R4RIN – MCQs, Mock Tests | NCERT Class 11 MCQ Questions for Class 11 Maths sets 3

The sum of series 1/2! + 1/4! + 1/6! + ….. is

1. e² – 1 / 2
2. (e – 1)² /2 e
3. e² – 1 / 2 e
4. e² – 2 / e

✅ Correct Answer: 2

The third term of a geometric progression is 4. The product of the first five terms is

1. 43
2. 45
3. 44
4. None of these

✅ Correct Answer: 2

Let Tr be the r th term of an A.P., for r = 1, 2, 3, … If for some positive integers m, n, we have Tm = 1/n and Tn = 1/m, then Tm n equals

1. 1/m n
2. 1/m + 1/n
3. 1
4. 0

✅ Correct Answer: 3

The sum of two numbers is 13/6 An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Then the number of means inserted is

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

✅ Correct Answer: 3

If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a, c/b are in

1. A.P.
2. G.P.
3. H.P
4. A.G.P.

✅ Correct Answer: 3

The 35th partial sum of the arithmetic sequence with terms an = n/2 + 1

1. 240
2. 280
3. 330
4. 350

✅ Correct Answer: 4

The first term of a GP is 1. The sum of the third term and fifth term is 90. The common ratio of GP is

1. 1
2. 2
3. 3
4. 4

✅ Correct Answer: 3

The sum of AP 2, 5, 8, …..up to 50 terms is

1. 3557
2. 3775
3. 3757
4. 3575

✅ Correct Answer: 2

If 2/3, k, 5/8 are in AP then the value of k is

1. 31/24
2. 31/48
3. 24/31
4. 48/31

✅ Correct Answer: 2

If the third term of an A.P. is 7 and its 7 th term is 2 more than three times of its third term, then the sum of its first 20 terms is

1. 228
2. 74
3. 740
4. 1090

✅ Correct Answer: 3

If the sum of the first 2n terms of the A.P. 2, 5, 8, ….., is equal to the sum of the first n terms of the A.P. 57, 59, 61, ….., then n equals

1. 10
2. 11
3. 12
4. 13

✅ Correct Answer: 2

If a is the A.M. of b and c and G1 and G2 are two GM between them then the sum of their cubes is

1. abc
2. 2abc
3. 3abc
4. 4abc

✅ Correct Answer: 2

The locus of a point, whose abscissa and ordinate are always equal is

1. x + y + 1 = 0
2. x – y = 0
3. x + y = 1
4. None of these

✅ Correct Answer: 2

The equation of straight line passing through the point (1, 2) and parallel to the line y = 3x + 1 is

1. y + 2 = x + 1
2. y + 2 = 3 × (x + 1)
3. y – 2 = 3 × (x – 1)
4. y – 2 = x – 1

✅ Correct Answer: 3

What can be said regarding if a line if its slope is negative

1. θ is an acute angle
2. θ is an obtuse angle
3. Either the line is x-axis or it is parallel to the x-axis.
4. None of these

✅ Correct Answer: 2

The equation of the line which cuts off equal and positive intercepts from the axes and passes through the point (α, β) is

1. x + y = α + β
2. x + y = α
3. x + y = β
4. None of these

✅ Correct Answer: 1

Two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are coincedent if

1. a1/a2 = b1/b2 ≠ c1/c2
2. a1/a2 ≠ b1/b2 = c1/c2
3. a1/a2 ≠ b1/b2 ≠ c1/c2
4. a1/a2 = b1/b2 = c1/c2

✅ Correct Answer: 4

The equation of the line passing through the point (2, 3) with slope 2 is

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

✅ Correct Answer: 3

The slope of the line ax + by + c = 0 is

1. a/b
2. -a/b
3. -c/b
4. c/b

✅ Correct Answer: 2

Equation of the line passing through (0, 0) and slope m is

1. y = mx + c
2. x = my + c
3. y = mx
4. x = my

✅ Correct Answer: 3

The angle between the lines x – 2y = y and y – 2x = 5 is

1. tan-1 (1/4)
2. tan-1 (3/5)
3. tan-1 (5/4)
4. tan-1 (2/3)

✅ Correct Answer: 3

Two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are parallel if

1. a1/a2 = b1/b2 ≠ c1/c2
2. a1/a2 ≠ b1/b2 = c1/c2
3. a1/a2 ≠ b1/b2 ≠ c1/c2
4. a1/a2 = b1/b2 = c1/c2

✅ Correct Answer: 1

In a ΔABC, if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is

1. (1, 4)
2. (7, – 2)
3. (4, 1)
4. None of these

✅ Correct Answer: 2

The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 150 degrees with the positive direction of the y-axis. Then the equation of line is

1. x + y = 14
2. √3y + x = 14
3. √3x + y = 14
4. None of these

✅ Correct Answer: 3

If two vertices of a triangle are (3, -2) and (-2, 3) and its orthocenter is (-6, 1) then its third vertex is

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

✅ Correct Answer: 4

The sum of squares of the distances of a moving point from two fixed points (a, 0) and (-a, 0) is equal to 2c² then the equation of its locus is

1. x² – y² = c² – a²
2. x² – y² = c² + a²
3. x² +c² – y² = a²
4. x² + y² = c² + a²

✅ Correct Answer: 3

The equation of the line through the points (1, 5) and (2, 3) is

1. 2x – y – 7 = 0
2. 2x + y + 7 = 0
3. 2x + y – 7 = 0
4. x + 2y – 7 = 0

✅ Correct Answer: 3

What can be said regarding if a line if its slope is zero

1. θ is an acute angle
2. θ is an obtuse angle
3. Either the line is x-axis or it is parallel to the x-axis.
4. None of these

✅ Correct Answer: 3

Two lines are perpendicular if the product of their slopes is

1. 0
2. 1
3. -1
4. None of these

✅ Correct Answer: 3

y-intercept of the line 4x – 3y + 15 = 0 is

1. -15/4
2. 15/4
3. -5
4. 5

✅ Correct Answer: 4

The equation of the locus of a point equidistant from the point A(1, 3) and B(-2, 1) is

1. 6x – 4y = 5
2. 6x + 4y = 5
3. 6x + 4y = 7
4. 6x – 4y = 7

✅ Correct Answer: 2

The locus of the point from which the tangent to the circles x² + y² – 4 = 0 and x² + y² – 8x + 15 = 0 are equal is given by the equation

1. 8x + 19 = 0
2. 8x – 19 = 0
3. 4x – 19 = 0
4. 4x + 19 = 0

✅ Correct Answer: 2

The perpendicular distance from the point (3, -4) to the line 3x – 4y + 10 = 0

1. 7
2. 8
3. 9
4. 10

✅ Correct Answer: 1

A man running a race course notes that the sum of the distances from the two flag posts from him is always 10 meter and the distance between the flag posts is 8 meter. The equation of posts traced by the man is

1. x²/9 + y²/5 = 1
2. x²/9 + y2 /25 = 1
3. x²/5 + y²/9 = 1
4. x²/25 + y²/9 = 1

✅ Correct Answer: 4

The center of the ellipse (x + y – 2)² /9 + (x – y)² /16 = 1 is

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

✅ Correct Answer: 4

The parametric coordinate of any point of the parabola y² = 4ax is

1. (-at², -2at)
2. (-at², 2at)
3. (a sin²t, -2a sin t)
4. (a sin t, -2a sin t)

✅ Correct Answer: 3

The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is

1. y² = 9x
2. y² = 9x/2
3. y² = 2x
4. y² = 2x/9

✅ Correct Answer: 2

At what point of the parabola x² = 9y is the abscissa three times that of ordinate

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

✅ Correct Answer: 2

The number of tangents that can be drawn from (1, 2) to x² + y² = 5 is

1. 0
2. 1
3. 2
4. More than 2

✅ Correct Answer: 2

In an ellipse, the distance between its foci is 6 and its minor axis is 8 then its eccentricity is

1. 4/5
2. 1/√52
3. 3/5
4. 1/2

✅ Correct Answer: 3

If the length of the tangent from the origin to the circle centered at (2, 3) is 2 then the equation of the circle is

1. (x + 2)² + (y – 3)² = 3²
2. (x – 2)² + (y + 3)² = 3²
3. (x – 2)² + (y – 3)² = 3²
4. (x + 2)² + (y + 3)² = 3²

✅ Correct Answer: 3

The equation of parabola whose focus is (3, 0) and directrix is 3x + 4y = 1 is

1. 16x² – 9y² – 24xy – 144x + 8y + 224 = 0
2. 16x² + 9y² – 24xy – 144x + 8y – 224 = 0
3. 16x² + 9y² – 24xy – 144x – 8y + 224 =0
4. 16x² + 9y² – 24xy – 144x + 8y + 224 = 0

✅ Correct Answer: 4

The parametric representation (2 + t², 2t + 1) represents

1. a parabola
2. a hyperbola
3. an ellipse
4. a circle

✅ Correct Answer: 1

The equation of a hyperbola with foci on the x-axis is

1. x²/a² + y²/b² = 1
2. x²/a² – y²/b² = 1
3. x² + y² = (a² + b²)
4. x² – y² = (a² + b²)

✅ Correct Answer: 2

The equation of parabola with vertex (-2, 1) and focus (-2, 4) is

1. 10y = x² + 4x + 16
2. 12y = x² + 4x + 16
3. 12y = x² + 4x
4. 12y = x² + 4x + 8

✅ Correct Answer: 2

If a parabolic reflector is 20 cm in diameter and 5 cm deep then the focus of parabolic reflector is

1. (0 0)
2. (0, 5)
3. (5, 0)
4. (5, 5)

✅ Correct Answer: 3

The radius of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is?

1. √57/4
2. √77/4
3. √77/2
4. √87/4

✅ Correct Answer: 3

If (a, b) is the mid point of a chord passing through the vertex of the parabola y² = 4x, then

1. a = 2b
2. 2a = b
3. a² = 2b
4. 2a = b²

✅ Correct Answer: 4

A rod of length 12 CM moves with its and always touching the co-ordinate Axes. Then the equation of the locus of a point P on the road which is 3 cm from the end in contact with the x-axis is

1. x²/81 + y²/9 = 1
2. x²/9 + y²/81 = 1
3. x²/169 + y²/9 = 1
4. x²/9 + y²/169 = 1

✅ Correct Answer: 1

The line lx + my + n = 0 will touches the parabola y² = 4ax if

1. ln = am²
2. ln = am
3. ln = a² m²
4. ln = a² m

✅ Correct Answer: 1

The center of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is?

1. (2,-3)
2. (-2,3)
3. (-4,6)
4. (4,-6)

✅ Correct Answer: 1

The cartesian equation of the line is 3x + 1 = 6y – 2 = 1 – z then its direction ratio are

1. 1/3, 1/6, 1
2. -1/3, 1/6, 1
3. 1/3, -1/6, 1
4. 1/3, 1/6, -1

✅ Correct Answer: 1

The image of the point P(1, 3, 4) in the plane 2x – y + z = 0 is

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

✅ Correct Answer: 1

Three planes x + y = 0, y + z = 0, and x + z = 0

1. meet in a line
2. meet in a unique point
3. meet taken two at a time in parallel lines
4. None of these

✅ Correct Answer: 2

The coordinate of foot of perpendicular drawn from the point A(1, 0, 3) to the join of the point B(4, 7, 1) and C(3, 5, 3) are

1. (5/3, 7/3, 17/3)
2. (5, 7, 17)
3. (5/3, -7/3, 17/3)
4. (5/7, -7/3, -17/3)

✅ Correct Answer: 1

The locus of a point which moves so that the difference of the squares of its distances from two given points is constant, is a

1. Straight line
2. Plane
3. Sphere
4. None of these

✅ Correct Answer: 2

The equation of the set of point P, the sum of whose distance from A(4, 0, 0) and B(-4, 0, 0) is equal to 10 is

1. 9x² + 25y² + 25z² + 225 = 0
2. 9x² + 25y² + 25z² – 225 = 0
3. 9x² + 25y² – 25z² – 225 = 0
4. 9x² – 25y² – 25z² – 225 = 0

✅ Correct Answer: 2

The maximum distance between points (3sin θ, 0, 0) and (4cos θ, 0, 0) is

1. 3
2. 4
3. 5
4. Can not be find

✅ Correct Answer: 3

A vector r is equally inclined with the coordinate axes. If the tip of r is in the positive octant and |r| = 6, then r is

1. 2√3(i – j + k)
2. 2√3(-i + j + k)
3. 2√3(i + j – k)
4. 2√3(i + j + k)

✅ Correct Answer: 4

The plane 2x – (1 + a)y + 3az = 0 passes through the intersection of the planes

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

✅ Correct Answer: 4

If the end points of a diagonal of a square are (1, -2, 3) and (2, -3, 5) then the length of the side of square is

1. √3 unit
2. 2√3 unit
3. 3√3 unit
4. 4√3 unit

✅ Correct Answer: 1

The coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the YZ plane is

1. (0, 17/2, 13/2)
2. (0, -17/2, -13/2)
3. (0, 17/2, -13/2)
4. None of these

✅ Correct Answer: 3

The angle between the vectors with direction ratios are 4, -3, 5 and 3, 4, 5 is

1. π/2
2. π/3
3. π/4
4. π/6

✅ Correct Answer: 2

The equation of plane passing through the point i + j + k and parallel to the plane r . (2i – j + 2k) = 5 is

1. r . (2i – j + 2k) = 2
2. r . (2i – j + 2k) = 3
3. r . (2i – j + 2k) = 4
4. r . (2i – j + 2k) = 5

✅ Correct Answer: 2

The points on the y- axis which are at a distance of 3 units from the point (2, 3, -1) is

1. either (0, -1, 0) or (0, -7, 0)
2. either (0, 1, 0) or (0, 7, 0)
3. either (0, 1, 0) or (0, -7, 0)
4. either (0, -1, 0) or (0, 7, 0)

✅ Correct Answer: 4

If α, β, γ are the angles made by a half ray of a line respectively with positive directions of X-axis Y-axis and Z-axis, then sin² α + sin² β + sin² γ =

1. 1
2. 0
3. -1
4. None of these

✅ Correct Answer: 4

If P(x, y, z) is a point on the line segment joining Q(2, 2, 4) and R(3, 5, 6) such that the projections of OP on the axes are 13/5, 19/5, 26/5 respectively, then P divides QR in the ration

1. 1 : 2
2. 3 : 2
3. 2 : 3
4. 1 : 3

✅ Correct Answer: 2

In a three dimensional space, the equation 3x – 4y = 0 represents

1. a plane containing Y axis
2. a plane containing Z axis
3. a plane containing X axis
4. None of these

✅ Correct Answer: 2

The value of the limit Limx→0 (cos x)cot2 x is

1. 1
2. e
3. e1/2
4. e-1/2

✅ Correct Answer: 4

The value of limit Limx→0 {sin (a + x) – sin (a – x)}/x is

1. 0
2. 1
3. 2 cos a
4. 2 sin a

✅ Correct Answer: 3

Limx→-1 [1 + x + x² + ……….+ x10] is

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

✅ Correct Answer: 2

The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²) is

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

✅ Correct Answer: 3

The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²) is

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

✅ Correct Answer: 3

Limx→0 log(1 – x) is equals to

1. 0
2. 1
3. 1/2
4. None of these

✅ Correct Answer: 1

Limx→0 {(ax – bx)/ x} is equal to

1. log a
2. log b
3. log (a/b)
4. log (a×b)

✅ Correct Answer: 3

The value of limy→0 {(x + y) × sec (x + y) – x × sec x}/y is

1. x × tan x × sec x
2. x × tan x × sec x + x × sec x
3. tan x × sec x + sec x
4. x × tan x × sec x + sec x

✅ Correct Answer: 4

Limy→∞ {(x + 6)/(x + 1)}(x+4) equals

1. e
2. e³
3. e5
4. e6

✅ Correct Answer: 3

The derivative of [1+(1/x)] /[1-(1/x)] is

1. 1/(x-1)²
2. -1/(x-1)²
3. 2/(x-1)²
4. -2/(x-1)²

✅ Correct Answer: 4

The expansion of log(1 – x) is

1. x – x²/2 + x³/3 – ……..
2. x + x²/2 + x³/3 + ……..
3. -x + x²/2 – x³/3 + ……..
4. -x – x²/2 – x³/3 – ……..

✅ Correct Answer: 4

If f(x) = x × sin(1/x), x ≠ 0, then Limx→0 f(x) is

1. 1
2. 0
3. -1
4. does not exist

✅ Correct Answer: 2