|
|
l |
l |
l |
l |
l |
1999 Mathematics
|
(1)
3n-1/2 (2) 3n+1/2 (3) 3n+1/2 (4) 3n -1/2 |
|
| 2. | The fourth, seventh and tenth terms of a G.P. are p, q and r respectively then |
|
(1) p2 = q2 + r2 (2) p2 = q2 (3) q2 = pr2 (4) r2 = p2 + q2 |
|
| 3. | cos 10cos 20cos 30 ........... cos 1790 = |
|
(1) 1/2
(2) 1 (3) 0 (4) 2 |
|
| 4. | The sum of the slopes of the lines represented by 4x2 + 2 hxy - 7y2 = 0 is equal to the product of the slopes. Then h is |
|
(1) -4 (2) 4 (3) -6 (4) -2 |
|
| 5. | If f(9) = 9 and (9) = 4 then |
|
(1) 3 (2) 4 (3) 1/2 (4) 2 |
|
| 6. | The value of sin2 50 + sin2 100+ sin2 150 +.........+ sin2 850 + sin 900 = |
|
(1) 7 (2) 8 (3) 9 (4) 9 1/2 |
|
| 7. | If the equation x2 + y2 + 2gx + 2fy + 1 =0 represents a pair of lines then |
|
(1) f2 -g2 =1 (2) f2 + g2 =1 (3) g2 -f2 =1 (4) f2 + g2 =1/2 |
|
| 8. | DABC is right angled at C, then tan A + tan B = |
|
(1) a + b2
(2) a2/bc (c) c2/ab (4) b2/ac |
|
| 9. | If the sum of the distances of a point from two perpendicular lines in a plane is I then its locus is |
|
(1) Circle
(2) square (3) straight line (4) intersecting lines |
|
| 10. | The value of cot 540/tan 360 + tan 200/ cot 700 = |
|
(1) 1 (2) 0 (3) 2 (4) 3 |
|
| 11. | The Vectors form a triangle which is |
|
(1) Equilateral (2) Isosceles (3) Right angled (4) Obtuse angled |
|
| 12. |
 |
|
(1) (2) (3) (4) |
|
| 13. |
 |
|
(1) (2) (3) (4) |
|
| 14. | If
q is the angle between the vectors |
|
(1) cot q
(2) - cot q (3) tan q (4) -tan q |
|
| 15. | If A and B are square matrices of order n x n then (A-B)2 is equal to |
|
(1) A2 - 2AB + B2 (2) A2 - B2 (3) A2 - 2BA + B2 (4) A2 - AB- BA + B2 |
|
| 16. | Choose the correct answer |
|
(1) Every scalar matrix is an
identity matrix (2) Every identity matrix is a scalar matrix (3) Every diagonal matrix is an identity matrix (4) A square matrix whose each element is 1 is an identity matrix |
|
| 17. | If f(a) = 2: f' (a) = 1, g(a) =- g'(a)
= 2 then |
|
(1) -5 (2) 1/5 (3) 5 (4) 0 |
|
| 18. | The function f(x) = loge (1 + ax) - log ( 1-bx)/x is undefined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0 is |
|
(1)
a - b (2) a + b/2 (3) a + b (4) loge(ab) |
|
| 19. | If f(x) = cos (log x) then f(x) -1/2 [f(y/x) + f(xy)] has the value: |
|
(1) 0 (2) 1 (3) 1/2 (4) -2 |
|
| 20. | The area of a circle centred at (1,2) and passing through (4, 6) is |
|
(1) 5psq. units (2) 15psq. units (3) 25psq. units (4) 30psq. units |
|
| 21. | The eccentricity of the hyperbola Ö1999/3 ( x2 + y2) = 1 is |
|
(1) 2 (2) 2Ö2 (3) Ö3 (4) Ö2 |
|
| 22. | In the coaxial system of circles x2 + y2 + 2gx + C = 0 when g is a parameter, if C > 0 then the circles are of. |
|
(1) non - intersecting type
(2) touching type (3) intersecting type (4) orthogonal |
|
| 23. | If the set A has p electrons, B has q elements, then the number of elements in A x B is |
|
(1) pq (2) p2 (3) p + q (4) P + q + 1 |
|
| 24. | If w is the nth root of unity then I + w + w2 + w3 + ..... + wn-1 is |
|
(1) 0 (2) 1 (3) -1 (4) 2 |
|
| 25. | The contrapositive of (p v q) r is |
|
(1) p ® (q v r) (2) r ® (p v q) (3) ~r ® ~ (p v p) (4) ~r ® (~p Ù ~q) |
|
| 26. | For the circuits shown below. |
|
(1) (p Ù
q) v ( p Ù ~q) (2) (~p Ù q) v ( p v ~q) (3) (~p Ù q) Ù ( ~q Ù p) (4) (~p Ù ~q) Ù ( q Ù p) |
|
| 27. |
 |
|
(1) X
(2) Y (3) ¥ (4) 1 |
|
| 28. | if Z = 1 + i then the multiplicative inverse of Z2 is |
|
(1) 1 - i (2) i/2 (3) -i/2 (4) 2i |
|
| 29. |
 |
|
(1) loge3 (2) loge2 (3) 0 (4) loge4 |
|
| 30. | Let f(x) = ò0x t sin t dt then f' (x) = |
|
(1) sin x + cos x (2) x sin x (3) x cos x (4) x2/2 |
|
| 31. | The value of ò0p/2 2sinx/2sin x+2cosx dx is |
|
(1) 2 (2) p (3) p/4 (4) p/2 |
|
| 32. |
 |
|
(1) 2 (2) loge2 (3) loge2/2 (4) 2 loge2 |
|
| 33. | If f(x) = cos-1 [1 - (log x)2/1 + (log x)2 ] then f' (e) = |
|
(1) 2/e (2) 1/e (3) 1 (4) does not exist |
|
| 34. |
 |
|
(1) p/4 - log 2 (2) p/2 + log 2 (3) p/2 - log 2 (4) p/4 + log 2 |
|
| 35. |  |
|
(1) p/ab (2) p/2ab (3) pab (4) p2ab |
|
| 36. | If x + iy = Öa + ib/ c + id then ( x2 + y2)2 = |
|
(1) a2 - b2/ c2
- d2 (2) Öa2 + b2/ c2 + d2 (3) a2 + b2/ c2 + d2 (4) c2 + d2/ a2 + b2 |
|
| 37. | The matrix is known as |
|
(1) Symmetric matrix (2) Diagonal matrix (3) Upper triangular matrix (4) Skew symmetric matrix |
|
| 38. | The number of improper subgroups of G = { I, -I, i, -i} w.r.t. multiplication is |
|
(1) 1
(2) 2 (3) 3 (4) 4 |
|
| 39. | In the group G = { 0, 1, 2, 3, 4, 5 } under addition modulo 6, the value of {3 x 5-1}-1 is |
|
(1) 3 (2) 5 (3) 4 (4) 2 |
|
| 40. | An ellipse has its centre at (1, -1) and semi major axis = 8, which passes through the point (1, 3) Then the equation of the ellipse is |
|
(1) (x + I)2/64 + (y + I)2/16 =1 (2) (x - I)2/64 + (y + I)2/ 16 =1 (3) (x - I)2/16 + (y + I)2/ 64 =1 (4) (x + I)2/64 + (y - I)2/ 16 =1 |
|
| 41. | In the multiplicative group of 2 x 2 matrices of the form a ¹ o and a Î R the inverse is |
|
(1)
(2) (3) (4) does not exist |
|
| 42. | The circle x2 + y2 - 8x + 4y + 4 = 0 touches |
|
(1) x - axis (2) y- axis (3) both x and y axes (4) does not touch the axes |
|
| 43. | Focus of the parabola (y- 2)2 = 20 ( x + 3 ) is |
|
(1) (2, 2) (2) (-3, 2) (3) (3, -2) (4) (2, -3) |
|
| 44. | The locus of the centre of a circle which touches externally the given two circles is |
|
(1) Circle (2) Parabola (3) Ellipse (4) Hyperbola |
|
| 45. | The line p = x cos α + y sin α becomes tangent to x2/a2 - y2/b2 =1 if |
|
(1) p = a cos
α -b sin α (2) p2 = a2 cos α -b2 sin α (3) p2 = a2 cos α + b2 sin2 α (4) p2 = a2 cos2 α -b2 sin2 α |
|
| 46. | Equation of the normal to the hyperbola x2/a2 - y2/b2 =1 at the point (a sec q) is |
|
(1) ax/ sec
q - by/tan
q = a2- b2 (2) ax/ sec q + by/tan q = a2+ b2 (3) ax/ sec q + by/tan q = a2- b2 (4) ax/ sec q - by/tan q = a- b |
|
| 47. | If tan-1 (x) + 2 cot-1 (x) = 2p/3 then x = |
|
(1) Ö3 (2) Ö2 (3) Ö3 -1/ Ö3 + 1 (4) 3 |
|
| 48. | The angle between the curve y2 = 4x and x2 + y2= 5 at (1, 2) is |
|
(1) p/2 (2) p/4 (3) tan-1 (3) (4) tan-1 (2) |
|
| 49. | For the curve yn = an-1 x the subnormal at the point is constant. The value of n must be |
|
(1) 0 (2) 1 (3) 2 (4) 3 |
|
| 50. | The maximum value of the function f(x) = x1/x is |
|
(1) e (2) e1/e (3) 1/e (4) 2/e |
|
| 51. | ò 1/sin x + cos x dx is |
|
(1) 1/Ö2
log (x/2 + p/8) +C (2) log tan (x/2 + p/8) +C (3) 1/2 log tan ( x/2 + p/8) +C (4) 1/Ö2 log tan (x + p/4) +C |
|
| 52. | ò ex (I + tan x + tan2 x) dx = |
|
(1) ex tan x + c (2) ex sec x + c (3) ex sin x + c (4) ex cos x + c |
|
| 53. | òp/20 a sin x + b cos x/ sin x + cos x dx = |
|
(1) p/4 (2) (a + b) p/2 (3) (a + b)p (4) (a + b)p/4 |
|
| 54. | òp/20 log (tan x) dx = |
|
(1) p/4 (2) p/2 (3) 0 (4) 1 |
|
| 55. | The area enclosed between the parabolas y2 = 4x and x2 = 4y is |
|
(1) 1/16 sq. units (2) 16/3 sq. units (3) 14/3 sq. units (4) 3/4 sq. units |
|
| 56. | Solution of the differential equation tan y sec2 x dx + tan x sec2 y dy =0 is |
|
(1) tan x + tan y = k (2) tan x - tan y = k (3) tan x /tan y = k (4) tan x tan y = k |
|
| 57. | The area bounded by the curve y = loge x, the X axis, and the straight line x = e is |
|
(1) e. sq. units (2) 1. sq. unit (3) 1- 1/e. sq. units (4) 1+ 1/e. sq. units |
|
| 58. | Let f be a polynomial. Then the second derivative of f(ex) is |
|
(1) f" (ex) ex.f'(ex) (2) f"(ex) e2x + f"(ex)ex (3) f"(ex) (4) f" (ex) e2x + f'(ex)ex |
|
| 59. | If m and n are the order and
degree of the differential equation |
|
(1) m = 3 , n = 3 (2) m = 3 , n = 2 (3) m = 3 , n = 5 (4) m = 3 , n = 1 |
|
| 60. | The value of  is |
|
(1) 0 (2) a + b + c (3) 4 abc (4) abc |
|
|
|
| Help Us to help U | l |
l |
l |
l |
|
l |
l |
l |
©
2003-2007, getTarget.com
Disclaimer
and Privacy Policy
Developed & Maintained by
Xyris IT Pvt. Ltd.
