VOCLET 2014 Mathematics Solution:-
1. If f(x) = loge sinx and g(x)=loge cosx, then e2f(x) + e2g(x) is equal to – A) 1
2. Each side of a regular hexagon is 10 cm. Its area is- C) 150v3
4. The angle between the lines x+y=4 and x-y=5 is- B) 90º
5. The polar coordinates of a point are (2v2,π/4); its Cartesian coordinates are – C) (2,2)
6. The period of the function sin x is equal to – B) 2π
7. lim xà 0 sin3x/2x is equal to – A) 3/2
8. A right prism of height 10 cm stands on a square base of side 3 cm, its volume is – C) 90 cm2
9. The ratio of diameter to the circumference of a circle is equal to – C) 1:π
10. ∫0 π/2 2sin2xdx is equal to – A) π/2
11.The function whose derivative 10x9+10xlog10/x10+10x is – C) log(x10+10x)
12. If ∫eax cosbx dx = eax sinbx/b + λ ∫eax sinbx dx then λ=?- D) –a/b
13. ∫-a a [f(x)+f(-x)][g(x)-g(-x)] dx = ? – D) 0
14. The order of the differential equation whose general solution is given by
y=(c1+c2)sin(x+c3)-c4ex+c5 is- D) 5
15. The value of log3log2logv3 81 is- A) 1
16. sin 105º + cos 105º is equal to – D) 1/v2
17. If tan x= cot x than a value of x is – B) π/4
18. The maximum value of 4sinxcosx is equal to – A) 2
19. sin-1x+cos-1x (-1<=x<=1) is equal to – B) π/2
20. If y= 2logex2, then d2y/dx2 is equal to- B) -4/x2
21. If the length of sides of a regular polygon is increased by 50%, then the area isincreased by – D) none of the above
22. The number of diagonals of a polygon having 10 sides is – A) 45
23. The length of the major axis and the minor axis of an ellipse are respectively 12 cm and 8 cm. Then its area is- B) 24π Sq. cm.
24. A right pyramid stands on a rectangular base of size 8 inch x 15 inch. Its volume is 120 cu. inch. The height of the pyramid is – A) 3 inch.
25. The height of an equilateral triangle of perimeter 24 cm is- A) 4v3 cm
26. The domain of definition of the function f(x) x2+x+5/ x2 -6x+8 is-- B) -∞<x<2, 2<x<4, 4<x<∞
27. Let f(x) = 3x+4 for 0<=x<=2
= 5x+λ for 2<x<=3
if f(x) is given to be continuous at x=2 then – D) λ=0
28. If y= tan-1 V(1-cosx/1+cosx) then dy/dx=? – A) ½
29. If x=et, y= sin t, then the value of d2y/dx2 at t= π/2 is – C) – e-π
30. If g(x)= x+1/x2-3x-4, then g(x) is undefined for – A) x=-1
31. 1/log(1.2) [log8 + log v27 – log v1000]= C) 3/2
32. If one root of x2+6x+m=0 is 1, the value of ‘m’ is – A) -7
33. If sec θ – tan θ=1/2 then θ lies in –A) the 1st quadrant
34. If sin θ + cosec θ=2, then sin9θ + cosec9θ - B) 2
35. The equation 2sinθ+cosθ=3 has – D) No solution
36. If tan2α = 2 tan2β, then cos2α + sin2β= ?- C) 0
37. If tan(cos-1x)=sin(tan-12) then x= ?- D) ±v5/3
38. The x-axis divides the line segment joining A(-3,2) and B(6,-4) in the ratio – D) 1:2
39. The acute angle between the lines (a+b)x=(a-b)y and ax+by+c=0, a≠b is – C) 45º
40. The straight line through the point (-a,-b) and (a,b) passes through the point – B) (a2,ab)
41. lim xà0 sin(πcos2x)/x2 = C) π/2
42. The differential of all straight lines passing through the point (1,0) is- C) y= dy/dx(x-1)
43. If the roots of the equation x2-2x+2=0 are p and q, then the value of p-1+q-1 is equal to – C) 1
44. If one root of the equation 5x2-6x-d=0 is reciprocal of the other, then the value of d is – B) -5
45. If f(x)=2x, then the value of f(x)f(1/x) is – D) 4
46. The modulus of 7-24i/3+4i is – C) 5
47. ∫-1 1 |x| dx is equal to – C) 1
48. If ω is an imaginary cube root of unity then ω+ ω2 is equal to – B) -1
49. (22n – 3. 22n-2) (3n-2.3n-2)/ 3n-4(4n+3-22n)=? – C) ¼
50. Evaluate: [i19 + (1/i)25]2, (i=v-1) - B) -4
1. If f(x) = loge sinx and g(x)=loge cosx, then e2f(x) + e2g(x) is equal to – A) 1
2. Each side of a regular hexagon is 10 cm. Its area is- C) 150v3
4. The angle between the lines x+y=4 and x-y=5 is- B) 90º
5. The polar coordinates of a point are (2v2,π/4); its Cartesian coordinates are – C) (2,2)
6. The period of the function sin x is equal to – B) 2π
7. lim xà 0 sin3x/2x is equal to – A) 3/2
8. A right prism of height 10 cm stands on a square base of side 3 cm, its volume is – C) 90 cm2
9. The ratio of diameter to the circumference of a circle is equal to – C) 1:π
10. ∫0 π/2 2sin2xdx is equal to – A) π/2
11.The function whose derivative 10x9+10xlog10/x10+10x is – C) log(x10+10x)
12. If ∫eax cosbx dx = eax sinbx/b + λ ∫eax sinbx dx then λ=?- D) –a/b
13. ∫-a a [f(x)+f(-x)][g(x)-g(-x)] dx = ? – D) 0
14. The order of the differential equation whose general solution is given by
y=(c1+c2)sin(x+c3)-c4ex+c5 is- D) 5
15. The value of log3log2logv3 81 is- A) 1
16. sin 105º + cos 105º is equal to – D) 1/v2
17. If tan x= cot x than a value of x is – B) π/4
18. The maximum value of 4sinxcosx is equal to – A) 2
19. sin-1x+cos-1x (-1<=x<=1) is equal to – B) π/2
20. If y= 2logex2, then d2y/dx2 is equal to- B) -4/x2
21. If the length of sides of a regular polygon is increased by 50%, then the area isincreased by – D) none of the above
22. The number of diagonals of a polygon having 10 sides is – A) 45
23. The length of the major axis and the minor axis of an ellipse are respectively 12 cm and 8 cm. Then its area is- B) 24π Sq. cm.
24. A right pyramid stands on a rectangular base of size 8 inch x 15 inch. Its volume is 120 cu. inch. The height of the pyramid is – A) 3 inch.
25. The height of an equilateral triangle of perimeter 24 cm is- A) 4v3 cm
26. The domain of definition of the function f(x) x2+x+5/ x2 -6x+8 is-- B) -∞<x<2, 2<x<4, 4<x<∞
27. Let f(x) = 3x+4 for 0<=x<=2
= 5x+λ for 2<x<=3
if f(x) is given to be continuous at x=2 then – D) λ=0
28. If y= tan-1 V(1-cosx/1+cosx) then dy/dx=? – A) ½
29. If x=et, y= sin t, then the value of d2y/dx2 at t= π/2 is – C) – e-π
30. If g(x)= x+1/x2-3x-4, then g(x) is undefined for – A) x=-1
31. 1/log(1.2) [log8 + log v27 – log v1000]= C) 3/2
32. If one root of x2+6x+m=0 is 1, the value of ‘m’ is – A) -7
33. If sec θ – tan θ=1/2 then θ lies in –A) the 1st quadrant
34. If sin θ + cosec θ=2, then sin9θ + cosec9θ - B) 2
35. The equation 2sinθ+cosθ=3 has – D) No solution
36. If tan2α = 2 tan2β, then cos2α + sin2β= ?- C) 0
37. If tan(cos-1x)=sin(tan-12) then x= ?- D) ±v5/3
38. The x-axis divides the line segment joining A(-3,2) and B(6,-4) in the ratio – D) 1:2
39. The acute angle between the lines (a+b)x=(a-b)y and ax+by+c=0, a≠b is – C) 45º
40. The straight line through the point (-a,-b) and (a,b) passes through the point – B) (a2,ab)
41. lim xà0 sin(πcos2x)/x2 = C) π/2
42. The differential of all straight lines passing through the point (1,0) is- C) y= dy/dx(x-1)
43. If the roots of the equation x2-2x+2=0 are p and q, then the value of p-1+q-1 is equal to – C) 1
44. If one root of the equation 5x2-6x-d=0 is reciprocal of the other, then the value of d is – B) -5
45. If f(x)=2x, then the value of f(x)f(1/x) is – D) 4
46. The modulus of 7-24i/3+4i is – C) 5
47. ∫-1 1 |x| dx is equal to – C) 1
48. If ω is an imaginary cube root of unity then ω+ ω2 is equal to – B) -1
49. (22n – 3. 22n-2) (3n-2.3n-2)/ 3n-4(4n+3-22n)=? – C) ¼
50. Evaluate: [i19 + (1/i)25]2, (i=v-1) - B) -4
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