Test Paper 1
The set of all integers x such that |x – 3| < 2 is equal to
(a) {1, 2, 3, 4, 5} (b) {1, 2, 3, 4}
(c) {2, 3, 4} (d) {-4, -3, -2}
2. The Range of the function f(x) = x 2
2 x
−
− is
(a) R (b) R – {1}
(c) (-1) (d) R – {-1}
3. The value of (i)i
is
(a) ω (b) ω2
(c) e-π/2 (d) 2√2
4. ( )
( )
4
5
cos isin
icos sin
θ+ θ
θ+ θ is equal to
(a) cos isin − θ (b) cos9 isin9 θ− θ
(c) sin icos θ− θ (d) sin 9 icos9 θ− θ
5. The roots of the quadratic equation 2 ax bx c 0 + + = will be reciprocal to each other if
(a) a = 1/c (b) a = c
(c) b = ac (d) a = b
6. If α, β are the roots of 2 ax 2bx c 0 − += then 33 23 32 α β +α β +αβ is
(a) ( ) 2
3
c c 2b
a
+ (b) 3
3
bc
a
(c) 2
3
c
a (d) None of these
7. The sixth term of a HP is 1/61 and the 10th term is 1/105. The first term of the H.P. is
(a) 1/39 (b) 1/28
(c) 1/17 (d) 1/6
8. Let Sn denote the sum of first n terms of an A.P.. If S2n = 3Sn, then the ratio S3n / 5n is equal to
(a) 4 (b) 6
(c) 8 (d) 10
9. Solution of |3 – x| = x – 3 is
(a) x < 3 (b) x > 3
(c) x > 3 (d) x < 3
10. If the product of n positive numbers in 1, then their sum is
(a) a positive integer (b) divisible by n
(c) equal to 1 n n + (d) never less than n
11. A lady gives a dinner party to six quests. The number of ways in which they may be selected from
among ten friends, if two of the friends will not attend the party together is (a) 112 (b) 140
(c) 164 (d) None of these
12. For 1 ≤ r ≤ n, the value of n1 n2 r
rr r nCr C C _ _ _ C is − − + + ++
(a) r 1 nC + (b) n 1Cr
+
(c) n 1Cr 1
+
+ (d) None of them.
13. 2n 1 3n 1 2.4 3 + + + is divisible by
(a) 2 (b) 9
(c) 11 (d) 27
14. If Pn denotes the product of the binomial coefficients in the expansions of (1 + x)n
, the n 1
n
P
P
+ equals
(a) n !
n!
+ (b) n n
n!
(c) ( )n 1 n 1
n!
+
+ (d) ( )
( )
n 1
!
n 1
n 1
+
+
+
15. If x is very large and n is a negative integer or a proper fraction, then an approximate value of n
1 x
x
⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ is
(a) x 1 n + (b) n 1 x +
(c) 1 1 x + (d) 1 n 1 x
⎛ ⎞ ⎜ ⎟ + ⎝ ⎠
16. If 4 log93 + 9 log24 = 10log x 83, (x ∈ R)
(a) 4 (b) 9
(c) 10 (d) None of these
17. The sum of the series 222
4 8 16 log log log _ _ _ _ −+ ∞to is
(a) e2
(b) loge2 + 1
(c) loge3 – 2 (d) 1 – loge2
18. tan 5x tan 3x tan2x is equal to
(a) tan5x tan3x tan 2x − − (b) sin5x sin3x sin 2x
cos5x cos3x cos2x
− −
− −
(c) 0 (d) None of these
19. If a = tan60
tan 420
and B = cot660
cot 780
(a) A = 2B (b) 1 A B
3 =
(c) A = B (d) 3A = 2B.
20. The value of 246 cos cos cos 777
πππ + + is
(a) 1 (b) -1
(c) 1/2 (d) -1/2
21. If 1 1 tan andsin , 7 10 α= β= where 0 , 2
π <αβ< , then 2β is equal to
) 4
π − α (b) 3
4
π −α
(c) 8
π − α (d) 3
8 2
π π −
22. If sin cos 2 sin θ+ θ= θ , then
(a) 2 cosθ (b) − 2 sinθ
(c) − θ 2 cos (d) None of these
23. Value of 20 40
40 20
sin 20 cos 20
sin 20 cos 20
+
+ is
(a) 1 (b) 2
(c) ½ (d) None of these
24. Value of 60 40 20 32cos 20 48cos 20 18cos 20 1 −+− is
(a) 1
2 − (b) 1
2
(c) 3
2 (d) None of these
25. If sin cosec 2 θ+ θ= , then value of 3 3 sin cosec θ+ θ is
(a) 2 (b) 4
(c) 6 (d) 8
If 5 cosec cot 2 θ+ θ= , then the value of tanθ is
(a) 15
16 (b) 21
20
(c) 15
21 (d) 20
21
27. General value of x satisfying the equation 3sin x cos x 3 + = is given by
(a) n 6
π π ± (b) ( )n
n 1
4 3
π π π+− +
(c) n 3
π π ± (d) ( )n
n 1
3 6
π π π+− −
28. If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then
length of the angle bisector of ∠ABC is
(a) 120 2 cm 23 (b) 60 2 cm 23
(c) 30 2cm
23 (d) None of these
29. A man from the top of a 100 metre high tower sees a car moving towards the tower at an angle of
depression of 300
. After sometimes, the angle of depression becomes 600
. The distance (in metres)
traveled by the car during this time is
(a) 100 3 (b) 200 3
3
(c) 100 3
3 (d) 200 3
30. The shadow of a tower of height (1 3 + ) metre standing on the ground is found to be 2 metre
longer when the sun’s elevation is 300
, then when the sun’s elevation was
(a) 300
(b) 450
(c) 600 (d) 750
31. 1 5 cos cos 4
− ⎛ ⎞ π ⎜ ⎟ ⎝ ⎠is equal to
(a) 4 −π (b) 4
π
(c) 3
4
π (d) 5
4
π
32. If 1 1 x y cos cos 2 36
− − π + = , then value of 2 2 x xy y
4 9 2 3
− + is
(a) 3
4 (b) 1
2
(c) 1
4 (d) None of these
33. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is
(a) 7/2 (b) 7/3
(c) 7/5 (d) 7/10
34. The straight lines x + y – 4 = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a traigle which is
(a) isosceles (b) right angled
(c) equilateral (d) None of these
35. Incentre of the triangle whose vertices are (6, 0) (0, 6) and (7, 7) is
(a) 9 9,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (b) 7 7,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠
(c) 11 11 , 2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (d) None of these
36. The area bounded by the curves y = |x| − 1 and y = − |x| + 1 is
(a) 1 (b) 2
(c) 2 2 (d) 4
37. The coordinates of foot of the perpendicular drawn from the point (2, 4) on the line x + y = 1 are
(a) 1 3,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (b) 1 3
, 2 2
⎛ ⎞ −
⎜ ⎟ ⎝ ⎠
(c) 3 1 ,
2 2
⎛ ⎞ − ⎜ ⎟ ⎝ ⎠ (d) 1 3
, 2 2
⎛ ⎞ − − ⎜ ⎟ ⎝ ⎠
38. Three lines 3x + 4y + 6 = 0, 2x 3y 2 2 0 + + = and 4x 7y 8 0 + + = are
(a) Parallel (b) Sides of a triangles
(c) Concurrent (d) None of these
39. Angle between the pair of straight lines x2
– xy – 6y2
– 2x + 11y – 3 = 0 is
(a) 450
, 1350
(b) tan-1 2, π = tan-1 2
(c) tan-1 3, π = tan-1 3
(d) None of these
1. (c)
2. (c)
3. (c)
4. (d)
5. (b)
6. (a)
7. (d)
8. (b)
9. (d)
10. (d)
11. (b)
12. (c)
13. (c)
14. (d)
15. (b)
16. (c)
17. (d)
18. (b)
19. (c)
20. (c)
21. (c)
22. (a)
23. (a)
24. (a)
25. (a)
26. (d)
27. (d)
28. (a)
29. (b)
30. (b)
31. (c)
32. (c)
33. (d)
34. (a)
35. (a)
36. (b)
37. (b)
38. (c)
39. (d)
ANSWER KEYS
2. (c)
3. (c)
4. (d)
5. (b)
6. (a)
7. (d)
8. (b)
9. (d)
10. (d)
11. (b)
12. (c)
13. (c)
14. (d)
15. (b)
16. (c)
17. (d)
18. (b)
19. (c)
20. (c)
21. (c)
22. (a)
23. (a)
24. (a)
25. (a)
26. (d)
27. (d)
28. (a)
29. (b)
30. (b)
31. (c)
32. (c)
33. (d)
34. (a)
35. (a)
36. (b)
37. (b)
38. (c)
39. (d)
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