# ACT Mathematics Objective Questions Paper 24

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Q-1. The equation are the sides of

(a) An equilateral triangle

(b) A Right angled triangle

(c) An isosceles triangle

(d) An obtuse angled triangle

Q-2. The tangents to the circle at the points and are

(a) Parallel

(b) At right angles

(c) Inclined at an angle of

(d) Inclined at an angle of

Q-3. If the direction cosines of a straight line are < k, k, k > , then

(a)

(b)

(c)

(d)

Q-4. Angle between the straight line

And the plane 4x-2y + 4z = 9 is

(a)

(b)

(c)

(d)

Q-5. The number of tangents to the circle through the point (-1,2) is

(a) 1

(b) 2

(c) 0

(d) none of these

Q-6. The distance between the line is

(a) 2

(b) 8

(c) -2

(d) None of these

Q-7. Radius of the sphere through the points (4,3, 0) , (0,4, 3) , (0,5, 0) and (4,0, 3) is

(a) 7

(b) 5

(c)

(d) none of these

Q-8. The medians AD and BE of a triangle with vertices at A (0, b) , B (0,0) and C (a, 0) are perpendicular to each other if

(a)

(b)

(c)

(d) b

Q-9. The straight line x + y = 0,3x + y-4 = 0, x + 3y-4 = 0, from a triangle which is

(a) Isosceles

(b) Equilateral

(c) Right angled

(d) None of these

Q-10. If the two variables X and Y have a perfect correction (direction indirect) , then they may be connected by a relation of the type

(a)

(b)

(c)

(d) none of these

Q-11.25 % of the items of a data are less than 35 and 25 % of the items are more than 75. Q. D of the data is

(a) 55

(b) 20

(c) 35

(d) 75

Q-12. The line passing through (1,1) and parallel to the line 2x-3y + 5 = 0 is

(a) 3x + 2y = 5

(b) 2x-3y + 1 = 0

(c) 3x-2y = 1

(d) 2x + 3y = 5

Q-13. The area of the triangle with vertices at the points (a, b + c) , (b, c + a) , (c, a + b) is

(a)

(b)

(c)

(d)

Q-14. Maximum and minimum magnitudes of resultant of two forces acting at a point are 18 and 4. The magnitudes of the two forces are

(a) 11 and 7

(b) 22 and 14

(c) 9 and 2

(d) none of these

Q-15. Two forces P and Q act at a point along perpendicular directions; the magnitude of their resultant is

(a)

(b)

(c)

(d)

Q-16. A particle starts from rest with uniform acceleration and acquires a velocity of 40 m/sec in 10 seconds. The displacement of the particle at the end of 10 seconds is

(a) 4m

(b) 200 m

(c) 20 m

(d) none of these

Q-17. Forces of magnitudes 3N, 5N, and 7N acting at a point are in equilibriums. The angle between the directions of the first two forces is

(a)

(b)

(c)

(d)

Q-18. A stone A is thrown vertically upwards with a velocity of 29.4 m/sec. After stone B is let fall from the same point. A will overtake B after

(a) 1

(b) 2

(c) 3

(d) 4 sec

Q-19. Which of the following statement is correct?

(a) Every L. P. P has at least on optimal solution

(b) Every L. P. P has a unique optimal solution

(c) If an L. P. P has a unique optimal solution

(d) None of these

Q-20. Decimal from of the numeral is

(a) 8

(b) 100

(c) 4

(d) None of these

Q-21. The number of significant digits in 0.0001 is

(a) 5

(b) 4

(c) 1

(d) None of these

Q-22. If is equal to

(a) 1

(b) 3

(c) 2

(d) None of these

Q-23. is equal to

(a)

(b)

(c)

(d) None of these

Q-24. Which of the following function is periodic?

(a)

(b)

(c) x. Sin x

(d)

Q-25.

(a) all x, y R

(b)

(c)

(d)

Q-26. holds good for all

(a)

(b)

(c)

(d) None of these

Q-27. If 3 then the value of is equal to

(a) 0

(b) -5

(c) 5

(d) None of these

Q-28. If and , then if and only if

(a)

(b)

(c)

(d)

Q-29. If a function F is such that F (0) = 2, F (1) = 3, F (n + 2) = 2F (n) -F (n-1) for then F (5) is equal to

(a) -7

(b) -3

(c) 7

(d) 13

Q-30. ABC is an equilateral triangle of the each side a (> 0) . The in radius of the triangle is

(a)

(b)

(c)

(d)

Q-31. The greatest angle of a cyclic quadrilateral is 3 times the least. The circle measure of the least angle is

(a)

(b)

(c)

(d) None of these

Q-32. The domain of the function

(a)

(b)

(c)

(d)

Q-33. Let A and B {1,2, 4} , then F = { (1,1) , (1,2) , (2,1) , (3,4) } is a

(a) One-one function from A to B

(b) Bisection from A to B

(c) Surjection from A to B

(d) None of these

Q-34.

(a)

(b)

(c)

(d)

Q-35. Circle measure of an angle of 1 radian is

(a) 90

(b)

(c) 1

(d) none

Q-36 is equal to

(a) 1

(b)

(c) 2

(d) 0

Q-37 is equal to

(1)

(2)

(3) Cosec x

(d) None of these

Q-38.

Is equal to

(a) 2

(b) 1

(c)

(d)

Q-39. If

(a)

(b)

(c)

(d)

Q-40. The function f (x) =

Assumes minimum value of x given by

(a) 5

(b) 3

(c)

(d) 2

Q. 41 The curve has at (0,0)

(a) A vertical tangent

(b) A horizontal tangent

(c) Oblique tangent

(d) No tangent

Q-42.

dx is equal to

(a) -1

(b) 2

(c)

(d) none of these

Q-43. if (x) = has the value

(a)

(b)

(c)

(d) none of these

Q-44. is equal to

(a)

(b)

(c)

(d) 2 sin x

Q-45. dx can be evaluated by the substitution

(a)

(b)

(c)

(d)