CLASS TEST

PHASE - I
6 4 2
1. The value of 64 sin 10º – 96 sin 10º + 36 sin 10º is
1 1
(A) (B) (C) 1 (D) 2
2 4

2. The minimum value of y  x  1  x  2  .......  x  10 is

(A) 25 (B) 20 (C) 30 (D) 0

dy
3. If y  x sin x then at x  0 is
dx
(A) 0 (B) 1 (C) –1 (D) Does not exist

4. Consider that n(S) represents the number of elements in set S.

If n  A  B  C  40, n  A  B' C'   5 , n B  A' C'   10, n  C  B ' A '   6 then number of
elements belongs to at least two of the sets is
(A) less than 19 (B) more than 19 (C) 19 (D) 20

5. The number of all possible triplet (a1, a2, a3) such that a1 + a2 sin x + a3 cos x = 0 holds for all x is
(A) zero (B) 1 (C) 2 (D) Infinite

Let p  x   cosx  cos2x  cos3x    sinx  sin2x  sin3x  then p(x) is equal to if
2 2
6.
 2 4  
x , 
 3 3 
(A) 1 + 2 cos x (B) – (2 cos x + 1) (C) 1 – 2 cos x (D) 1 – 2 sin x

64 sin3 .cos 
7. Maximum value of the expression is
1  tan2 
(A) 8 (B) 16 (C) 4 (D) 6

2 4 8 16 a
8. If sin  sin  sin  sin  where a, b  N and are relatively prime, then the value
15 15 15 15 b
of a + b is
(A) 16 (B) 19 (C) 12 (D) 15

9. If 2ycos = x sin  and 2 x sec  – y cosec  = 3 then the value of x 2  4y 2 is

(A) 3 (B) 4 (C) 1 (D) 2

Space for rough solution

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  
If cosec (x + y) – sin (y – x) + sin (2x – y) = cos (x – y) and x, y   0,  then the value of sin x
2 2 2 2
10.
 2
+ cos 3 y is
3 1 1
(A) 1 (B) (C) (D) 
2 2 2

 2 6
11. Let A = sec 0 + sec + sec  .....  sec
7 7 7
and B  cot1o  cot 3º  cot 5º ..........  cot179º
then A 2  B2 is
(A) 3 (B) 4 (C) 1 (D) 2

If x 2   y  2   16 then maximum value of 3x + 4y is

2
12.
(A) 12 (B) 28 (C) 20 (D) 5

13. The value of

1  cot 3º 1  cot 7º 1  cot11º 1  cot13º  1  cot 32º 1  cot 34º  1  cot 38º 1  cot 42º 
is equal to
(A) 3 (B) 2 (C) 27 (D) 16

14. A rectangle PQRS joins the points P, Q, R, S. Co-ordinates of P and R be (2, 3) and (8, 11)
respectively. The line QS is known to be parallel to the y-axis. Then co-ordinates of Q and S are
(A) (0, 7) and (10, 7) (B) (5, 2) and (5, 12)
(C) (7, 6) and (7, 10) (D) (7, 2) and (7, 12)

15. Let ABC be a triangle whose vertices are A(–5, 5) and B(7, –1) . If vertex C lies on the circle with
director circle has equation x + y = 100, then the locus of orthocenter of ABC is
2 2

(A) x  y  4x  8y  30  0
2 2
(B) x2  y2  4x  8y  20  0
(C) x2  y2  4x  8y  30  0 (D) x2  y2  4x  8y  0

2
16. The equation y = sin 2x sin (2x + 4) + cos (2x + 2) + x, represents
(A) straight line passing through  17, 9  (B) circle
2
(C) the equation is not a straight line (D) straight line passing through (– cos 2, 0)

17. Consider the OAB, where O is the origin. If B  (3, 4) and orthocentre of the triangle is
P  (1, 4), then the co-ordinates of A are
 19   19   4 4  19 
(A)  , 0  (B)  0,  (C)  ,  (D)  0, 
 4   4   19 19   2 

Space for rough solution

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 18. If a vertex of a triangle is (1, 1) and the midpoint of two sides through this vertex are (–1, 2) and
(3, 2), then the centroid of the triangle is
1 7  7  1 7  7
(A)  ,  (B)  1,  (C)   ,  (D)  1, 
3 3  3  3 3  3

19. The equation of a circle which has normals (x + y –2)(2x + 11y – 13) = 0 and a tangent 3x + 4y –
1 = 0 is
111 11
(A) x2  y2  4x  4y  0 (B) x2  y2  4x  4y  0
117 17
114 14
(C) x 2  y 2  2x  2y  0 (D) x 2  y 2  2x  2y  0
125 25

Given a circle  x  4    y  2   25. Another circle is drawn passing through (–4, 2) and
2 2
20.
touching the given circle internally at the point A(–4, 7) AB is the chord of length 8 units of the
larger circle intersecting the other circle at the point C. Then AC will be
(A) 4 units (B) 17 units (C) 5 units (D) 3 units

21. A, B and C are 3 points on a circle with centre O. The chord BA is extended to point T such that
CT becomes a tangent to the circle at point C. If ATC = 20º and ACT = 40º then BOA is
(A) 120º (B) 150º (C) 160º (D) 170º

22. If origin is moved to a point such that the transformed expression for the expression
f  x, y   x2  4y2  6x  8y  3 will be free from first degree terms, then the point is
(A)  3,  1 (B) 1,  3  (C)  3,  1 (D)  3, 1

23. Equation of a circle touching the lines x  1  y  2  4 will be

(A)  x  1   y  2   4 (B)  x  1   y  2   8
2 2 2 2

(C)  x  1   y  2   12 (D)  x  1   y  2   16
2 2 2 2

24. Which of the following is the negation of the preposition “If a number is prime, then it is odd” ?
(A) If a number is not a prime, then it is odd (B) If a number is not odd, then it is a prime
(C) If a number is not prime, then it is not odd (D) A number is prime and it is not odd.

x 2
25. If [x] denotes the greatest integer function  x, then lim is equal to
x 0 3  x 
2 1 2
(A)  (B) (C) (D) Does not exist
3 3 3

Space for rough solution

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 26. The proposition  ~ p v p ~ q is equivalent to
(A) p  q (B) p  q (C) p  ~ q (D) q  p

2 2
27. If the tangent and normal to x + y = 4 at a point cut –off intercepts a1, a2 on the x-axis
respectively and b1, b2 on the y-axis respectively, then the min value of a1b1  a2b2 is
(A) 4 (B) 8 (C) 16 (D) 2

28. Number of solution of the equation 4  x  1  3  5x can have for all x  R

(A) 0 (B) 1 (C) 2 (D) 4

29. The number of integral value of x satisfying the inequality

 x 4  1  25  x2 
 0 is
 x3  8 2  x 4  32
(A) 8 (B) 0 (C) 9 (D) 10

30. For log x2 1  4  x 2   1, number of integral values of x is

(A) 0 (B) 2 (C) 4 (D) 6

Space for rough solution

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