# 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.xÂ²/9 + yÂ²/5 = 1

2. xÂ²/9 + y2 /25 = 1

3.xÂ²/5 + yÂ²/9 = 1

4. xÂ²/25 + yÂ²/9 = 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. xÂ²/81 + yÂ²/9 = 1

2.xÂ²/9 + yÂ²/81 = 1

3.xÂ²/169 + yÂ²/9 = 1

4.xÂ²/9 + yÂ²/169 = 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`

1.2âˆš3(i â€“ j + k)

2.2âˆš3(-i + j + k)

3. 2âˆš3(i + j â€“ k)

4. 2âˆš3(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. aÂ² = 2b

4.2a = bÂ²

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.âˆš3 unit

2. 2âˆš3 unit

3.3âˆš3 unit

4.4âˆš3 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)Â² + (y â€“ 3)Â² = 3Â²

2. (x â€“ 2)Â² + (y + 3)Â² = 3Â²

3.(x â€“ 2)Â² + (y â€“ 3)Â² = 3Â²

4.(x + 2)Â² + (y + 3)Â² = 3Â²

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, â€“ 2)

3. (4, 1)

4.None of these

## Question: ```In a three dimensional space, the equation 3x â€“ 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/âˆš52

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 (aÃ—b)

1. e

2.eÂ³

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. Ï€/2

2.Ï€/3

3.Ï€/4

4.Ï€/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)Â²

2.-1/(x-1)Â²

3. 2/(x-1)Â²

4. -2/(x-1)Â²

## Question: `The equation of a hyperbola with foci on the x-axis is`

1.xÂ²/aÂ² + yÂ²/bÂ² = 1

2.xÂ²/aÂ² â€“ yÂ²/bÂ² = 1

3. xÂ² + yÂ² = (aÂ² + bÂ²)

4. xÂ² â€“ yÂ² = (aÂ² + bÂ²)

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

1.16xÂ² â€“ 9yÂ² â€“ 24xy â€“ 144x + 8y + 224 = 0

2. 16xÂ² + 9yÂ² â€“ 24xy â€“ 144x + 8y â€“ 224 = 0

3. 16xÂ² + 9yÂ² â€“ 24xy â€“ 144x â€“ 8y + 224 =0

4.16xÂ² + 9yÂ² â€“ 24xy â€“ 144x + 8y + 224 = 0

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

1. 10y = xÂ² + 4x + 16

2.12y = xÂ² + 4x + 16

3. 12y = xÂ² + 4x

4. 12y = xÂ² + 4x + 8

1. yÂ² = 9x

2.yÂ² = 9x/2

3.yÂ² = 2x

4.yÂ² = 2x/9

## Question: ```The equation of plane passing through the point i + j + k and parallel to the plane r . (2i â€“ j + 2k) = 5 is ```

1.r . (2i â€“ j + 2k) = 2

2. r . (2i â€“ j + 2k) = 3

3.r . (2i â€“ j + 2k) = 4

4.r . (2i â€“ 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 Ã— (x + 1)

3.y â€“ 2 = 3 Ã— (x â€“ 1)

4.y â€“ 2 = x â€“ 1

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

1. 2x + y â€“ 1 = 0

2.2x â€“ y + 1 = 0

3.2x â€“ y â€“ 1 = 0

4.2x + y + 1 = 0

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

1. 2x â€“ y â€“ 7 = 0

2. 2x + y + 7 = 0

3.2x + y â€“ 7 = 0

4.x + 2y â€“ 7 = 0

## Question: `The equation of the line which cuts off equal and positive intercepts from the axes and passes through the point (Î±, Î²) is`

1.x + y = Î± + Î²

2. x + y = Î±

3. x + y = Î²

4.None of these

1. 6x â€“ 4y = 5

2.6x + 4y = 5

3. 6x + 4y = 7

4.6x â€“ 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`

1.9xÂ² + 25yÂ² + 25zÂ² + 225 = 0

2.9xÂ² + 25yÂ² + 25zÂ² â€“ 225 = 0

3. 9xÂ² + 25yÂ² â€“ 25zÂ² â€“ 225 = 0

4.9xÂ² â€“ 25yÂ² â€“ 25zÂ² â€“ 225 = 0

## Question: ```The expansion of log(1 â€“ x) is ```

1. x â€“ xÂ²/2 + xÂ³/3 â€“ â€¦â€¦..

2.x + xÂ²/2 + xÂ³/3 + â€¦â€¦..

3. -x + xÂ²/2 â€“ xÂ³/3 + â€¦â€¦..

4. -x â€“ xÂ²/2 â€“ xÂ³/3 â€“ â€¦â€¦..

1.1

2.2

3.3

4.4

1.(-3, 5, 2)

2.(3, 5, 2)

3. (3, -5, 2)

4. (3, 5, -2)

## Question: `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. âˆš3y + x = 14

3.âˆš3x + y = 14

4.None of these

1. ln = amÂ²

2.ln = am

3.ln = aÂ² mÂ²

4.ln = aÂ² m

1.Straight line

2. Plane

3.Sphere

4.None of these

1. x + y + 1 = 0

2.x â€“ y = 0

3.x + y = 1

4.None of these

1.8x + 19 = 0

2.8x â€“ 19 = 0

3.4x â€“ 19 = 0

4.4x + 19 = 0

## Question: `The maximum distance between points (3sin Î¸, 0, 0) and (4cos Î¸, 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 yÂ² = 4ax is`

1. (-atÂ², -2at)

2. (-atÂ², 2at)

3.(a sinÂ²t, -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 â€“ (1 + a)y + 3az = 0 passes through the intersection of the planes`

1.2x â€“ y = 0 and y + 3z = 0

2.2x â€“ y = 0 and y â€“ 3z = 0

3.2x + 3z = 0 and y = 0

4.2x â€“ 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. âˆš57/4

2. âˆš77/4

3.âˆš77/2

4.âˆš87/4

1. a/b

2. -a/b

3.-c/b

4.c/b

1. 3557

2.3775

3.3757

4.3575

## Question: `The sum of series 1/2! + 1/4! + 1/6! + â€¦.. is`

1.eÂ² â€“ 1 / 2

2.(e â€“ 1)Â² /2 e

3. eÂ² â€“ 1 / 2 e

4.eÂ² â€“ 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 2cÂ² then the equation of its locus is`

1.xÂ² â€“ yÂ² = cÂ² â€“ aÂ²

2.xÂ² â€“ yÂ² = cÂ² + aÂ²

3.xÂ² +cÂ² â€“ yÂ² = aÂ²

4.xÂ² + yÂ² = cÂ² + aÂ²

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 limyâ†’0 {(x + y) Ã— sec (x + y) â€“ x Ã— sec x}/y is ```

1.x Ã— tan x Ã— sec x

2.x Ã— tan x Ã— sec x + x Ã— sec x

3.tan x Ã— sec x + sec x

4. x Ã— tan x Ã— 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 â‰  c1/c2

2.a1/a2 â‰  b1/b2 = c1/c2

3.a1/a2 â‰  b1/b2 â‰  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 â‰  c1/c2

2.a1/a2 â‰  b1/b2 = c1/c2

3. a1/a2 â‰  b1/b2 â‰  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. Î¸ is an acute angle

2.Î¸ 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.Î¸ is an acute angle

2. Î¸ 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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