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TS EAMCET 2017 Mathematics Question & Answers

MATHS 2

1.

2

If 2x – 10xy + 2y + 5x – 16y – 3 = 0 represents a pair of straight lines, then point of intersection of those lines is 7  3    1) (2, –3) 2) (5, –16) 3)  10,  4)  10,  2  2    Key-3 2. A village has 10 players, A team of 6 players is to be formed. 5 members are chosen first out of these 10 players and then the captain is chosen from the remaining players. Then the total number of ways of choosing such team is 1) 1260 2) 210 3) ( 10 C6 )5! 4) ( 10 C5 )6! Key-1 3. If f is differentiable, f  x  y   f  x  f  y  for all x,y  R, f(3)=3, f’(0)=11, then f’(3)= 1)

3 11

2)

11 3

3) 8

4) 33

Key-4 4. A point on the plane that passes through the points (1,-1,6), (0,0,7) and perpendicular to the plane x-2y+z=6 is 1) (1, - 1,2) 2) (1,1,2) 3) (-1,1,2) 4) (1,1,-2) Key-2 5. For the parabola y 2  6 y  2 x  5 I) The vertex is (-2,-3) II) The directrix is y+3=0 Which of the following is correct? 1) Both I and II are correct 2) I is true, II is false 3) Both I and II are false 4) I is false, II is true Key-2 3 2 6. sin 1  sin 1  2 3  3 2  3 2 1) sin 1 2)   sin 1   2 3  2 3   3 2  3 2 3)   sin 1  4)   sin 1     2 3   2 3  Key-2         7. Let a  2i  j  3k and b  i  3 j  2k . Then the volume of the parallelepiped having conterminous edges        as a, b and c , where c is the vector perpendicular to the plane of a , b and c =2 is 1) 2 195 Key-1

2) 24

3)

200

4) 195

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8.

TS EAMCET 2017 Mathematics Question & Answers

3

The sum of the complex roots of the equation  x  1  64  0 is

1) 6 Key-2 9.

cos 1   2 

If tan 1  k cot 2 , then 1)

3) 6i

2) 3

1 k 1 k

cos 1   2 

2)

4) 3i



1 k 1 k

3)

k 1 k 1

4)

k 1 k 1

Key-2 10. A parallelogram has vertices A(4, 4, -1), B(5,6,-1) C(6, 5, 1) and D(x, y, z). Then vertex D is 1) (5, 1, 0) 2) (-5, 0, 1) 3) (5, 3, 1) 4) (5, 1, 3) Key-3 11. The solution of  y  3x 2  dx  xdy  0 is 1) y  x   sin x  3) y  x   x 2 

1 C x2

2) y  x   cos x 

C x

4) y  x   x 

1 C x2

C x

Key-3 12. In ABC , if a  1, b  2, C  600 then 4  2  c 2  1) 6

3 2

2) 3

3)

2 2) 4

2 3) 6

4) 9

Key-1 

13.

 4 cos 0

2

xdx  x  9sin 2 x

2 1) 12

2 4) 3

Key-1 14. The lengths of the sides of a triangle are 13, 14 and 15. If R and r respectively denote the circum radius and inradius of that triangle, then 8R + r = 65 1) 84 2) 3) 4 4) 69 8 Key-4 8 1 15. The product of all the real roots of x 2  8 x  9   2  0 is x x 1) 2 2) 1 3) 3 4) 7 Key-2 1 5 6

16.

1 0

1

1

If   0 1 7 and   3 0 3 , then 0 0 1 4 6 100

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TS EAMCET 2017 Mathematics Question & Answers

2

2)    1   3    1   2  0

1)  2  31  0 2

3)    1   3    1   5  0

4)   31  1  0

Key-2    17. If the vectors a  i  j  k , b  i  j  2 k and c  xi   x  2  j  k are coplanar, then x  1) 1 2) 2 3) 0 4) -2 Key-4                 18. If a , b and c are unit vectors such that a  b  c  0 and a, b  , then a  b  b  c  c  a  3 3 3 3 1) 2) 0 3) 4) 3 2 2 Key-3 19. Two circles of equal radius ‘a’ cut orthogonally. If their centres are (2, 3) and (5, 6) then radical axis of these circles passes through the point  5a  1) (3a, 5a) 2) (2a, a) 3)  a,  4) (a, a)  3  Key-3

 

n

20.

For any integer n  1,  K  K  2   K 1

1)

n  n  1 n  2

2)

n  n  1 2n  7 

3)

n  n  1 2n  1

4)

n  n  1 2n  8

6 6 6 6 Key-2 21. Consider the circles x2 + y2 – 6x + 4y = 12. The equation of a tangent to this circle that is parallel to the line 4x + 3y + 5 = 0 is 1) 4x + 3y + 10 = 0 2) 4x + 3y – 9 = 0 3) 4x + 3y + 9 = 0 4) 4x + 3y – 31 = 0 Key-4 22. Match the following List – I List – II 1  i)  x x dx a) 1 2  a   4  3sin x   2 dx ii)  2 1  log  b) f  x dx   0 0 4  3cos x    a

 f  x dx iv)  f  x  dx iii)

c)

0 a

e) (1) (3)

a

0

 f  x   f   x dx

d) 0

a

I d d



II a c

III e a

IV c e

(2) (4)

I d a

a

 f  a  x  dx 0

II a d

III c b

IV b c

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TS EAMCET 2017 Mathematics Question & Answers

Key-1       1  cos  12   i sin  12         1  cos     i sin           12   12  

23.

1) zero

2) –1

3) 1

4)

1 2

Key-3 24.

If  and  are the roots of the equation ax2 + bx + c = 0 and the equation having roots

is px2 + qx + r = 0, then r = 1) a + 2b 2) ab + bc + ca 3) a + b + c Key-3 x2  5 A Bx  C then A + B + C = 25. If 2   2  x  1  x  2  x  2 x  1 1) –1

2)

2 5

3)

1  1  and  

4) abc

3 5

4) 0

Key-3 26.

If the imaginary part of

2z 1 is –2, then the locus of the point representing z in the complex plane is iz  1 2) a parabola 3) a straight line 4) an ellipse

1) a circle Key-3 27. The mean deviation from the mean 10 of the data 6, 7, 10, 12, 13,  , 12, 16 is 1) 3.5 2) 3.25 3) 3 4) 3.75 Key-3 28. The angle between the curve x2 = 8y and xy = 8 is  1   1  1) tan 1   2) tan 1  3  3) tan 1  3 4) tan 1    3  3 Key-3 x2 y 2 d2 y   1,  29. If 2 then a b2 dx 2 b4 b2 b3 b3 1) 2 3 2) 3) 4) a y ay 2 a 2 y3 a2 y2 Key-2 30. If the slope of the tangent to the curve y = ax3 + bx + 4 at (2, 14) is 21, then the value of a and b are respectively. 1) 2, –3 2) 3, –2 3) –3, –2 4) 2, 3 Key-1





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31.

The solution of

TS EAMCET 2017 Mathematics Question & Answers

dy x  y  is dx x  y

 y  y 2) tan 1    log x 2  y 2  C 1) tan 1    log x 2  y 2  C x x  y y 3) sin 1    log x 2  y 2  C 4) cos 1    log x 2  y 2  C x x Key-1 32. If the line x – y = –4k is a tangent to the parabola y2 = 8x at P, then the perpendicular distance normal at p from (K, 2K) is 5 7 9 1 1) 2) 3) 4) 2 2 2 2 2 2 2 2 Key-3 33. If the pair of straight lines xy – x – y + 1 = 0 and the line x + ay – 3 = 0 are concurrent, then the acute angle between the pair of lines ax2 – 13xy – 7y2 + x + 23y – 6 = 0  5   1   5   1  2) cos1  3) cos1  4) cos1  1) cos 1       218   10   173   5 Key-2 dx 34.   x  x 4  1

 x4  1   x4  1 1 1 3) log  x 4  1  C 1) log  4   C 2) log  4   C 4 4 4  x   x 1 Key-2 35. The local maximum of y = x3 – 3x2 + 5 is attained at 1) x = 0 2) x = 2 3) x = 1 Key-1   2   2 2 36. If a is a unit vector, then a  i  a  j  a  k 

 x4  1 4) log  4 C 4  x 2

4) x = –1

1) 2 2) 4 3) 1 4) 0 Key-1 37. The area of the region bounded between the curves x = y2 – 2, x = y is 9 9 9 1) 2) 9 3) 4) 4 2 7 Key-3 38.  and  are the roots of x2 + 2x + C = 0. If  3   3  4 , then the value of C is 1) –2 2) 3 3) 2 4) 4 Key-3 39. The equation of the straight line passing through the point of intersection of 5x – 6y – 1 = 0, 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0 is

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TS EAMCET 2017 Mathematics Question & Answers

1) 5x + 3y + 18 = 0 2) –5x – 3y + 18 = 0 3) 5x + 3y + 8 = 0 Key-3 40. The probability distribution of a random variable X is given below X=k P(X=k)

0 0.1

1 0.4

4) 5x + 3y – 8 = 0

2 0.3

3 0.2

4 0

Then the variance of x is

41.

1) 1.6 2) 0.24 3) 0.84 Key-3 If  e 2 x f '  x  dx  g  x  , then   e 2 x f  x   e 2 x f '  x   dx  1 2x  e f  x   g  x    C 2 1 (3)  e 2 x f  2 x   g  x    C 2

4) 0.75

1 2x  e f  x   g  x    C 2 1 (4)  e 2 x f '  2 x   g  x    C 2

(1)

(2)

Key-2 42. The sides of a triangle are in the ratio 1: 3 : 2 . Then the angles are in the ratio (1) 1:2:3 (2) 1:2:4 (3) 1:4:5 (4) 1:3:5 Key-1 43. If A and B are events having probabilities, P(A) = 0.6, P(B) = 0.4 and P  A  B   0 , then the probability that neither A nor B occurs is 1 1 (2) 1 (3) (4) 0 (1) 4 2 Key-4 44. The probability distribution of a random variable X is given below: X P(X=x)

1 a

2 a

3 a

4 b

5 b

If mean of X is 4.2, then a and b are respectively equal to (1) 0.3, 0.2 (2) 0.1, 0.4 (3) 0.1, 0.2

6 0.3 (4) 0.2, 0.1

Key-3 45. If the conjugate of  x  iy 1  2i  is 1  i  , then (1) x  iy  1  i

(2) x  iy 

1 i 1  2i

(3) x  iy 

1 i 1  2i

(4) x  iy 

1 i 1 i

Key-2 46.

If tan 200   , then

tan1600  tan1100  1   tan1600  tan1100 

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(1)

1 2 2

TS EAMCET 2017 Mathematics Question & Answers

(2)

1 2 

(3)

1  2 

(4)

1  2 2

Key-4     47. If a  xiˆ  yjˆ  zkˆ, then a  iˆ . iˆ  ˆj  a  ˆj . ˆj  kˆ  a  kˆ . kˆ  iˆ 



(1) x  y  z



 

(2) x  y  z



 

(3) x  y  z





(4)  x  y  z

Key-2 48. A straight line makes an intercept on the Y-axis twice as long as that on X-axis and is at a unit distance from the origin. Then the line is represented by the equations (1) 2 x  3 y   5 (2) x  y  2 (3) x  y  2

(4) 2 x  y   5

Key-4 49.

x2 y2   1 then k = 9 4 13 5 (4)  (3)  5 13

If the line x  y  k  0 is a normal to the hyperbola (1) 

5 13

(2) 

13 5

Key-2       50. If the magnitudes of a, b and a  b are respectively 3, 4 and 5, then the magnitude of a  b is



(1) 3 Key-4 51. If cosh 1 x  2 log e

(2) 4



(3) 6



(4) 5



2  1 , then x =

(1) 1 (2) 2 (3) 4 (3) Key-4 52. An integer is choosen from 2k /  9  k  10 . The probability that is divisible by both 4 and 6 is (1)

1 10

(2)

1 20

(3)

1 4

(4)

3 20

Key-4 53.

 1 2  Lim  2  4   y 1  y 1 y 1  1 1 (1) (2) 2 3

(3)

1 4

(4) 0

Key-1 54. If A   5, 3 , B   3, 2  and a point P is such that the area of the triangle PAB is 9, then the locus of P represents (1) a circle (2) a pair of coincident lines (3) a pair of parallel lines (4) a pair of perpendicular lines Key-3

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55.

TS EAMCET 2017 Mathematics Question & Answers

If the range of the function f  x   3x  3 is 3, 6, 9, 18 , then which of the following elements is not in the domain of f ? (1) -1 (2) -2 (3) 1 (4) 2

Key-1

56.

if x  0 sin x  2 2 If f  x    x  a if 0  x  1 is continuous of bx  2 if 1  x  2 0 if x  2

(1) -2

(2) 0

, then a  b  ab 

(3) 2

(4) -1

Key-4 57. If A and B are the variances of the 1st ‘n’ even numbers and 1st ‘n’ odd numbers respectively then (1) A=B (2) A>B (3) A
 5  21  (1)  ,  2   10   2  21  , 2  (3)   10 

 5  21  (2)  2,  10    2  21  (4)  2,  10  

Key-2 60.

1 0 If A   0 2  1 1 0.5  0  (1)  0.5 0  0 0  0

1 T 0  , A  B  C , B  BT and C  C , then C =  4  0 0 0  0   0 (2)  0 0 0.5    0 0.5 0  0 

0.5 0.5 0 0  0.5 0 0 

(3)  0.5 

 0

(4)  0.5   0

0.5

0  0 0.5  0.5 0 

Key-2 61.

 1  If the slope of the tangent to the circle S  x 2  y 2 13  0 at (2, 3) is m, then the point  m,  is  m (1) an external point with respect to the circle S = 0

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TS EAMCET 2017 Mathematics Question & Answers

(2) an internal point with respect to the circle S = 0 (3) the centre of the circle S = 0 (4) a point on the circle S = 0 Key-2 62. The radical centre of the circles x 2  y 2  4 x  6 y  5  0, x2  y 2  2 x  4 y  1  0, x 2  y 2  6 x  2 y  0 lies on the line (1) x  y  5  0 (2) 2 x  4 y  7  0 (3) 4 x  6 y  5  0 (4) 18 x  12 y  1  0 Key-4 63. Using the letters of the word TRICK, a five letter word with distinct letters is formed such that C is in the middle. In how many ways this is possible? (1) 6 (2) 120 (3) 24 (4) 72 Key-3 n

64.

n

 x  y The equation of tangent to the curve       2 at the point  a, b  is a b x y x y x y x y (2)   2 (3)  (4)   n (1)   a b a b a b a b

Key-2 th th 42 65. If the coefficients of  2r  1 term and  r  1 term in the expansion of 1  x  are equal then r can be (1) 12 (2) 14 (3) 16 (4) 20 Key-2 n 66. In the expansion of 1  x  , the coefficients of pth and (p+1)th terms are respectively p and q, then p+q = (1) n  3 (2) n  2 (3) n (4) n  1 Key-4 67. If f : ( , 0]  [0, ) is defined as f  x   x 2 . The domain and range of its inverse is (1) Domain of  f 1   [0, ), Range of  f 1   (, 0] (2) Domain of  f 1   [0, ), Range of  f 1   (, ) (3) Domain of  f 1   [0, ), Range of  f 1   [0, )

(4) f 1 does not exist

x  x x   2 x  is 1, then If rank of  x x  x x x  1   (1) x  0  or  x  1 (2) x  1

(4) x  0

Key-1 68.

(3) x  0

Key-3 69. The differential equation of the simple harmonic motion given by x  A cos  nt    is (1)

d 2x 2 n x  0 dt 2

(2)

d 2x  n2 x  0 2 dt

(3)

dx d 2 x  0 dt dt 2

(4)

d 2 x dx   nx  0 dt 2 dt

Key-2     70. If a and b are unit vectors and  is the angle between them, then a  b is a unit vector when cos  

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TS EAMCET 2017 Mathematics Question & Answers

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Key-1 71.

Let f :  1,1 

2

be a differentiable function with f  0   1 and f '  0   1 . If g  x    2 f  x   2  ,

then g '  0   (1) 0

(2) -2 (3) 4 (4) -4 Key-4 72. The number of solutions of cos 2  sin  in  0, 2  is (1) 4 (2) 3 (3) 2 (4) 5 Key-2 73. If cosec  cot   2017, then the quadrant in which  lies is (1) I (2) IV (3) III (4) II Key-4 74. In order to eliminate the first degree terms from the equation 4 x2  8xy  10 y 2  8 x  44 y  14  0 the point to which the origin has to be shift (1) (-2, 3) (2) (2, -3) (3) (1, -3) (4) (-1, 3) Key-1 4 2x 75.  x e dx 

e2 x (1) 2 x 4  4 x 3  6 x 2  6 x  3  C  4 e2 x (3)  2 x 4  4 x 3  6 x 2  6 x  3  C 8

e2 x (2) 2 x 4  4 x 3  6 x 2  6 x  3  C  2 e2 x (4)   2 x 4  4 x 3  6 x 2  6 x  3  C 4

Key-1 76. If the perpendicular distance between the point (1, 1) to the line 3 x  4 y  c  0 is 7, then the possible values of c are (1) -35,42 (2) 35, 28 (3) 42, -28 (4) 28, -42 Key-4     77. If A   , B   are the points on the circle represented in parametric from with centre (0, 0) and radius 3 6 12 then the length of the chord AB is (1) 6 6  2 (2) 6 6  3 (3) 2 3  1 (4) 6 3  1

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Key-1 78. Let f  x  be a quadratic expression such that f  0   f 1  0 . If f  2   0 , then

 2  (1) f    0  5 

2 (2) f    0 5

 3  (3) f    0  5 

 3 (4) f    0 5

Key-4 79. Let S and S1 be the foci an ellipse and B be one end of its minor axis. If SBS1 is an isosceles right angled then the eccentricity of the ellipse is

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TS EAMCET 2017 Mathematics Question & Answers

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Key-1 80. A bag contains 5 red balls, 3 black balls and 4 white balls. Three balls are drawn at random. The probability that they are not of same colour is (1)

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Key-1

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http://www.myengg.com/engg/info/tag/ts-eamcet/ PHYSICS

81.

A parallel beam of light of intensity I 0 is incident on a coated glass plate. If 25% of the incident light is reflected from the upper surface and 50% of light is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflect light is

1   (1)  2 1  2 

3  8 3 8 

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1   (2)  4 1  2 

3  8 3 8 

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Key-1 82.

A wire has resistance of 3.1  at 30 C and 4.5  at 100 C. The temperature coefficient of resistance of the wire is (1) 0.0012 C 1

(2) 0.0024 C 1

(3) 0.0032 C 1

(4) 0.0064 C 1

Key-0 83.

The Young’s modulus of a material is 2  1011 N / m 2 and its elastic limit is 1  108 N / m 2 . For a wire of 1 m length of this material, the maximum elongation achievable is (1) 0.2 mm

(2) 0.3 mm

(3)0.4 mm

(4) 0.5 mm

Key-4 84.

A sound wave of frequency ‘ ’ Hz initially travels a distance of 1 km in air. Then it gets reflected into a water reservoir of depth 600 m. The frequency of the wave at the bottom the reservoir is Vair  340 m / s; Vwater  1484 m / s  . (1) >  Hz

(2) <  HZ

(3)  Hz

(4) 0 (the sound wave gets attenuated by water complete). Key-3 85.

Which of the following principles is being used in Sonar Technology ? (1) Newton’s laws of motion

(2) Reflection of electromagnetic waves

(3) Laws of thermodynamics

(4) Reflection of ultrasonic waves