www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE
NARAYANA JUNIOR COLLEGE AP EAMCET-2016 SET-A ============================================= MATHS 1.
The domain of the function f x log 0.5 x ! 1. {0,1,2,3,…}
2. {1,2,3,…}
3. 0,
4. {0,1}
KEY: 4 HINT: log1/ 2 x 0
log1/ 2 x log1/ 2 1 x 1 x 0,1 If f x x 1 x 2 x 3 , 2 x 3 , then f is 1. an onto function but not one-one 3. a bijection KEY: 3 HINT: 2 x 3 f x x 1 x 2 x 3
2.
3.
2. One-one function but not onto 4. Neither one-one nor onto
x 1 x 2 x 3 x The greatest positive integer which divides n 16 n 17 n 18 n 19 , for all positive
integers n, is 1. 6 2. 24 3. 28 KEY: 2 HINT: Product of four consecutive positive integers is divisible by 4
4. 20
a b c 4.
If a,b,c are distinct positive real numbers, then the value of the determinant b c a is c a b
1. 0 2. 0 KEY: 1 HINT: 3abc a 3 b 3 c 3 a 3 b3 c 3 3abc
3. 0
4. 0
a b c a 2 b 2 c 2 ab bc ca 0
5.
If x1 , x2 , x3 as well as y1 , y2 , y3 are in geometric progression with the same common ratio, then
the points x1 , y1 , x2 , y2 , x3 , y3 are 1. vertices of an equilateral triangle 3. vertices of a right angled isosceles triangle KEY: 4 HINT: x1 , x2 , x3 a, ar, ar 2 are in G.P
2. vertices of a right angled triangle 4. Collinear
y1 , y2 , y3 b, br, br 2 are in G.P Slope of line joining x1 , y1 x2 , y2 = Slople of line joining x1 , y1 and x3 , y3 Page 1 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 6.
The equations x y 2 z 4 , 3 x y 4 z 6 , x y z 1 have 1. unique solution 2. infinitely many solutions 3. no solution KEY: 2 HINT: x y 2 z 4,3 x y 4 z 6 4 x 6 z 10 3 x y 4 z 6, x y z 1 2 x 3 z 5 a1 b1 c1 a2 b2 c2
4. two solutions
2
2
The locus of the point representing the complex number z for which z 3 z 3 15 is 1. a circle 2. a parabola 3. a straight line 4. an ellipse KEY: 3 7.
2
HINT: z x iy x 3 y 2
x 3
2
y 2 15
12 x 15 2016
8.
1 i 2014 1 i
1. 2i KEY: 1
2. 2i
2016
HINT: 9.
1 i 2014 1 i
2
4. -2
1008
1 i 1 i 2
3. 2
1007
1008
2i 1007 2i
2i
If z1 1, z2 2, z3 3 and 9 z1 z2 4 z1 z3 z 2 z3 12 , then the value of z1 z2 z3 is
1. 3 KEY: 4 HINT: z1 1, z2 2, z3 3
2. 4
3. 8
4. 2
9 z1 z2 4 z1 z3 z 2 z3 12 z1 z1 z1 z1
z1
2
2
z1
9 4 1 12 z3 z2 z1
z1 z2 z3
2
2
2
z z z (1) (2) (3) 3 2 1 12 z3 z2 z1 z3 z2 z1 2
z1 z2 z3 2 If 1, z1 , z2 ,..., zn 1 are the nth roots of unity, then 1 z1 1 z2 ... 1 zn1 1. 0 2. n 1 3. n KEY: 3 HINT: verification (taking n = 3) 1 z1 1 z2 ... 1 zn1 n 10.
4. 1
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 11.
2
If 124 2 x 24 3 1.
3 x2 2
, then x
13 12
2.
14 15
3.
12 13
4.
5 14
KEY: 2 2
HINT: 12 4 2 x 24 3 8 4 x 2
2 3
12.
3x 2 2
3 3 x2 2
2 3
8 4 x2 9 x2 6 5 x 2 14 14 x 5 The product and sum of the roots of the roots of the equation x 2 5 x 24 0 are respectively
1. -64, 0 KEY: 1 HINT: x 2 5 x 24 0
2. -24, 5
3. 5, -24
4. 0, 72
2
x 8 x 3 x 24 0 x x 8 3 x 8 0 x 8,
x 3
x 8 impossible Sum = 0, product = -64 13. The number of real roots of the equation x5 3 x 3 4 x 30 0 is 1. 1 2. 2 3. 3 KEY: 1 HINT: x 5 3 x 3 4 x 30 0 f x no positive root
4. 5
f x x5 3x3 4 x 30 0 …..+ one-ve root number of real roots = 1 14. If the coefficients of the equation whose roots are k times the roots of the equation 1 1 1 x3 x 2 x , are integers then a possible value of k is 4 16 144 0 1. 3 2. 12 3. 9 4. 4 KEY: 2 1 1 1 HINT: f x x 3 x 2 x 0 4 16 144 3 2 1 x 1 x x 1 x f 3 0 2 k k 4 k 16 k 144 1 2 1 2 k3 3 x kx k x 4 16 144 K = 4,8,12,16… K = 4,8,12 … Possible value of K = 12
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 15.
The sum of all 4-digit numbers that can be formed using the digits 2,3,4,5,6 without repetition, is 1. 533820 2. 532280 3. 533280 4. 532380 KEY: 3 HINT: 2,3, 4,5, 6 sum of four digit number without repetition
2 3 4 5 6 51 P41 1111 20 24 1111 533280 16.
If a set A has 5 elements, then the number of ways of selecting two subsets P and Q from A such that P and Q are mutually disjoint, is 1. 64 2. 128 3. 243 4. 729 KEY: 3 HINT: A a1 , a2 , a3 , a4 , a5 subset P,Q P Q so each element has three possibilities
3 3 3 3 3 35 243 17.
4
The coefficient of x 4 in the expansion of 1 x x 2 x 3 is
1. 31 KEY: 1 4 HINT: cot x 4 1 x x 2 x 3
2. 30
3. 25
1 x x 2 x 3 x 4 x 5 ... x 4 x 5 x 6 1 1 x x 4 1 x x 2 x3 ... 1 1 1 x x 4 1 x
1 x
4
4. -14
4
4
4
4 4
1 x
4 4 1 2 4 4 1 4 2 3 4 4 1 4 2 4 3 4 1 4 x x x x ..... 2! 3! 4! 4 8 x 1 4cx 4c2 x ...
1 35 34
18.
4.5.6.7 cot x 4 1 4 1 1.2.3.4 4 35 31 2n If the middle term in the expansion of 1 x is the greatest term, then x lies in the interval
n n 1 , 1. n 1 n KEY: 1 HINT: 1 x P
2n
n 1 n , 2. n n 1
middle ten T
3.
n 2, n
4.
n 1, n
2n 1 Tn 1 2
Q 2 n 1 X 1 X
p n n p n 1 n
2n 1 x 1 x
n 1
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE x n n 1 2n 1 1 x 2n 1 2n 1 1 x 2n 1 n x n 1
2n 1 1 2n 1 1 n x n 1 2n 1 1 2n 1 1 1 n x n 1 n 1 1 n n x n 1 n n 1 x n 1 n 19.
2x 1 n 1 n 1
To find the coefficient of x 4 in the expansion of
3x , the interval in which the x 2 x 1
expansion is valid, is 1 1 2. x 2 2
1. 2 x
3. 1 x 1
4. x
KEY: 3 HINT:
3x x 2 x 1
x 1, 2
3x x 2 1 1 x 2
x 1
x 2, x 1 2 x 2, 1 x 1 Common interval is 1 x 1
If 1 tan 1 tan 4 2, 0, , then 16 1. 2. 20 30 KEY: 1 HINT: 1 Tan 1 Tan4 2, 0, 16 1 TanA1 TanB 2 A B 4 4 4 20 20.
cos cos , then one of the values of tan is 1 cos cos 2 1) cot tan 2) tan tan 3) tan cot 2 2 2 2 2 KEY: 1 HINT:
3.
40
4.
60
21.If cos
4) tan 2
tan 2 2 2
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 1 1 cos cos cos cos cos By componendo dividendo 1 cos (1 cos ) (1 cos ) 1 cos 1 cos 1 cos We tan 2 tan 2 cot 2 . 2 2 2 22.
The value of the expression
1) 0
2) 1
1 sin 2 1 3 sin 2 cot cot is 3 4 2 2 2 cos(2 2 ) tan 4 3) sin 2 4) sin2 2
KEY: 4 HINT: 2 tan 1 2 1 tan 2 sin 2 . 2 1 tan 1 tan 4 tan 1 tan 2 1 tan (1 tan )2 1 4sin .cos .cos . (1 tan )2 4 sin 1
1 – cos2 = sin2 23.
If
1 sin , cos and tan are in geometric progression, then the solution set of is 6
6
1) 2n
3
2) 2n
3
3) n (1)n
3
4) n
KEY: 2 HINT:
1 sin 2 . 6 cos 6 cos3 = 1 – cos2 6 cos3 + cos2 - 1 = 0 1 cos satisfied 2 2n , n z . 2 cos 2
4 1 If x sin(2 tan 1 2) and y sin tan 1 , then 3 2 1) x > y 2) x = y 3) x = 0 = y KEY: 1 HINT: 2(2) 4 x sin sin 1 1 22 5
24.
4) x < y
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 1 cos 1 4 and y sin = 3 2 2 5 4 tan 3
Let tan 1 25.
If cosh( x) 1)
61 16
5 , then cosh (3x) = 4 63 2) 16
3)
65 16
4)
61 63
KEY: 3 HINT: Cosh 3x = 4 cosh3x – 3 cos hx A B C B C C A A B then(x + y + z) = In ABC if x tan tan , y tan tan and z tan tan 2 2 2 2 2 2 1 1) x y z 2) –x y z 3) 2 x y z 4) x y z 2 KEY: 2 HINT: bc 1 x b x bc 1 x c 1 y c 1 z a Similarly , 1 y a 1 z b
26.
1 x 1 y 1 z . . 1 1 x 1 y 1 z
x + y + z = -xyz 27.
In ABC, if the sides a, b, c are in geometric progression and the largest angle exceeds the smallest angle by 60º, then cosB = 1)
13 1 4
2)
1 13 4
3) 1
4)
13 1 4
KEY: 4 HINT: b 2 = ac
[ A C 60º ] [ A C 180 B ]
sin2B = sinA sinC 2 sin2B = 2 sinA sinC 2 – 2 cos2B = cos (A – C) – cos (A + C) 2 – 2 cos2B = cos (60º) + cos B 4 cos2B + 2 cos B – 3 = 0
R In a ABC if A = 90º, then cos 1 is equal to r2 r3 1) 90º 2) 30º 3) 60º KEY: 3
28.
4) 45º Page 7 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE
A HINT: r2 + r3 = 4R cos2 2 (Put A = 90º)
R 1 1 cos1 cos 2 R 2 3 29.
The Cartesian equation of the plane whose vector equation is
(1 ) i (2 ) j (3 2 2 )k where , are scalars is 1) 2x + y = 5 2) 2x – y = 5 3) 2x – z = 5 KEY: 4 HINT: r [ i 2 j 3k ] [ i j 2k ] [ i 2k ]
4) 2x + z = 5
x 1 y 2 z 3 1 1
1 0
2 0 2
For three vectors p, q and r , if r 3 p 4 q and 2r p 3q then 1) | r | 2 | q | and r , q have the same direction 2) | r | 2 | q | and r .q have opposite directions 3) | r | 2 | q | and r .q have opposite direction 4) | r | 2 | q | and r .q have the same direction KEY: 2 HINT: r 3[2r 3q ] 4q 5r 13q 13 r q [r , q opposite signs] 5 | r | 2 | q | 30.
If a 2i 3 j 5k , b mi nj 12k and a b 0 , then (m, n) = 24 36 24 36 24 36 24 36 1) , 2) , 3) , 4) , 5 5 5 5 5 5 5 5 KEY: 1 i j k
31.
HINT: a b 2 m
3 5 i [36 5n ] j [24 5m] k [2n 3m] 0 n 12
If | a | 3,| b | 4 and the angle between a and b is 120º, then | 4a 3b | is equal to 1) 25 2) 7 3) 13 4) 12 KEY: 4 HINT: | 4a 3b |2 16a 2 9b 2 24 | a || b |cos(120º ) 32.
33.
1 If a , b , c are non-zero vectors such that ( a b ) c | b || c | a , c a and is the angle between 3
the vectors b , c then sin = 1)
2 2 3
2)
1 3
3)
2 3
4)
2 3
KEY: 1 Page 8 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE HINT: 1 (a .c )b (b .c ) a | b | | c | a 3 1 0 (b .c ) a | b || c | a 3 1 | b || c |cos | b || c | 3 1 cos 3
sin 1 cos 2 1 34.
1 8 2 2 . 9 9 3
If a( ) b( ) c( a ) 0 and atleast one of the scalars a, b, c is non-zero, then the vectors , , are
1) Parallel 2) non coplanar KEY: 3 HINT: , ae coplanar
3) coplanar
4) mutually perpendicular
[ ] 0 [ ]2 0 [ ] 0 35.
If the mean of 10 observations is 50 and the sum of the squares of the deviations of the observations from the mean is 250, then the coefficient of variation of those observations is 1) 25 2) 50 3) 10 4) 5 KEY: 3 HINT: x 50 1 ( xi2 x )2 250 2 10 250 25 S .D 5 C.V 100 100 10 . x 50 36.
The variance of the first 50 even natural members is 833 1) 2) 833 3) 437 4 KEY: 2 HINT: 2 4 .... 100 x 50 50(51) = 51 50 1 2 2 = [2 4 2 ..... 100 2 ] (51) 2 50 = 833
4)
437 4
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 37.
3 out of 6 vertices of a regular hexagon are chosen at a time at random. The probability that the triangle formed with these three vertices is an equilateral triangle is 1 1 1 1 1) 2) 3) 4) 2 5 10 20 KEY: 3 HINT: n(s) = 6C3 n(A) = 2 2 1 P(A) = 20 10 38.
A speaks truth in 75% of the cases and B in 80% of the cases. Then the probability that their statements about an incident do not match is 7 3 2 5 1) 2) 3) 4) 20 20 7 7 KEY: 1 75 80 HINT: P ( A) P( B) 100 100 R.P = P( A) P( B ) P( A) P( B) =
3 1 1 4 7 . . 4 5 4 5 20
39.
If the mean and variance of a binomial distribution are 4 and 2 respectively, then the probability of 2 successes of that binomial variate X, is 1 219 37 7 2) 3) 4) 1) 2 256 256 64 KEY: 4 HINT: np = 4, npq = 2 then n = 8, p = 1/2, q = 1/2 p(x = 2) = 8C2 (1/2)8 = 7/64
40.
In a city 10 accidents take place in a span of 50 days. Assuming that the number of accidents follow the Poisson distribution, the probability that three or more accidents occur in a day, is 3 e k e k e k e k , 0.2 2) , 0.2 , 0.2 4) , 0.2 1) 3) 1 k! k k! k! k 3 k 3 k 0 k 0
KEY: 1 HINT:
10 0.2 50
e k , 0.2 k! k 3
P( x 3) 41.
Equation of the locus of the centroid of the triangle whose vertices are a cos k , a sin k ,
b sin k , b cos k and (1,0), where k is a parameter, is 2 2 1) 1 3x 9 y 2 a 2 b2 2) 3x 1 9 y 2 2a 2 2b2 2 2 2 2 3) 3x 1 3 y a 2 b2 4) 3x 1 3 y 3a 2 3b2 KEY:1 Page 10 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE Hint
a cos k b sin k 1 a sin k b cos k 0 x, y , : 3 3 2
2
3 x 1 3 y a 2 b 2
42.
If the coordinate axes are rotated through an angle equation of
about the origin, then the transformed 6
3x 2 4 xy 3 y 2 0 is
1) 3 y 2 xy 0 2) x 2 y 2 0 3) 3 y 2 xy 0 4) 3 y 2 2 xy 0 KEY :3 x x cos y sin , y x sin y cos Hint : 3x y x 3y x ,y 2 2 43. If the lines x 3 y 9 0, 4 x by 2 0, and 2 x y 4 0 are concurrent, then the equation of the line passing through the point (b,0) and concurrent with the given lines, is 1) 2 x y 10 0 2) 4 x 7 y 20 0 3) x y 5 0 4) x 4 y 5 0 KEY :4 Hint : Point of intersection of x 3 y 9 0 and 2 x y 4 0 is (3,2) lies on 4 x by 2 0 b 5 . req line is x 4 y 5 0 44. The midpoint of the line segment joining the centroid and the orthocentre of the triangle whose vertices are a, b , a, c and d , c is
a 5d 5b c 5a d b 5c , , 2) 4) 0, 0 1) 3) a, c 6 6 6 6 KEY :1 2a d b 2c G , Hint : 3 , orthocenter ‘O’= (a,c) 3 OG req point = 2 45. The distance from the origin to the image of (1,1) with respect to the line x y 5 0 is 1) 7 2 2) 3 2 3) 6 2 4) 4 2 KEY :3 Hint : Image of (1,1) w.r. to x+y+5=0 is P=(-6,-6) 6 2 . OP= 46. The equation of the pair of lines joining the origin to the points of intersection of x2 y 2 9 and x y 3 , is 2
2
1) x 2 3 y 9
2) 3 y y 2 9
3) x2 y 2 9
4) xy 0
KEY :4
x2 y 2 9
with
x y 3
Hint
: Homegenising
47.
x y x2 y 2 9 xy 0 3 The orthocenter of the triangle formed by the lines x y 1 and 2 y 2 xy 6 x2 0 is 4 4 2 2 2 2 4 4 1) , 2) , 3) , 4) , 3 3 3 3 3 3 3 3
2
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE KEY :1 Hint : Lne passing through origin and perpendicular to x+y=1 is x-y=0 (altitude) 2 x y 3 x 2 y 0 Given pair of lines are 1 2 2 x y 0, x y 1 , Point of intersection of is 3 3 . Another altitude =
y
2 3
2 1 x 6x 9 y 4 0 3 3
4 4 orthocentre P.O.I . of x y 0,6 x 9 y 4 0 O , 3 3 48. Let L be the line joining the origin to the point of intersection of the lines represented by 2 x2 3xy 2 y 2 10 x 5 y 0. If L is perpendicular to the line kx y 3 0, then k 1 1 1 1) 2) 3) 1 4) 2 2 3 KEY :2 Hint : P.O.I. of given pair = (-1,2) = P 20 OP 2 Slope of 1 0 1 m1 m2 2 k 1 K 2 49. A circle S 0 with radius 2 touches the line x y z 0 at 1,1. Then the length of the tangent drawn from the point 1, 2. to S 0 is 3) 3 1) 1 2) 2 4) 2 KEY :3 Hint : Given question is wrong. Given x+y-z=0 Instead of x+y-2=0 50. The normal drawn at P 1, 2 on the circle x2 y2 2 x 2 y 3 0 meets the circle at another point Q . Then the coordinates of Q are 1) 3,0
2) 3, 0
3) 2, 0
4) 2, 0
KEY :1 Hint
: Centre
1, 2 Q PQ 1,1 2 2
Q 3, 0
51.
(other end of diameter) If the lines kx 2 y 4 0 and 5 x 2 y 4 0 are conjugate with respect to the circle
x2 y 2 2 x 2 y 1 0 , then k 1) 0 2) 1 3) 2 4) 3 KEY :2 r 2 l1l2 m1m2 l1 g m1 f n1 l2 g m2 f n2 Hint : 52. The angle between the tangents drawn from the origin to the circle x2 y 2 4 x 6 y 4 0 is 5 5 12 13 1) tan 1 2) tan 1 3) tan 1 4) tan 1 13 12 5 5 KEY :3
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE Hint
Tan : 2
r S11
If the angle between the circles x2 y 2 2 x 4 y c 0 and x2 y 2 4 x 2 y 4 0 is 60o , then c is equal to 3 5 6 5 9 5 7 5 1) 2) 3) 4) 2 2 2 2 KEY :4 d 2 r12 r22 cos Hint : 2 r1r2
53.
54.
A
circle
S
cuts
three
circles
x2 y 2 4 x 2 y 4 0,
x2 y 2 2 x 4 y 1 0, and
x2 y 2 4 x 2 y 1 0 orthogonally. Then the radius of S is 1)
29 8
2)
28 11
3)
29 7
29 5
4)
KEY :1
S 11 : Find the Radical centre and then find . The distance between the vertex and the focus of the parabola x2 2 x 3 y 2 0 is 4 3 1 5 2) 3) 4) 1) 5 4 2 6 KEY :2 2 x 1 3 y 1 4a 3 a 3 / 4 Hint : SA a 3 / 4
Hint 55.
56.
If
x1 , y1
and x2 , y2 are the end points of a focal chord of the parabola y2 5x, then
4x1 x2 y1 y2
1) 25
2) 5
3) 0
4)
5 4
KEY :3 t t 1 x1 x2 a 2 , y1 y2 4a 2 Hint : 1 2 4 x1 x2 y1 y2 0 57. The distance between the focii of the ellipse x 3cos , y 4 sin is 1) 2 7 2) 7 2 3) 7 4) 3 7 KEY :1 x2 y 2 x2 y 2 1 SS 1 2bc 2 7 1 Hint : 9 16 9 16 58. The equation of the latus recta of the ellipse 9 x2 25 y 2 36 x 50 y 164 0 are 1) x 4 0, x 2 0 2) x 6 0, x 2 0 3) x 6 0, x 2 0 4) x 4 0, x 5 0 KEY :2 2 2 x 2 y 1 1 Hint : Given ellipse is 25 9 x h ae x 6 0, x 2 0 x h ae Page 13 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 59.
The values of the m for which the line y mx 2 becomes a tangent to the hyperbola
4 x2 9 y2 36 is 1)
2 3
2)
2 2 3
3)
8 9
4)
4 2 3
KEY :2 2 2
Hint 60.
2 2 2 2 : c a m 6 m 3 . The harmonic conjugate of 2,3, 4 with respect to the points 3, 2, 2 , 6, 17, 4 is
4 1 1 1 18 1) , , 2) , 5, 5 2 3 4 5 KEY :2 P 2,3, 4 , A 3, 2, 2 , B 6, 17, 4 Hint :
18 5 4 , , 3) 5 4 5
4 18 4) , 5, 5 5
B 4A 5 If a line makes angles , , and with the four diagonals of a cube, then the value of
‘P’ divides AB in the ratio = 1: 4 ' Q ' divides AB in the ratio 1:4 Q
61.
sin 2 sin 2 sin 2 sin 2 is 4 8 7 1) 2) 3) 3 3 3 KEY: 2
4)
w.k .t cos 2 cos 2 cos 2 cos 2
HINT:
5 3 4 3
4 8 3 3 If the plane 56 x 4 y 9 z 2016 meets the coordinate axes in A, B, C then the centroid of the triangle ABC is 1) 12,168, 224 2) 12,168,112 sin 2 sin 2 sin 2 sin 2 4
62.
224 224 4) 12, 168, 3) 12,168, 3 3 KEY: 3 HINT : Given plane is 56 x 4 y 9 z 2016 Convert to x y z 1 a
b
c
x x x y y y z z z G 1 2 3, 1 2 3 , 1 2 3 3 3 3
Then A, B , C . 63.
1 x
3 x
,
x 1
The value(s) of x for which the function f x 1 x 2 x , 1 x 2 fails to be
continuous is (are) 1) 1 2) 2 KEY: 2 HINT : Discontinuous at x 2 Lt
,
3) 3
x2
4) All real numbers
Lt
R.H .L x 2 f x 1
L.H .L x 2 f x 0
L.H .L R.H .L Page 14 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE x
Lt
64.
x
x
6 3 2 1 x2 1) loge 2 log e 3 x0
2) loge 5
3) loge 6 KEY: 1
4) 0 Lt
x0
HINT :
= x 0 2 1 3 1 log 2.log 3
3x 2 x 1 1 2 x 1 x2
Lt
x
x
x
x
2
x bx c , x 1 . If f x is differentiable at x 1, then b c Define f x , x 1 x 1) -2 2)0 3) 1 4) 2 KEY:1 65.
Lt
x
2
bx c 1
1 x 1 L.H.D = x1 x 1 x 1 bx c Lt 1 x1 x 1 x 1 x 1 b 2 Lt 0 1 x1 1 b 1 b c 1 1 2 If x a is a root of multiplicity two of a polynomial equation f x 0 , then
HINT: R.H.D = 1,
66.
1) f ' a f " a 0
2) f " a f a 0
3) f ' a 0 f " a
4) f a f ' a 0; f " a 0
KEY: 4 HINT: Conceptual 67.
If y log 2 log 2 x , then
dy dx
1)
log e 2 x log e x
2)
3)
1 x log e x log e 2
4)
1 log e 2 x
x
1 x log 2 x
2
KEY: 3
2y
log x and then differentiate log 2
HINT: 68. The angle of intersection between the curves y 2 x 2 a 2 2 and x 2 y 2 a 2 , is 1) 2) 3) 4) 3 4 6 12 KEY: 2 m m2 tan 1 1 m1m2 HINT: 69. If A 0, B 0 and A B , then the maximum value of tan A tan B is 3 Page 15 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 1 3
1)
2)
1 3
3)
1 2
4)
3
KEY: 2 A B HINT:
3
AB Put
6 1 1 1 . 3 3 3
ta n A . ta n B
The equation of the common tangent drawn to the curves y 2 8 x and xy 1 is 1) y 2 x 1 2) 2 y x 6 3) y x 2 4) 3 y 8 x 2 KEY: 3 a y 2 8 x, y mx m HINT: 2 y mx . It also touches xy 1 . Then m 1 m y x2
70.
71.
Suppose f x x x 3 , x 1, 4 , Then a value of c in 1, 4 satisfying f ' c 10 is 1) 2
2)
5 2
3) 3
4)
7 2
KEY: 1 HINT:
f x x x 2 x 6 x3 x 2 6 x
f x 3x 2 2 x 2 6 10 3 x 2 2 x 16 0 x 3x 8 2 3x 8 0
3x 8 x 2 0 x 2 or 72.
If
8 3
x 3 e 5 x dx
e5 x 54
f x c
then f x =
x3 3x 2 6 x 6 1) 5 52 53 54 3) 52 x 3 15 x 2 30 x 6 KEY: 4 HINT: Integration by parts 73. x dx 2 2
x
2x 2
2) 5 x 3 52 x 2 53 x 6 4) 53 x 3 75 x 2 30 x 6
2
1)
3)
x 2 1 tan 1 x 1 c 2 x 2x 2 2 x2 2
1 tan 1 x 1 c 4 x 2x 2 2
2
x2 2
2)
1 tan 1 x 1 c 2 x 2x 2 2
4)
1 tan 1 x 1 c x 2x 2 2
2
2 x 1
2
Page 16 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE KEY: 1
x 1 tan HINT: 74. If log a 2 x 2 dx h x c, then h x =
1) x log x
x 2 tan
x a x 2) x 2 x 2 x2 2 tan 1 a x 3) x log a 2 x 2 2a tan 1 a x 4) x 2 a 2 x 2 2 x a 2 tan 1 a KEY: 3 HINT: Integration by parts 5 5 4 3 2 75. For x 0 , if log x dx x A log x B log x C log x D log x E log x F + constant then A B C D E F 1) 44 2) 42 3) 40 4) 36 KEY: 1 HINT: Reduction formulae x2 8a 3 76. The area included between the parabola y and the curve y is 4a x 2 4a 2
2
2
1
2 8 4 1) a 2 2 2) a 2 2 3) a 2 3 3 3 KEY: 4 HINT: P.I. of the x-coordinates -2a and 2a 2a 8a 3 x2 A 2 dx 2 a x 4a 2 4a Required area 2a 8a3 x2 2 2 dx 2 0 4a x 4a 4 a 2 2 3 77. By the definition of the definite integral, the value of Lim 1 1 1 is equal to n ..... n 2 1 2 2 2 2 n 2 n n 1 1)
2)
2
3)
4 4) a 2 2 3
4
4)
6
KEY: 2 n 1
x Lt
HINT:
r 1
1 n2 r 2 Page 17 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE n1
x
Lt
1
2
1
0
r 1 n /4 x 4 / 4 2 cos 2 x dx r 1
78.
1 n
8 3 1) 5 KEY: 4
1 1 x2
dx sin 1 x
1
0
2
4 2 3 3) 9
2 3 2) 9
/4
2 4) 6 3
/4
x 1 dx dx 4 / 4 2 cos 2 x HINT: / 4 2 cos 2 x 0
2
2
79.
6 3
/4
0
1 dx 2 cos 2 x
put tan x t and then integrate
x e dydx 1 y tan 1 y
2
The solution of the differential equation 1 y 2 x e tan 1) x e tan
3) 2 x e KEY: 3
1
y
tan 1 y c
tan 1 y
e
2 tan 1 y
1
2) x e2 tan 4) x 2 e
c
y
1
dydx 0, is
y
tan 1 y
e tan 4e
1
y
c
2 tan 1 y
c
dy xe 1 y dx HINT: tan 1 y
2
x e tan 1 y 1 y2
dx dy 1
dx x e tan y dy 1 y 2 1 y 2 I.F. e tan
1
y 1
G.S = x.e
2 x.e tan 80.
tan 1 y
1 y
e tan y tan1 y .e dy 1 y2
e 2 tan
1 y
put tan 1 y t and then integrate.
c dy x 2 y 1 0 is dx 2) log 2 2 x 4 y 3 2 x 2 y c
The solution of the differential equation 2 x 4 y 3 1) log 2 x 4 y 3 x 2 y c
3) log 2 x 2 y 5 2 x y c 4) log 4 x 2 y 5 4 x 2 y c KEY: 4 dy 1 dt dy x 2 y 1 1 put x 2 y t dx 2 dx 2 x 2y 3 HINT: dx Page 18 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 1 dt t 1 1 2 dx 2t 3 2t 3 dt dx 4t 5 1 1 2 4t 2 5 dt dx And then integrate and substitute t x 2 y log 4 x 2 y 5 4 x 2 y c
PHYSICS 81.
Match the list-I with list-II List-I List-II A) Boltzmann constant I) MLT B) Coefficient of viscosity II) ML1T 1 C) Water equivalent III) MLT 3 K 1 D) Coefficient of thermal conductivity IV) ML2T 2 K 1 (1) A-III; B-I; C-II; D-IV (2) A-III; B-II; C-I; D-IV (3) A-IV; B-II; C-I; D-III (4) A-IV; B-I;C-II; D-III KEY: 3 HINT: Boltzmann’s constant 2E K 3T ML2T 2 K ML2T 2 K 1 K F Coefficient of viscosity dv A dx 2 F MLT 2 1 ML1T 1 dv LT A dx 82. Two trains, which are moving along different tracks in opposite directions are put on the same track by mistake. On noticing the mistake, when the trains are 300 m apart the drivers start slowing down the trains. The graphs given below show decrease in their velocities as function of time. The separation between the trains when both have stopped is
(1) 120m
(2) 20m
(3) 60m
(4) 280m Page 19 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE KEY: 2 HINT:
From given graph retardation of two trains are a1 4ms 2 , a2 2.5ms 2 (Slope of given graphs) Stopping distances 40 40 x1 200 m 2 4 20 20 x2 80m 2 2.5 d D ( x1 x2 ) 300 (200 80) 20m 83. A point object moves along an arc of a circle of radius ‘R’. lts velocity depends upon the distance covered ‘S’ as V K S where ‘K’ is a constant. If ' ' is the angle between the total acceleration and tangential acceleration, then S S S 2S (2) tan (3) tan (1) tan (4) tan R 2R 2R R KEY: 4 HINT: V K S v2 K 2S ar R R dv d K2 at (K S ) dt dt 2 ar 2 S tan at R 84. A body projected from the ground reaches a point ‘X’ in its path after 3 seconds and from there it reaches the ground after further 6 seconds. The vertical distance of the point ‘X’ from the ground is (acceleration due to gravity 10ms 2 ) (1) 30m (2) 60m (3) 80m (4) 90m KEY: 4 HINT: Let u be velocity of projection 2u Time of flight T 9sec g 9 10 u 45m / s 2 1 x ut gt 2 2 1 45(3) (10)9 2 135 45 90m
Page 20 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 85.
A particle of mass ‘m’ is suspended from a ceiling through a string of length ‘L’. If the particle moves in a horizontal circle of radius ‘r’ as shown in the figure, then the speed of the particle is
(1) r
g L2 r 2
(2) g
r L2 r 2
(3) r
g L r2 2
(4) g
r L r2 2
KEY: 1 HINT: According to dimensional analysis first option is correct
LT 2 LT 1 velocity 2 2 L L r A particle is placed at rest inside a hollow hemisphere of radius ‘R’. The co-efficient of friction 1 between the particle and the hemisphere is . The maximum height upto which the 3 particle can remain stationary is 3 R 3R 3 (1) (2) 1 R (4) (3) R 2 2 8 2 r
86.
g
L
KEY: 2
1 h R 1 2 1 HINT: 1 R 1 1 1 3 3 R 1 2 87. A 1kg ball moving with a speed of 6ms 1 collides head-on with a 0.5 kg ball moving in the 1 opposite direction with a speed of 9ms 1 . If the co-efficient of restitution is , the energy lost in 3 the collision is (1) 303.4J (2) 66.7J (3) 33.3J (4) 67.8J KEY: 3 HINT: m1 1kg m2 0.5kg Page 21 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE
88.
u1 6m / s u 2 9m / s 1 m1m2 U (u1 u2 ) 2 (1 e2 ) 2 m1 m2 33.3J A ball is thrown vertically down from a height of 40 m from the ground with an 1rd initial velocity ‘v’. The ball hits the ground, loses of its total mechanical energy and 3 rebounds back to the same height. If the acceleration due to gravity is 10ms 2 , the value of ‘v’ is (1) 5 ms 1
(2) 10ms 1
(3) 15ms 1
(4) 20ms 1
KEY: 4 1 KEi mgh mv 2 2 HINT: 1 KEi 400 v 2 m 2 2 1 KE f 400m mv 2 m 10 40 3 2 2 2 v 400 400 3 2
89.
v2 400 600 2 2 v 200 2 v 20m / s Three identical uniform thin metal rods from the three sides of an equilateral triangle. If the moment of inertia of the system of these three rods about an axis passing through the centroid of the triangle and perpendicular to the plane of the triangle is ‘n’ times the moment of inertia of one rod separately about an axis passing through the centre of the rod and perpendicular to its length, the value of ‘n’ is (1) 3 (2) 6 (3) 9 (4) 12
KEY: 2 HINT: tan 30
x
a
x a 2
l
2 3 2 3 ml 2 ml 2 ml 2 I 12 4 3 6 3ml 2 ml 2 I net 6 2 Page 22 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 2
ml 12 2 ml ml 2 n 2 12 n6 I net n
90.
Two smooth and similar right angled prisms are arranged on a smooth horizontal plane as shown in the figure. The lower prism has a mass ‘3’ times the upper prism. The prisms are held in an initial position as shown and are then released. As the upper prism touches the horizontal plane, the distance moved by the lower prism is
(1) a b
(2)
a b 3
(3)
ba 2
(4)
a b 4
KEY: 4 HINT: ml cos m1 m2 ml cos ml cos x m1 m2 m 3m x
ab 4 91. A particle is executing simple harmonic motion with an amplitude of 2m. The difference in the magnitudes of its maximum acceleration and maximum velocity is 4. The time period of its oscillation and its velocity when it is 1m away from the mean position are respectively. 7 22 44 (1) 2 s, 2 3ms 1 (2) (3) (4) s, 4 3ms 1 s, 2 3ms 1 s, 4 3ms 1 22 7 7 KEY: 3 SOL: Aw2 Aw 4 4 w2 w 2 2 w w 1 2 , w 2
Relative displacement
V w A2 V w
A2 4
2 2 3 A2 w 3 V 2 3 T 4 w 2
Page 23 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 92.
Two bodies of masses ‘m’ and ‘9m’ are placed at a distance ‘r’. The gravitational potential at a point on the line joining then, where gravitational field is zero, is(G is universal gravitational constant) 14GM 16GM 12GM 8GM (2) (3) (4) (1) r r r r KEY: 2 r SOL: x m2 1 m1 Gm G.9m V .4 x4 r 3r 4Gm 12Gm Gm V 16 r r r , 93. When a load of 80N is suspended from a string, its length is 101mm. If a load of 100N is suspended, its length is 102mm. If a load of 160N is suspended from it, then length of the string is (Assume the area of cross-section unchanged) (1) 15.5 cm (2) 13.5 cm (3) 16.5 cm (4) 10.5 cm KEY: 4 SOL: 80 101 l 100 102 l 4 101 l 5 102 l 505 5l 408 4l 505 408 l l 97 m Now 160 x 97 100 5 160 x 97 8 x 97 x 105mm x 10.5cm 94. A sphere of material of relative density 8 has a concentric spherical cavity and just sinks in water. If the radius of the sphere is 2cm, then the volume of the cavity is 76 3 79 3 82 3 88 3 (1) (2) (3) (4) cm cm cm cm 3 3 3 3 KEY: 4
4 SOL: r 3 x1x g V x 8 x g 3 1 4 x x 23 V V 6 3 4 4 4 Vc r 3 23 1 3 3 3 4 22 88 3 x x7 cm 3 7 3
Page 24 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 95.
A hunter fired a metallic bullet of mass ‘m’ kg from a gun towards an obstacle and it just melts 1 when it is stopped by the obstacle. The initial temperature of the bullet is 300K. If th of heat 4 is absorbed by the obstacle, then the minimum velocity of the bullet is [Melting point of bullet = 600K, Specific heat of bullet = 0.03ca l g 1 oC 1 ,
Latent heat of fusion of bullet = 6calg1 ] (1) 410ms 1 (2) 260ms 1 (3) 460ms 1 (4) 310ms 1 KEY: 1 3 SOL: K .E ms mL 4 3 1 2 mv ms 600 300 mL 4 2 3 x V 2 0.03x 4200 x 300 6 x 4200 8 900 x 42 25200 8 V 2 63000 x 3 2 V 168000 V 409.87 m / s 410ml 96. ‘M’ kg of water at ‘t’ o C is divided into two parts so that one part of mass ‘m’ kg when m is converted into ice at 00 C would release enough heat to vapourise the other part, then M equal to [Specific heat of water = 1cal g 1 oC 1 , Latent heat of fusion of ice = 1cal g 1 oC 1 , Latent heat of steam = 540cal g 1 ] 720 t 640 t (1) 640 – t (2) (3) 640 720 KEY: 4 SOL: mcwt mLice M m CW 100 t M m Lsteam
(4)
640 t 720
m 640 t M 720 A diatomic gas 1.4 does 300J work when it is expanded isobarically. The heat given to the
97.
gas in this process is (1) 1050 J (2) 950 J KEY: 1 SOL: dq ncv dT dw
Pn
(3) 600 J
(4) 550 J
R dT dw rT
300 300 300 1050 joule 300 dq p 0.4 7 1 5 Page 25 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 98.
When the absolute temperature of the source of a Carnot heat engine is increased by 25% its efficiency increases 80%. The new efficiency of the engine is (1) 12% (2) 24% (3) 48% (4) 36% KEY: 4 T T SOL: n 1 2 T1 100 T2 100 100 T2 80k 125 T2 180 125 T1 T2 x100 n2 T1 125 80 45 9 x100 125 125 25 36% 99. A cylinder of fixed capacity 67.2 litres contains helium gas at STP. The amount of heat needed to rise the temperature of the gas in the cylinder by 200 C is R 8.31 J mol 1 K 1 (1) 748 J KEY: 1 SOL: dq v ncv dT
(2) 374 J
(3) 1000 J
(4) 500 J
3R x 20 2 =90R 3x
90 x 8.3 748joule 100. For a certain organ pipe, three successive resonance frequencies are observed at 425, 595 and 765Hz, respectively. The length of the pipe is (speed of sound in air =340 ms-1) (1) 0.5 m (2) 1 m (3) 1.5 m (4) 2 m KEY: 4 V SOL: 2n 1 425 4l V 2 n 1 1 595 4l V 2n 3 595 4l V 2 170 4l 101. A student holds a tuning fork oscillating at 170 Hz. He walks towards a wall at a constant speed of 2ms-1. The beat frequency observed by the student between the tuning fork and its echo is (Velocity of sound = 342ms 1 ) 1) 2.5Hz 2) 3Hz 3)1Hz 4) 2Hz KEY : 4 2u Hint : n v u n
Page 26 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 102.
An infinitely long rod lies along the axis of a concave mirror of focal length ‘f’. the nearer end of the rod is at a distance u, u f from the mirror. It’s image will have a length 1)
uf u f
2)
uf u f
3)
f2 u f
4)
f2 u f
KEY : 4 Hint : Volume – 1 103. In Yooung’s double slit experiment, red light of wavelength 6000A is used and then nth bright fringe is obtained at a point ‘P’ on the screen. Keeping the same setting, the source of light is th replaced by green light of wavelength 5000A and now n 1 bright fringe is obtained at the point P on the screen. The value of ‘n’ is 1) 4 2) 5 3) 6 4) 3 KEY : 2 Hint : n11 n2 2 104. Two charges each of charge +10c are kept on Y-axis at y=-a and y=+a respectively. Another point charge 20µc is placed at the origin and given a small displacement x x a along X-axis. The force acting on the point charge is ( x and a are in metres, 1 9 109 Nm 2C 2 ) 4 0 1)
3.6x N a2
2)
2.4x2 N a
3)
3.6x N a3
4)
4.8x N a2
KEY : 3 Hint : Conceptual 105. Three identical charges each 2C lie at the verticles of a right angled triangle as shown the figure. Forces on the charge at B due to the charges at A and C respectively are F1 F2 . The angle between their resultant force and F2.
9 9 16 7 1) tan 1 2) tan 1 3) tan 1 4) tan 1 16 7 9 8 KEY : 3 F Hint : Tan 1 F2 106. The figure shows equipotential surfaces concentric at ‘O’. The magnitude of electric at a distance ‘r’ meters from ‘O’ is 1)
9 Vm 1 2 r
2)
16 1 Vm r2
3)
2 Vm 1 2 r
4)
6 Vm 1 2 r
Page 27 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE KEY : 4
dv dr A region contains a uniform electric field E 10i 30 j Vm 1 . A and B are two points int eh
Hint : E 107.
field at (1,2,0) and (2,1,3)m respectively. The work done when a charge of 0.8C moves from A to B in a parabolic path is 1) 8J 2) 80J 3) 40J 4) 16J KEY : 4 Hint : W vq &V E.dr 108.
When a long straight uniform rod is connected across an ideal cell, the drift velocity of electron in it is v. if a uniform hole is made along the axis of the rod and the same battery is used, then the drift velocity electrons becomes. 1) v 2) >v 3)
q R 2 2
(2)
q R 2
(3) q R 2
(4)
q 2R
KEY: 1 M iA
qv r2 2 r
HINT: 112. A magnetic dipole of moment 2.5 Am2 is free to rotate about a vertical axis passing through its centre. It is released from East-West direction. Its kinetic energy at the moment is takes North-South
position is BH 3 105 T . (1) 50 J (2) 100 J (3) 175 J (4) 75 J KEY: 4 HINT: Gain in KE = loss in PE = MB 113. A branch of a circuit is shown in the figure. If current is decreasing at the rate of 103 As 1, the potential difference between A and B is Page 28 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE
(1) 1 V (2) 5 V (3) 10 V (4) 2 V KEY: 1 VA 2 7 4 9 10 3 103 VB HINT: 114. The natural frequency of an LC circuit is 125 kHz. When the capacitor is totally filled with a dielectric material, the natural frequency decreases by 25 kHz. Dielectric constant of the material is nearly (1) 3.33 (2) 2.12 (3) 1.56 (4) 1.91 KEY: 3
2
f f1 K K 1 HINT: f 2 f2 115. Choose the correct sequence of the radiation sources in increasing order of the wavelength of electromagnetic waves produced by them. (1) X-ray tube, Magnetron valve, Radio active source, Sodium lamp (2) Radio active source, X-ray tube, Sodium lamp, Magnetron valve (3) X-ray tube, Magnetron valve, Sodium lamp, Radio active source (4) Magnetron valve, Sodium lamp, X-ray tube, Radio active source KEY: 2 HINT: Conceptual 116. A photo sensitive metallic surface emits electrons when X-rays of wavelength ‘ ’ fall on it. The de Broglie wavelength of the emitted electrons is (Neglect the work function of the surface, m is mass of the electron. H-Planck’s constant, c-velocity of light) (1)
2mc h
(2)
KEY: 2 hc P2 KE P 2m HINT:
h 2mc
(3)
mc h
(4)
h mc
2mhc
h h P 2mc 117. An electron in a hydrogen atom undergoes a transition from a higher energy level to a lower energy level. The incorrect statement of the following is (1) Kinetic energy of the electron increases (2) Velocity of the electron increases (3) Angular momentum of the electron remains constant (4) Wavelength of de-Broglie wave associated with the motion of electron decreases KEY: 3 HINT: Conceptual 118. The radius of germanium (Ge) nuclide is measured be twice the radius of 94 Be . The number of nucleons in Ge will be (1) 72 (2) 73 (3) 74 (4) 75 KEY: 1
m
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 1/ 3
R A1/ 3 HINT: 119.
R2 A2 R1 A1
23
A2 9
For a common-emitter transistor amplifier, the current gain is 60. If the emitter current is 6.6 mA then its base current is (1) 6.492 mA (2) 0.108 mA (3) 4.208 mA (4) 0.343 mA
KEY: 2 IE I 1 IB E 1 HINT: I B 120. If a transmitting antenna of height 105m is placed on a hill, then its coverage area is (1) 4224 km2 (2) 3264 km2 (3) 6400 km2 (4) 4864 km2 KEY: 1 A d 2 2RhT HINT:
CHEMSITRY 121.
In which of the following, the product of uncertainity in velocity and uncertainity in position of a micro particle of mass ‘m’ is not less than h h 3 h 1 1) h 2) m 3) 4) m 3 4 m 4 m KEY: 3 h 1 h mv.n v.n 4 4 m HINT: 122.
An element has Ar 3d 1 configuration in its +2 oxidation state. Its position in the periodic table
is 1) period-3, group-3 2) period-3, group-7 3) period-4, group-3 4) period-3, group-9 KEY: 3 4 s 2 3d 1 Scandium HINT: Period: 4, group:3 123. In which of the following molecules all bond lengths are not equal? 1) SF 6 2) PCl 5 3) BCl 3 4) CCl 4 KEY: 2 PCl 5 2arial HINT: 3 Equitorial Arial>equatorial 124. In which of the following molecules maximum number of lone pairs is present on the central atom? 1) NH 3 2) H 2 O 3) ClF3 4) XeF2 KEY: 4 HINT: In XeF2 2 bond pairs , 3 lone pairs Page 30 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 125.
Which one of the following is the kinetic energy of a gaseous mixture containing 3g of hydrogen and 80g of oxygen at temperature T(K)? 1) 3RT 2) 6RT 3) 4RT 4) 8RT KEY: 2 3 80 4 HINT: n 2 32 3 3 KE nRT 4 RT 6 RT 2 2 126. A, B, C and D are four different gases with critical temperatures 304.1, 154.3, 405.5 and 126.0K respectively. While cooling the gas which gets liquefied first is 1) B 2) A 3) D 4) C KEY: 4 HINT: High critical temperature easily liquificable 127. 40ml of x M KMnO4 solution is required to react completely with 200ml of 0.02M oxalic acid solution in acidic medium. The value of x is 1) 0.04 2) 0.01 3) 0.03 4) 0.02 KEY: 1 HINT: N1V1 N 2V2
40 5 x 200 0.02 2 x 0.04 128.
Given that C s O2 g CO2 g ; H o x kJ
2CO g O2 g 2CO2 g ; H o y kJ The enthalpy of formation of CO will be y 2x y 2x 2x y 2) 3) 1) 3 2 2 KEY: 2 y 2x HINT: E q 1 E q 2 2 2 129. At 400K, in a 1.0L vessel N 2O4 is allowed to attain equilibrium N 2O4 g 2 NO2 g
4)
x y 2
At equilibrium the total pressure is 600mm Hg, when 20% of N 2O4 is dissolved. The K p value for the reaction is 1) 50 2) 100 KEY: 2 HINT: N 2O4 2 NO2 C O 4C 2C 5 5 4C 2C 6C 600 5 5 5
3) 150
4) 200
C 500 2
Kp
2C C 500 5 100 4C 5 5 5
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 130.
In which of the following salts only cationic hydrolysis is involved? 1) CH 3COONH 4 2) CH 3COONa 3) NH 4Cl 4) Na2 SO4 KEY: 3 HINT: cationic hydrolysis S.A.+W.B. NH 4 Cl NH 3 HCl W .B. S . A. 131. Calgon is (1) Na2 HPO4 (2) Na3 PO4 (3) Na6 P6O18 (4) NaH 2 PO4 KEY: 3 SOL: Na6 P6O18 132. Consider the following statements. I) Cs+ ion is more highly hydrated than other alkali metal ions II) Among the alkali metals only lithium forms a stable nitride by direct combination with nitrogen III) Among alkali metals Li, Na, K, Rb, the metal Rb has the highest melting point IV) Among alkali metals Li, Na, K, Rb only Li forms peroxide when heated with oxygen (1) I (2) II (3) III (4) IV KEY: 2 SOL: Due to more Hydration energy 133.
KEY: SOL: 134.
KEY: SOL: 135. KEY: SOL: 136.
KEY: SOL:
Assertion (A) : AlCl3 exists as a dimer through halogen bridged bonds. Reason (R) : AlCl3 gets stability by accepting electrons from the bridged halogen (1) Both (A) and (R) are true and (R) is the correct explanation of (A) (2) Both (A) and (R) are true but (R) is not the correct explanation of (A) (3) (A) is true, but (R) is not true (4) (A) is not true, but (R) is true 1 Due to completion of octet Which of the following causes “Blue baby syndrome” (1) High concentration of lead in drinking water (2) High concentration of sulphates in drinking water (3) High concentration of nitrates in drinking water (4) High concentration of copper in drinking water 3 High concentration of Nitrate Which of the following belongs to the homologous series of C5 H 8O2 N 1) C6 H10O3 N 2) C6 H 8O2 N 2 3) C6 H10O2 N 2 4) C6 H10O2 N 4 due to difference of CH 2 In Dumas method, 0.3g of an organic compound gave 45mL if nitrogen at STP. The percentage of nitrtogen is 1) 16.9 2) 18.7 3) 23.2 4) 29.6 2 28 45 %N x x100 18.75% 22400 0.3 Page 32 of 36
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 137.
The IUPAC name of
C H 3 2 C H
CH CH CH CH CH CH CH 3
is
C2H 5
1) 2, 7-dimethyl -3, 5-nonadiene 2) 2, 7-dimehtyl -2-ehtylheptadiene 3) 2-methyl -7 –ethyl-3, 5-octadiene 4) 1, 1-dimethyl-6-ethyl-2, 4-heptadiene KEY: 1 CH 3 CH CH CH CH CH CH CH CH 2 CH 3 SOL: CH 3 CH 3 138. Match the following LIST – I LIST-II A) Ferromagnetic 1) O2 2) CrO2 3) MnO 4) Fe3O4
B) Anti ferro magnetic C) Ferri magnetic D) Para magnetic
5) C6 H 6
KEY: SOL: 139.
KEY: SOL:
A B C D (1) 3 2 4 1 (2) 2 3 4 1 (3) 1 3 5 4 (4) 4 2 3 5 2 conceptual The vapour pressures of pure benzene and toluene are 160 and 60mm Hg respectively. The mole fraction of benzene is vapour phase incontact with equimolar solution of benzene and toluene is 1) 0.073 2) 0.027 3) 0.27 4) 0.73 4 1 1 1 PT 160 x 60 x 110 PB PBO x B 160 x 2 2 2 PB PT X B 80 110.YB
80 0.73 110 140. 6g of a non volatile , non electrolyte (1) 60 (2) 140 KEY: 4 SOL: T f K t m YB
(3) 180
(4) 120
6 1000 x GMW 120 GMW 100 141. The products obtained at the cathode and anode respectively during the electrolysis of aqueous K 2 SO4 solution using platinum electrodes are 1) O2 , H 2 2) H 2 , O2 3) H 2 , SO2 4) K , SO4 KEY : 2 Hint : Conceptual 142. The slope of the graph drawn between /nk and 1/T as per Arrhenius equation gives the value (R = gas constant, Ea = Activation energy) 0.93 1.86 x
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 1)
R Ea
2)
Ea R
3)
Ea R
4)
R Ea
KEY : 3 Hint : Conceptual 143. Which is not the correct statement in respect of chemisorptions? 1) Highly specific adsorption 2) Irreversible adsorption 3) Multilayered adsorption 4) High enthalpy of adsorption KEY : 3 Hint : Conceptual 144. Which of the following is carbonate ore? 1) Cuprite 2) Sideritc 3) Zineite 4) Bauxite KEY : 2 Hint : Fe CO3 145. Which one of the following statement is not correct? 1) O3 is used as germicide 2) In O3, O-O bond length is identical with that of molecular oxygen 3) O3 is an oxidizing agent 4) The shape of O3 molecule is angular KEY : 2 Hint : Conceptual 146. Which of the following reactions does not take place? 1) F2 2Cl 2 F Cl2 2) Br2 2l 2 Br l2 3) Cl2 2 Br 2Cl Br2 4) Cl2 2 F 2Cl F2 KEY : 4 Hint : Cl2 cannot displace F2 147. Which of the following statements regarding sulphur is not correct? 1) At about 1000K, it mainly consists of S2 molecules 2) The oxidation state of sulphur is never less than +4 in its compounds 3) S2 molecule is paramagnetic 4) Rhombic sulphur is readily soluble in CS2 KEY : 2 Hint : Conceptual 148. Which of the following reactions does not involve, liberation of oxygen? 1) XeF4 H 2O 2) XeF4 O2 F2 3) XeF2 H 2O2 4) XeF6 H 2O KEY : 3 Hint : X e F6 3 H 2 FeO3 6 HF 149. Select the correct IUPAC name 1) Penta ammonia carbonate cobalt (III) chloride 2) Pentammine carbonate cobalt chloride 3) Pentammine carbonato cobalt (III) chloride 4) Cobalt (III) pentammine carbonate chloride KEY : 3 Hint : Conceptual 150. Which of the following characteristics of the transition metals is associated with their catalytic activity? 1) Color of hydrated ions 2) Diamagnetic behavior 3) Paramagnetic behavior 4) Variable oxidation KEY : 4 Hint : Conceptual
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 151.
Observe the following polymers PHBV Nylon 2-nylon 6 Giyptal Bakelite (A) (B) (C) (D) (1) (D) (2) (A), (B) (3) (D) (4) (C), (D) KEY: 2 HINT: Conceptual 152. Observe the following statements i) Sucrose has glycosidic linkage ii) Cellulose is present in both plants and animals iii) Lactose contains D-galactose and D-glucose units (1) (i), (ii), (iii) (2) (i), (ii) (3) (ii), (iii) (4) (i), (iii) KEY: 4 HINT: Conceptual 153. Identify the antioxidant used in foods (1) Aspartame (2) Sodium benzoate (3) Ortho-sulpho benzimide (4) Butylated hydroxyl toluene KEY: 4 HINT: Conceptual 154.
This reaction is know as (1) Wurtz-Fittig reaction (3) Fittig reaction
(2) Wurtz reaction ($) Friedel-crafts reaction
KEY: 1 HINT:
155.
Reaction between alkal halide and aryl halide with sodium metal in the presence of dry ether What is Z in the following sequence of reactions? Mg H 2O 2-methyl-2-bromo propane X Z dry ether
(1) Propane (2) 2-methyl propene (3) 2-methyl propane KEY: 3 HINT: Mg H 2O 2-methyl-2-bromo propane X Z dry ether
MgBr | X CH 3 C CH 3 | CH 3
(4) 2-methyyl butane
Y CH 3CH CH 3 CH 3
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www.myengg.com AP EAMCET 2016 Question Paper & Solutions by Narayana NARAYANA JUNIOR COLLEGE 156.
In which of the following reactions the product is not correct? LiAlH 4 (1) CH 3CHO CH 3CH 2OH Zn Hg CH 3COCH 3 CH 3 CH CH 3 HCl | (2) OH (i ) H 2 N NH 2 (3) CH 3CH 2CHO CH 3CH 2CH 3 ( ii ) KOH , ethylene glycol /
KMnO4 (4) CH 3CH 2CHO CH 3CH 2COOH
KEY: 2 Zn Hg CH 3COCH 3 CH 3 CH 2 CH 3 HCl HINT: 157. Identify the name of the following reaction
(1) Gatterman – Koch reaction (2) Gatterman reaction (3) Stephen reaction (4) Etard reaction KEY: 4 HINT: Conceptual 158. What is C in the following sequence of reactions? PCl3 KCN hydrolysis CH 3OH A B C
(1) CH 3CH 2OH
(2) CH 3CHO
(3) CH3COOH
(4) HOCH 2 CH 2OH
KEY: 3 HINT: PCl3 KCN hydrolysis CH 3OH A B C 159.
A CH3Cl , B CH3CN , C CH 3COOH The order of basic strength of the following in aqueous solution is C6 H5 NH 2 NH 3 CH3 NH 2 CH 3 3 N
CH 3 2 NH
1 2 3 4 5 (1) 4 > 1 > 5 > 3 > 2 (2) 2 > 5 > 4 > 3 > 1 (3) 5 > 4 > 2 > 3 > 1 (4) 4 > 3 > 5 > 2 > 1 KEY: 3 HINT: Conceptual 160. Yellow dye can be prepared by a coupling reaction of benzene diazonium chloride in acid medium with X. Identify X from the following (1) Aniline (2) Phenol (3) Cumene (4) Benzene KEY: 1 HINT: Benzene diazonium chloride undergoes coupling with aniline in acidic medium
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