VOCLET 2013 Solved question paper mathematics part

VOCLET 2013 solved question Mathematics part
1. If a regular hexagon has a side of 8 cm, then its area is (in sq.cm.) : Ans: B) 96√2	2. If the radius of a circle is increased by 100%, then its area is increased by: Ans: C) 300%
3. A chord of a circle measures 24 cm. and its distance from the center is 4 cm. Then the radius of the circle is (in cm.) : Ans: B) 12.64	4. A right prism stands on a hexagonal base of side √3 cm. and height is 12 cm., its volume is : Ans: C) 54√3
5. The value of lim(x->0) tanpx/tanqx is : Ans: B) p/q	6. if f(x)=log sin ax, then df/dx= : Ans: C) a cot ax
7. If x= a cos4θ, y= a sin4θ, then dy/dx at θ=3Π/4 is : Ans: A) -1	8. If y= A cos px + B sin px, then : Ans: C) d2y/dx2 + p2y=0
9. If f(x)= x2-(p+2)x+2p/(x-2), for x ≠2 and f(x)=2, for x=2, is continuous at x=2, then p=: Ans: A) 0	10. ∫cos2x dx is : Ans: C) 1/2(x + 1/2 sin 2x)+ C
11. ∫sin-1x/√(1-x2) dx is: Ans: A) 1/2(sin-1x)2 +C	12. ∫√(1 + sin x) dx is : Ans: B) 2 (sin x/2 - cos x/2) + C
13. ∫x ex^2 dx is: Ans: D) 1/2 ex^2 + C	14. ∫ex(1+tanx+tan2x) dx is : Ans: C) ex tanx + C
15. ∫(sin 6x + cos 6x + 3 sin2x cos2x) dx is: Ans: A) x + C	16. ∫π/20 cos 2x dx is: Ans: C) 0
17. ∫1-1 |x| dx is : Ans: A) 1	18. The general solution of the differential equation d2y/dx2 + 4y=f(x) contains: Ans:
19. The general solution of the differential equation d2y/dx2 - 3 dy/dx +2y =0 is : Ans:	20. The product of the roots of x2-4x+4log2 λ=0 is: Ans: B) 2√2
21. The diameter of the base of a right circular cone is 12 cm and height is 8 cm. Its curved surface area is : Ans: 60π cm2	22. A right pyramid of height 15 cm stands on a square base of side 16 cm. It's volume is: Ans: B) 1280 cm3
23. If d/dx [F'(x)]=f(x), then ∫f(x) dx = : Ans: B) F'(x) + C	24. ∫(e5logx - e4logx)/(e3logx - e2logx) dx =: Ans: C) x3/3 + C
25. If a=bx, b=cy, c=az, then the value of xyz is : Ans: A) 1	26. 1,ω,ω2 are cube roots of unity, then the value of (1+ω)3 - (1+ω2)3 is: Ans: B) 0
27. If n is an integer and i=√-1, then in+in+1+in+2+in+3 is : Ans: A) 0	28. the value of log2 log2log4256 + 2 log√22 is: Ans:D) 5
29. If loga(ab)=x, then logb(ab) is : Ans: B) x/(x-1)	30. If x is real, then the least value of 4x2 - 4x+2 is : Ans: C) 1
31. The Cartesian co-ordinates of the point whose polar co-ordinates are (3, π/6) are : Ans: B) (3√3/2, 3/2)	32. Equation of a straight line perpendicular to 3x-2y+3=0 and passing through orgin is : Ans: D) 2x+3y=0
33. Length of the perpendicular from (1,2) to the straight line 3x+4y=1 is : Ans: B) 2	34. The co-ordinates of foot of perpendicular from (0,0) upon the straight line x+y=2 are : Ans: A) (1,1)
35. Angle between straght lines x√3 - y = 2 and x + y√3 = 1 is: Ans: B) π/2	36. If each angle of a regular polygon be 108°, then the number of sides be : Ans: A) 5
37. If tan 3x=1, then tan 2x=: Ans: D) 1/√3	38. The value of sin 1755° is : Ans: D) - 1/√2
39. The value of log tan 1° + log tan 2° + .... + log tan 89° is: Ans: A) 0	40. The greatest value of sin x cos x is : Ans: D) 1/2
41. If (1+tan A) (1+tan B)=2, then A+B is : Ans: C) 45°	42. The area of a tringle with vertices (-4,1), (1,2) and (4,-3) in sq. unit is : Ans: A) 14
43. d/dx(sin x°) = : Ans: D) π/180 cos x°	44. If f(x)= |x|/x, then for any λ>0, |f(λ) - f(-λ)|= : Ans: D) 0
45. The function f(x)=(2x+1)/(2x-1) is : Ans: B) odd	46. lim(x->5) (xn-5n)/(x-5) = 500. Then n= : Ans: C) 4
47. If α, β are real roots of x2 - ax + b=0, then lim (x->α) (ex^2 - ax + b -1)/(x-α) =: Ans: B) α- β	48. If a>0, lim(x->∞) x [ a1/x -1] =: Ans: D) None of the above
49. The order and degree of the differential equation {1 + (dy/dx)2}3/2= c d2y/dx2 are respectively: Ans: B) 2,2	50. Given dy/dx=yex such that when x=0, y=e. The value of y (y>0) when x=1 will be : Ans: C) ee
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