# NCERT Class 11/MCQ Questions for Class 11 Maths sets 3 Sample Test,Sample questions

## Question: `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

## Question: `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

## Question: `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)

1.(1, 1)

2.(3, 1)

3.(-3, 1)

4.(-3, -3)

1. y = mx + c

2.x = my + c

3.y = mx

4. x = my

1.a = 2b

2.2a = b

3. a² = 2b

4.2a = b²

1.31/24

2. 31/48

3.24/31

4. 48/31

1.abc

2. 2abc

3.3abc

4.4abc

1.(0 0)

2.(0, 5)

3. (5, 0)

4.(5, 5)

1.1

2.0

3.-1

4.does not exist

1.1

2.0

3.-1

4.None of these

1.1 : 2

2.3 : 2

3.2 : 3

4.1 : 3

1.√3 unit

2. 2√3 unit

3.3√3 unit

4.4√3 unit

## Question: `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

1.10

2.11

3.12

4.13

1.A.P.

2.G.P.

3.H.P

4.A.G.P.

1. 228

2.74

3.740

4.1090

1.(5, 3)

2.(-5, 3)

3. (5, -3)

4.(-5, -3)

1.(1, 4)

2.(7, – 2)

3. (4, 1)

4.None of these

## Question: ```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

1. 4/5

2.1/√52

3. 3/5

4.1/2

1.1/m n

2.1/m + 1/n

3.1

4. 0

1.0

2.1

3.-1

4.2

1. 0

2.1

3.1/2

4.None of these

1. log a

2. log b

3.log (a/b)

4.log (a×b)

1. e

2.e³

3.e5

4. e6

1. 240

2.280

3.330

4.350

1. tan-1 (1/4)

2.tan-1 (3/5)

3.tan-1 (5/4)

4. tan-1 (2/3)

1. π/2

2.π/3

3.π/4

4.π/6

1.1/3, 1/6, 1

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

3. 1/3, -1/6, 1

4.1/3, 1/6, -1

1.(2,-3)

2. (-2,3)

3. (-4,6)

4.(4,-6)

1.(0, 0)

2.(0, 1)

3.(1, 0)

4.(1, 1)

## Question: `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)

## Question: ```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

1.1/(x-1)²

2.-1/(x-1)²

3. 2/(x-1)²

4. -2/(x-1)²

## Question: `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)

## Question: `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

## Question: `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

1. y² = 9x

2.y² = 9x/2

3.y² = 2x

4.y² = 2x/9

## Question: ```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

## Question: ```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

## Question: `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

## Question: `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

1.x + y = α + β

2. x + y = α

3. x + y = β

4.None of these

1. 6x – 4y = 5

2.6x + 4y = 5

3. 6x + 4y = 7

4.6x – 4y = 7

## Question: `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

## Question: ```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 – ……..

1.1

2.2

3.3

4.4

1.(-3, 5, 2)

2.(3, 5, 2)

3. (3, -5, 2)

4. (3, 5, -2)

1. x + y = 14

2. √3y + x = 14

3.√3x + y = 14

4.None of these

1. ln = am²

2.ln = am

3.ln = a² m²

4.ln = a² m

1.Straight line

2. Plane

3.Sphere

4.None of these

1. x + y + 1 = 0

2.x – y = 0

3.x + y = 1

4.None of these

1.8x + 19 = 0

2.8x – 19 = 0

3.4x – 19 = 0

4.4x + 19 = 0

## Question: `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

1. 0

2.1

3.2

4.More than 2

## Question: `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)

1. a parabola

2. a hyperbola

3.an ellipse

4.a circle

1.7

2.8

3.9

4.10

## Question: `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

## Question: `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)

1. √57/4

2. √77/4

3.√77/2

4.√87/4

1. a/b

2. -a/b

3.-c/b

4.c/b

1. 3557

2.3775

3.3757

4.3575

1.e² – 1 / 2

2.(e – 1)² /2 e

3. e² – 1 / 2 e

4.e² – 2 / e

## Question: `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

1.2

2.4

3.6

4.8

1. 43

2.45

3.44

4.None of these

1. 0

2.1

3.2 cos a

4.2 sin a

1.0

2.1

3.2

4.-2

1.0

2.1

3.2

4.-2

## Question: ```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

1. 1

2.e

3.e1/2

4. e-1/2

## Question: `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

## Question: `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

## Question: `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

1.0

2.1

3.-1

4.None of these

## Question: `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

## Question: `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

1. -15/4

2.15/4

3.-5

4.5

## More MCQS

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