R4RIN – MCQs, Mock Tests | Mathematics Mathematics MCQs Set-8

What will be the equation of the normal to the hyperbola xy = 4 at the point (2, 2)?

1. x + y = 0
2. x – y = 0
3. 2x – y = 0
4. x + 2y = 0

✅ Correct Answer: 2

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

1. (-2, -2)
2. (-2, 2)
3. (2, -2)
4. (0, 2)

✅ Correct Answer: 1

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?

1. 172 cm
2. 176 cm
3. 178 cm
4. 174 cm

✅ Correct Answer: 2

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?

1. 38.5cm
2. 37.5cm
3. 38cm
4. 39.5cm

✅ Correct Answer: 1

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?

1. 22m
2. 22(2/9)m
3. 22(1/9)m
4. 22(4/9)m

✅ Correct Answer: 2

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

1. 0.85 cm
2. 0.84 cm
3. 0.83 cm
4. 0.82 cm

✅ Correct Answer: 3

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?

1. 6 seconds
2. 8 seconds
3. 4 seconds
4. 2 seconds

✅ Correct Answer: 2

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)?

1. 0
2. 1
3. -1
4. Can’t be determined

✅ Correct Answer: 1

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?

1. 30 cm
2. 31 cm
3. 32 cm
4. 33 cm

✅ Correct Answer: 2

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?

1. 11m/sec
2. 31 cm/sec
3. 21m/sec
4. 41m/sec

✅ Correct Answer: 1

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?

1. xy = 2
2. xy = -1
3. x – y = 2
4. x + y = 2

✅ Correct Answer: 4

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)?

1. Parabola
2. Hyperbola
3. Ellipse
4. Circle

✅ Correct Answer: 4

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?

1. When they are equal distance from the junction
2. When they are in unequal distance from the junction
3. When they form a right angle at the junction
4. Data not sufficient

✅ Correct Answer: 1

____ is the angle between the normals to two planes.

1. Normal between the planes
2. The angle between the planes
3. Tangent between the planes
4. Distance between the planes

✅ Correct Answer: 2

Which trigonometric function is used to find the angle between two planes?

1. Tangent
2. Cosecant
3. Secant
4. Sine

✅ Correct Answer: 2

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

1. 21
2. – 7
3. 12
4. – 8

✅ Correct Answer: 4

_____ planes have an angle 90 degrees between them.

1. Orthogonal
2. Tangential
3. Normal
4. Parallel

✅ Correct Answer: 1

Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.

1. 38.2
2. 19.64
3. 89.21
4. 54.54

✅ Correct Answer: 4

Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0.

1. 69.69
2. 84.32
3. 63.25
4. 83.25

✅ Correct Answer: 3

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

1. 4
2. 2
3. 6
4. 8

✅ Correct Answer: 2

Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y – 2z + 6 = 0.

1. 30.82
2. 34.91
3. 11.23
4. 7.54

✅ Correct Answer: 2

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

1. 21
2. 17
3. 12
4. 11

✅ Correct Answer: 4

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. 1:2 (internally)
2. 1:2 (externally)
3. 2:1 (externally)
4. 2:1 (internally)

✅ Correct Answer: 2

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

1. 2:5 (internally)
2. 2:5 (externally)
3. 2:9 (externally)
4. 2:9 (internally)

✅ Correct Answer: 3

In what ratio is the line segment joining the points A(2, 4) and B(6, 5) divided by the y-axis?

1. 2:1 (internally)
2. 2:1 (externally)
3. 3:1 (internally)
4. 3:1 (externally)

✅ Correct Answer: 4

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?

1. (-5, -12)
2. (5, -12)
3. (5, 12)
4. (-5, 12)

✅ Correct Answer: 3

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?

1. a = 0, b = -1
2. a = -1, b = 1
3. a = 1, b = 1
4. a = 0, b = 1

✅ Correct Answer: 4

Which of the following sets of planes are parallel to each other?

1. 2x+3y+4z=8 and 3x+9y+12z=7
2. 2x+3y+4z=2 and 4x+6y+8z=9
3. 3x+2y+4z=0 and 3x+4y+2z=0
4. 2x+4y+8z=9 and 4x+2y+7z=0

✅ Correct Answer: 2

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

1. True
2. False
3.
4.

✅ Correct Answer: 1

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

1. 0
2. -1
3. 2
4. 1

✅ Correct Answer: 4

What is the area of the triangle if the vertices are (0,2), (0, 0), (3, 0)?

1. 1 sq.unit
2. 5 sq.units
3. 2 sq.units
4. 3 sq.units

✅ Correct Answer: 4

Find the equation of the line joining A(2,1) and B(6,3) using determinants.

1. 2y-x=0
2. 2y-x=0
3. y-x=0
4. y-2x=0

✅ Correct Answer: 1

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

1. 3 sq.units
2. 2 sq.units
3. 0
4. 1 sq.unit

✅ Correct Answer: 3

Find the equation of the line joining A(5,1), B(4,0) using determinants.

1. 4x-y=4
2. x-4y=4
3. x-y=4
4. x-y=0

✅ Correct Answer: 3

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

1. 2
2. 5
3. 4
4. 9

✅ Correct Answer: 1

Which of the following is not a property of determinant?

1. The value of determinant changes if all of its rows and columns are interchanged
2. The value of determinant changes if any two rows or columns are interchanged
3. The value of determinant is zero if any two rows and columns are identical
4. The value of determinant gets multiplied by k, if each element of row or column is multiplied by k

✅ Correct Answer: 1

Function f should be _____ on [a,b] according to Rolle’s theorem.

1. continuous
2. non-continuous
3. integral
4. non-existent

✅ Correct Answer: 1

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

1. True
2. False
3.
4.

✅ Correct Answer: 1

What is the relation between f(a) and f(b) according to Rolle’s theorem?

1. Equals to
2. Greater than
3. Less than
4. Unequal

✅ Correct Answer: 1

Does Rolle’s theorem applicable if f(a) is not equal to f(b)?

1. Yes
2. No
3. Under particular conditions
4. May be

✅ Correct Answer: 2

Another form of Rolle’s theorem for the differential condition is _____

1. f is differentiable on (a,ah)
2. f is differentiable on (a,a-h)
3. f is differentiable on (a,a/h)
4. f is differentiable on (a,a+h)

✅ Correct Answer: 4

Another form of Rolle’s theorem for the continuous condition is _____

1. f is continuous on [a,a-h]
2. f is continuous on [a,h]
3. f is continuous on [a,a+h]
4. f is continuous on [a,ah]

✅ Correct Answer: 3

What is the relation between f(a) and f(h) according to another form of Rolle’s theorem?

1. f(a) < f(a+h)
2. f(a) = f(a+h)
3. f(a) = f(a-h)
4. f(a) > f(a+h)

✅ Correct Answer: 2

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

1. False
2. True
3.
4.

✅ Correct Answer: 1

What are/is the conditions to satify Lagrange’s mean value theorem?

1. f is continuous on [a,b]
2. f is differentiable on (a,b)
3. f is differentiable and continuous on (a,b)
4. f is differentiable and non-continuous on (a,b)

✅ Correct Answer: 3

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

1. True
2. False
3.
4.

✅ Correct Answer: 1

Lagrange’s mean value theorem is also called as _____

1. Euclid’s theorem
2. Rolle’s theorem
3. a special case of Rolle’s theorem
4. the mean value theorem

✅ Correct Answer: 4

Rolle’s theorem is a special case of _____

1. Euclid’s theorem
2. another form of Rolle’s theorem
3. Lagrange’s mean value theorem
4. Joule’s theorem

✅ Correct Answer: 3

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

1. False
2. True
3.
4.

✅ Correct Answer: 1

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?

1. 32.65 m
2. 32.87 m
3. 31.87 m
4. 32.85 m

✅ Correct Answer: 2