

10. A software engineer has the capability of thinking 100 lines of code in five minutes and

(4)

can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour? (a) 200

(b) 225

(c) 250

(d) 300

11. If every alternative letter starting from B of the English alphabet is written in small

(4)

letter, rest all are written in capital letters, how the month September be written. (a) SeptEMbEr (b) SEpTeMBEr ¶ µ ¶ µ 2x 1+ x , then f =? 12. If f ( x) = log 1− x 1 + x2 ¡ ¢2 ¡ ¢3 (a) f ( x) (b) f ( x) ³ ¡ ¢´ 1 13. If f ( x) = 1 − , then f f 1x = x

(a) f ( x)

(c) SeptembeR

(d) None of the above (4)

(c) 2 f ( x)

(d) 3 f ( x)

.

(b) f ( x) − 1

(c)

(4)

x x−1

14. Let f : Q → Q defined by f ( x) = x2 . Then f −1 ( x) = © ª (a) − 3, 3 (b) 3 (c) ;

(d) 1 −

x x−1 (4)

(d) none of the above

15. Let f be the exponential function and g be the logrithmic function with the same base

a. Then ( f g)(1) = (a) a

(b) 1

(c) 0

(d) cannot be determined

16. In the figure if TP and TQ are tangents to a circle with center at O then the value of x + y + z = (a) 120◦

(b) 150◦

(c) 180◦

(d) 360◦

(4)

(4)

17. A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth.

(4)

The percentage of decrease in area is (a) 10%

(b) 10.08%

(c) 20%

(d) 28%

18. A forester wants to plant 66 apple trees, 88 banana trees and 110 mango trees in equal

(4)

rows (in terms of number of trees). Also he wants to make distinct rows of trees (i.e., only one type of trees in one row). The number of minimum rows required are (a) 2

(b) 3

(c) 10

.

(d) 12

19. A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm.

(4)

How many revolutions will the smaller wheel make when the larger one makes 15 revolutions ? (a) 23 20. Set of values of x, if (a) {1}

(b) 24 p

(c) 25

(d) 26

p x + 8 + 2 x + 2 = 1, is

(b) {1,17}

(4)

(c) {17}

(d) ;

21. 1100 boys and 700 girls are examined in a test; 42% of the total students are passed.

(4)

Then the failed is (a) 58%

(b) 62 23 %

(c) 64%

(d) 78%

22. The equation representing the given graph is y 2 x + 7 y = 11 ; 4 x + 35 2

(4)

(a) 7 x + 2 y = 11 ; y − 2 x = 3

(b)

(c) 3 x − 7 y = 10 ; 8 y − 6 x = 4

(d) 3 x − 4 y = 1 ; 8 y − 6 x = 4

= 25

23. On the set f all real numbers, define a relation R = {(a, b) : a ≤ b}. Then R is (a) Equivalence relation

(b) reflexive,symmetric,not transitive

(c) reflexive,not symmetric, transitive

(d) not reflexive,not symmetric, transitive

24. If A and B are two ses containing four and two wlements, respectively. Then, the number of subsets of the set A × B each having atleast three elements are (a) 219

(b) 256

(c) 275

(d) 510

(4)

(4)

v  s u q u 1 1 1 1 . . . is 25. The value of 6 + log 3  p t4 − p 4− p 4− p 3 2 2 3 2 3 2 3 2 

(a) 2

(b) 4

(c) 5

(4) (d) 10

MATH-QUIZ(Preliminary)-Answer Key: p 1. (c) 10( 2 + 1) m 2. (a)

3 4

3. (c) 3 4. (c) 2 x2 + 16 x + 34 5. (b) 8 p 6. (b) 2(2π − 3 3)

7. (a) 0 8. (a) 3 9. (b) 60kmph 10. (c) 250 11. (d) None of the above 12. (c) 2 f ( x)

x x−1 © ª 14. (a) − 3, 3

13. (d) 1 −

15. (c) 0 16. (c) 180◦ 17. (d) 28% 18. (d) 12 19. (c) 25 20. (d) ; 21. (a) 58% 22. (d) 3 x − 4 y = 1 ; 8 y − 6 x = 4 23. (c) reflexive,not symmetric, transitive 24. (a) 219 25. (b) 4

zzzzz

preliminary-quiz.pdf

(a) ©. −3,3. a. (b) 3 (c) ; (d) none of the above. 15. Let f be the exponential function and g be the logrithmic function with the same base (4). a. Then (f g)(1) = (a) a (b) 1. (c) 0 (d) cannot be determined. 16. In the figure if TP and TQ are tangents to a circle with center at O (4). then the value of x+ y+ z = (a) 120◦. (b) 150◦. (c) 180◦.

116KB Sizes 0 Downloads 279 Views

Recommend Documents

No documents