Mathematics MCQ Quiz Hub

1. What will be the equation of the normal to the hyperbola xy = 4 at the point (2, 2)?
x + y = 0
x – y = 0
2x – y = 0
x + 2y = 0

2. At which point does the normal to the hyperbola xy = 4 at (2, 2) intersects the hyperbola again?
(-2, -2)
(-2, 2)
(2, -2)
(0, 2)

3. A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the value of space described?
172 cm
176 cm
178 cm
174 cm

4. A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the described by the particle during the 10th second of its motion?
38.5cm
37.5cm
38cm
39.5cm

5. A motor car travelling at the rate of 40 km/hr is stopped by its brakes in 4 seconds. How long will it go from the point at which the brakes are first applied?
22m
22(2/9)m
22(1/9)m
22(4/9)m

6. A bullet fired into a target loses half of its velocity after penetrating 2.5 cm. How much further will it penetrate?
0.85 cm
0.84 cm
0.83 cm
0.82 cm

7. A particle moving in a straight line with uniform retardation described 7cm in 5th second and after some time comes to rest. If the particle describes 1/64 part of the total path during the last second of its motion, for how long was the particle in motion?
6 seconds
8 seconds
4 seconds
2 seconds

8. If a, b, c be the space described in the pth, qth and rth seconds by a particle with a given velocity and moving with uniform acceleration in a straight line then what is the value of a(q – r) + b(r – p) + c(p – q)?
0
1
-1
Can’t be determined

9. A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds,respectively.What is the distance described by the particle in 3 seconds?
30 cm
31 cm
32 cm
33 cm

10. A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds, respectively.What is the velocity of the particle in 3 seconds?
11m/sec
31 cm/sec
21m/sec
41m/sec

11. A curve passes through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve is in the first quadrant and has its area equal to 2. What will be the equation of the curve?
xy = 2
xy = -1
x – y = 2
x + y = 2

12. If, A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant length k. What kind of curve is passing through (0, k)?
Parabola
Hyperbola
Ellipse
Circle

13. Two straight railway lines meet at right angles. A train starts from the junction along one line and at the same time instant, another train starts towards the junction from a station on the other line and they move at the same uniform velocity.When will they be nearest to each other?
When they are equal distance from the junction
When they are in unequal distance from the junction
When they form a right angle at the junction
Data not sufficient

14. ____ is the angle between the normals to two planes.
Normal between the planes
The angle between the planes
Tangent between the planes
Distance between the planes

15. Which trigonometric function is used to find the angle between two planes?
Tangent
Cosecant
Secant
Sine

16. Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
21
– 7
12
– 8

17. _____ planes have an angle 90 degrees between them.
Orthogonal
Tangential
Normal
Parallel

18. Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.
38.2
19.64
89.21
54.54

19. Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0.
69.69
84.32
63.25
83.25

20. The planes 5x + y + 3z + 1 = 0 and x + y – kz + 6 = 0 are orthogonal, find k.
4
2
6
8

21. Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y – 2z + 6 = 0.
30.82
34.91
11.23
7.54

22. Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.
21
17
12
11

23. What will be ratio in which the line 3x + y – 11 = 0 divides the line segment joining the points (0, -1) and (-3, -4)?
1:2 (internally)
1:2 (externally)
2:1 (externally)
2:1 (internally)

24. In what ratio is the line segment joining the points A(-5, 2) and B(3, 9) divided by the x-axis?
2:5 (internally)
2:5 (externally)
2:9 (externally)
2:9 (internally)

25. In what ratio is the line segment joining the points A(2, 4) and B(6, 5) divided by the y-axis?
2:1 (internally)
2:1 (externally)
3:1 (internally)
3:1 (externally)

26. What will be the coordinates of the fourth vertex S, if P(-1, -1), Q(2, 0), R(2, 3) are the three vertices of a parallelogram?
(-5, -12)
(5, -12)
(5, 12)
(-5, 12)

27. What will be the value of a and b, if (-5, a), (-3, -3), (-b, 0) and (-3, 3) are the vertices of the parallelogram?
a = 0, b = -1
a = -1, b = 1
a = 1, b = 1
a = 0, b = 1

28. Which of the following sets of planes are parallel to each other?
2x+3y+4z=8 and 3x+9y+12z=7
2x+3y+4z=2 and 4x+6y+8z=9
3x+2y+4z=0 and 3x+4y+2z=0
2x+4y+8z=9 and 4x+2y+7z=0

29. The area of the triangle formed by three collinear points is zero.
True
False

30. Find the value of k for which (1,2), (3,0), (2,k) are collinear.
0
-1
2
1

31. What is the area of the triangle if the vertices are (0,2), (0, 0), (3, 0)?
1 sq.unit
5 sq.units
2 sq.units
3 sq.units

32. Find the equation of the line joining A(2,1) and B(6,3) using determinants.
2y-x=0
2y-x=0
y-x=0
y-2x=0

33. Find the area of the triangle with the vertices (2,3), (4,1), (5,0).
3 sq.units
2 sq.units
0
1 sq.unit

34. Find the equation of the line joining A(5,1), B(4,0) using determinants.
4x-y=4
x-4y=4
x-y=4
x-y=0

35. Find the value of k for which the points (3,2), (1,2), (5,k) are collinear.
2
5
4
9

36. Which of the following is not a property of determinant?
The value of determinant changes if all of its rows and columns are interchanged
The value of determinant changes if any two rows or columns are interchanged
The value of determinant is zero if any two rows and columns are identical
The value of determinant gets multiplied by k, if each element of row or column is multiplied by k

37. Function f should be _____ on [a,b] according to Rolle’s theorem.
continuous
non-continuous
integral
non-existent

38. Function f is differential on (a,b) according to Rolle’s theorem.
True
False

39. What is the relation between f(a) and f(b) according to Rolle’s theorem?
Equals to
Greater than
Less than
Unequal

40. Does Rolle’s theorem applicable if f(a) is not equal to f(b)?
Yes
No
Under particular conditions
May be

41. Another form of Rolle’s theorem for the differential condition is _____
f is differentiable on (a,ah)
f is differentiable on (a,a-h)
f is differentiable on (a,a/h)
f is differentiable on (a,a+h)

42. Another form of Rolle’s theorem for the continuous condition is _____
f is continuous on [a,a-h]
f is continuous on [a,h]
f is continuous on [a,a+h]
f is continuous on [a,ah]

43. What is the relation between f(a) and f(h) according to another form of Rolle’s theorem?
f(a) < f(a+h)
f(a) = f(a+h)
f(a) = f(a-h)
f(a) > f(a+h)

44. Function f is not continuous on [a,b] to satisfy Lagrange’s mean value theorem.
False
True

45. What are/is the conditions to satify Lagrange’s mean value theorem?
f is continuous on [a,b]
f is differentiable on (a,b)
f is differentiable and continuous on (a,b)
f is differentiable and non-continuous on (a,b)

46. Function f is differentiable on [a,b] to satisfy Lagrange’s mean value theorem.
True
False

47. Lagrange’s mean value theorem is also called as _____
Euclid’s theorem
Rolle’s theorem
a special case of Rolle’s theorem
the mean value theorem

48. Rolle’s theorem is a special case of _____
Euclid’s theorem
another form of Rolle’s theorem
Lagrange’s mean value theorem
Joule’s theorem

49. ∆ABC is a right angled triangle, where AB = 5cm, BC = 10cm, AC = 15cm.
False
True

50. What will be the distance of the foot of ladder from the building, if the ladder of 12 m high reaches the top of a building 35 m high from the ground?
32.65 m
32.87 m
31.87 m
32.85 m