# Mathematics Objective Questions for Competitive ExamsPaper 21

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Q-1. In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals

(a)

(b)

(c) 1

(d) 0

Q-2. If for what value, if any, of x is ?

(a)

(b)

(c) 0

(d) no value

Q-3. The principle value of

(a)

(b)

(c)

(d)

Q-4. if the angles of a triangles are in the ratio 1: 23: , then the sides are in the ratio

(a)

(b)

(c)

(d)

Q-5. The equation 2 sin x + cos x = 3 has

(a) Only one solution

(b) No solution

(c) Infinitely many solution

(d) Finitely many solution

Q-6 then

(a)

(b)

(c)

(d)

Q-7. The function is increasing in

(a) 1

(b)

(c)

(d)

Q-8. If sin , then equals

(a)

(b)

(c)

(d) None of these

Q-9 In , the function is

(a) An increasing function

(b) A decreasing function

(c) A constant function

(d) None of these

Q-10. Let then f (x) is

(a) An even function

(b) An odd function

(c) An increasing function

(d) A decreasing function

Q-11. If

(a)

(b)

(c)

(d) None of these

Q-12. The values of is equal to

(a) 0

(b) 2

(c)

(d) None of these

Q-13. If cos mx, then is equal to

(a)

(b)

(c) My

(d) None of these

Q-14. If

(a) 1

(b) 3

(c) 2

(d) 0

Q-15. The value of dx is equal to

(a) sin (log 3)

(b) cos (log 3)

(c)

(d) 1

Q-16. dx is equal to

(a)

(b)

(c)

(d) None of these

Q-17. Differential coefficient of a function with respect to the function g (x) is

(a)

(b)

(c)

(d) None of these

Q-18. If

(a)

(b)

(c)

(d)

Q-19. The degree of the differential equation is

(a) 1

(b) 2

(c) 3

(4) 4

Q-20. The unit vector perpendicular to each of vectors

(a)

(b)

(c)

(d) None of these

Q-21. If G is the centurion of a triangle ABC and O is any point, then is equals to

(a)

(b)

(c)

(d) None of these

Q-22. The order and degree of the differential equation are respectively.

(a) 2,4

(b) 4,1

(c) 4,2

(d) 2,2

Q-23.

(a) 1

(b) 2

(c) 0

(d) 3

Q-24. The length of projection of the vector on the is

(a)

(b)

(c)

(d) None of these

Q-25. If

(a)

(b)

(c)

(d)

Q-26. The area bounded by the curve and axis is

(a)

(b)

(c)

(d)

Q-27. Vector projection of a vector on another vector is

(a)

(b)

(c)

(d)

Q-28. If are two vectors, then is equal to

(a)

(b) , where

(c)

(d) None of these

Q-29. The parabola and the circle touch each other at the point

(a) (0,0)

(b) (a, 0)

(c) (0, a)

(d) None of these

Q-30. Length of the common chord of the parabolas and is

(a) 1

(b)

(c)

(d) None of these

Q-31. The points (0,2, 0) , and are the vertices of

(a) A scalene triangle

(b) An equilateral triangle

(c) As isosceles triangle degree equation in

(d) None of these

Q-32. The locus of a first degree equation in x, y and x is a

(a) Straight line

(b) Plane

(c) Sphere

(d) None of these

Q-33. The point of contract of and is

(a) (1,1)

(b) (-1,1)

(c) (1, -1)

(d) (-1, -1)

Q-34. Three points A, B and C are collinear if the area of triangle ABC is

(a) Greater than zero

(b) Less than zero

(c) Zero

(d) None of these

Q-35. Area of whose vertices are and C (2, -1,3) is

(a) 9

(b) 0

(c)

(d) None of these

Q-36. If the four points (3, -2,1) , (2, -3, -4) , (-1,1, 2) and are coplanar, then is equal to

(a) 0

(b)

(c)

(d) None of these

Q-37. The locus of a point, whose abscissa and ordinate are always equal is

(a)

(b)

(c)

(d)

Q-38. The equation represents a

(a) Plane

(b) Sphere of radius 4

(c) Sphere of radius 3

(d) None of these

Q-39. The number of sphere of a given radius which touch the coordinate planes is

(a) 8

(b) 4

(c) 2

(d) 1

Q-40. Area of a triangle is 5 units, its two vertices are (2,1) and (3, -2) . Third vertex is on the line y = x + 3. The coordinates of that vertex are

(a)

(b) (8,14)

(c)

(d)

Q-41. The projection of a line segment on the coordinates are 1,2, 4 and 3 respectively.

The length of the line segment is

(a) 19

(b) 16

(c) 13

(d) 15

Q-42. The co-ordinates of the intersection of the line and the plane are

(a)

(b)

(c)

(d)

Q-43. If cov (x, y) = 0, then the two lines of the regression are

(a) Parallel

(b) Coincident

(c) At right angles

(d) None of these

Q-44. If the lines of regression are at right angles, then is equal to

(a) 1

(b) -1

(c) 10 r -1

(d) 0

Q-45. Two unlike parallel forces P and Q (P ) act distinct points of a rigid body. The magnitude of their resultant is

(a) P-Q

(b) Q-P

(c) IP-Q1

(d) None of these