# 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

Posted Date:-2021-12-26 08:10:59

## 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

Posted Date:-2021-12-26 08:25:41

## 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)

Posted Date:-2021-12-26 08:35:38

## Question: `At what point of the parabola xÂ² = 9y is the abscissa three times that of ordinate`

1.(1, 1)

2.(3, 1)

3.(-3, 1)

4.(-3, -3)

Posted Date:-2021-12-26 08:14:04

## Question: `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

Posted Date:-2021-12-25 16:46:13

## Question: `If (a, b) is the mid point of a chord passing through the vertex of the parabola yÂ² = 4x, then`

1.a = 2b

2.2a = b

3. aÂ² = 2b

4.2a = bÂ²

Posted Date:-2021-12-26 08:24:51

## Question: `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

Posted Date:-2021-12-25 15:39:36

## Question: ```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

Posted Date:-2021-12-25 16:36:30

## Question: `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)

Posted Date:-2021-12-26 08:23:26

## Question: ```If f(x) = x Ã— sin(1/x), x â‰  0, then Limxâ†’0 f(x) is ```

1.1

2.0

3.-1

4.does not exist

Posted Date:-2021-12-26 09:03:50

## Question: ```If Î±, Î², Î³ are the angles made by a half ray of a line respectively with positive directions of X-axis Y-axis and Z-axis, then sinÂ² Î± + sinÂ² Î² + sinÂ² Î³ = ```

1.1

2.0

3.-1

4.None of these

Posted Date:-2021-12-26 08:48:20

## Question: `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

Posted Date:-2021-12-26 08:49:55

## Question: `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.âˆš3 unit

2. 2âˆš3 unit

3.3âˆš3 unit

4.4âˆš3 unit

Posted Date:-2021-12-26 08:38:49

## 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

Posted Date:-2021-12-26 08:16:54

## Question: `If the sum of the first 2n terms of the A.P. 2, 5, 8, â€¦.., is equal to the sum of the first n terms of the A.P. 57, 59, 61, â€¦.., then n equals`

1.10

2.11

3.12

4.13

Posted Date:-2021-12-25 15:41:34

## Question: `If the sum of the roots of the quadratic equation axÂ² + 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.

Posted Date:-2021-12-25 15:35:17

## Question: `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

Posted Date:-2021-12-25 15:40:29

## Question: `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)

Posted Date:-2021-12-25 16:49:56

## Question: `In a Î”ABC, 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, â€“ 2)

3. (4, 1)

4.None of these

Posted Date:-2021-12-25 16:48:29

## 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

Posted Date:-2021-12-26 08:50:58

## Question: `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/âˆš52

3. 3/5

4.1/2

Posted Date:-2021-12-26 08:16:01

## Question: `Let Tr be the r th term of an A.P., for r = 1, 2, 3, â€¦ 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

Posted Date:-2021-12-25 15:32:45

## Question: ```Limxâ†’-1 [1 + x + xÂ² + â€¦â€¦â€¦.+ x10] is ```

1.0

2.1

3.-1

4.2

Posted Date:-2021-12-26 08:53:49

## Question: ```Limxâ†’0 log(1 â€“ x) is equals to ```

1. 0

2.1

3.1/2

4.None of these

Posted Date:-2021-12-26 08:55:36

## Question: `Limxâ†’0 {(ax â€“ bx)/ x} is equal to`

1. log a

2. log b

3.log (a/b)

4.log (aÃ—b)

Posted Date:-2021-12-26 08:57:15

## Question: ```Limyâ†’âˆž {(x + 6)/(x + 1)}(x+4) equals ```

1. e

2.eÂ³

3.e5

4. e6

Posted Date:-2021-12-26 09:00:32

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

1. 240

2.280

3.330

4.350

Posted Date:-2021-12-25 15:36:53

## Question: `The angle between the lines x â€“ 2y = y and y â€“ 2x = 5 is`

1. tan-1 (1/4)

2.tan-1 (3/5)

3.tan-1 (5/4)

4. tan-1 (2/3)

Posted Date:-2021-12-25 16:46:51

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

1. Ï€/2

2.Ï€/3

3.Ï€/4

4.Ï€/6

Posted Date:-2021-12-26 08:42:42

## Question: `The cartesian equation of the line is 3x + 1 = 6y â€“ 2 = 1 â€“ 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

Posted Date:-2021-12-26 08:30:23

## Question: `The center of the circle 4xÂ² + 4yÂ² â€“ 8x + 12y â€“ 25 = 0 is?`

1.(2,-3)

2. (-2,3)

3. (-4,6)

4.(4,-6)

Posted Date:-2021-12-26 08:28:54

## Question: `The center of the ellipse (x + y â€“ 2)Â² /9 + (x â€“ y)Â² /16 = 1 is`

1.(0, 0)

2.(0, 1)

3.(1, 0)

4.(1, 1)

Posted Date:-2021-12-26 08:11:36

## 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)

Posted Date:-2021-12-26 08:32:40

## 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

Posted Date:-2021-12-26 08:39:56

## Question: ```The derivative of [1+(1/x)] /[1-(1/x)] is ```

1.1/(x-1)Â²

2.-1/(x-1)Â²

3. 2/(x-1)Â²

4. -2/(x-1)Â²

Posted Date:-2021-12-26 09:01:27

## 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)

Posted Date:-2021-12-26 08:20:25

## 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

Posted Date:-2021-12-26 08:17:47

## 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

Posted Date:-2021-12-26 08:22:34

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

1. yÂ² = 9x

2.yÂ² = 9x/2

3.yÂ² = 2x

4.yÂ² = 2x/9

Posted Date:-2021-12-26 08:13:06

## 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

Posted Date:-2021-12-26 08:44:14

## 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

Posted Date:-2021-12-25 16:38:58

## 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

Posted Date:-2021-12-25 16:44:48

## 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

Posted Date:-2021-12-25 16:51:49

## 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

Posted Date:-2021-12-25 16:40:45

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

1. 6x â€“ 4y = 5

2.6x + 4y = 5

3. 6x + 4y = 7

4.6x â€“ 4y = 7

Posted Date:-2021-12-25 16:55:28

## 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

Posted Date:-2021-12-26 08:34:10

## 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€¦..

Posted Date:-2021-12-26 09:02:25

## Question: `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

Posted Date:-2021-12-25 15:37:59

## Question: `The image of the point P(1, 3, 4) in the plane 2x â€“ y + z = 0 is`

1.(-3, 5, 2)

2.(3, 5, 2)

3. (3, -5, 2)

4. (3, 5, -2)

Posted Date:-2021-12-26 08:31:07

## 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

Posted Date:-2021-12-25 16:49:07

## Question: `The line lx + my + n = 0 will touches the parabola yÂ² = 4ax if`

1. ln = amÂ²

2.ln = am

3.ln = aÂ² mÂ²

4.ln = aÂ² m

Posted Date:-2021-12-26 08:27:09

## Question: ```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

Posted Date:-2021-12-26 08:33:24

## Question: `The locus of a point, whose abscissa and ordinate are always equal is`

1. x + y + 1 = 0

2.x â€“ y = 0

3.x + y = 1

4.None of these

Posted Date:-2021-12-25 16:38:07

## Question: ```The locus of the point from which the tangent to the circles xÂ² + yÂ² â€“ 4 = 0 and xÂ² + yÂ² â€“ 8x + 15 = 0 are equal is given by the equation ```

1.8x + 19 = 0

2.8x â€“ 19 = 0

3.4x â€“ 19 = 0

4.4x + 19 = 0

Posted Date:-2021-12-26 08:09:40

## 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

Posted Date:-2021-12-26 08:34:51

## Question: `The number of tangents that can be drawn from (1, 2) to xÂ² + yÂ² = 5 is`

1. 0

2.1

3.2

4.More than 2

Posted Date:-2021-12-26 08:14:59

## 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)

Posted Date:-2021-12-26 08:12:19

## Question: ```The parametric representation (2 + tÂ², 2t + 1) represents ```

1. a parabola

2. a hyperbola

3.an ellipse

4.a circle

Posted Date:-2021-12-26 08:18:38

## Question: `The perpendicular distance from the point (3, -4) to the line 3x â€“ 4y + 10 = 0`

1.7

2.8

3.9

4.10

Posted Date:-2021-12-26 08:10:13

## 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

Posted Date:-2021-12-26 08:38:09

## 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)

Posted Date:-2021-12-26 08:47:18

## Question: `The radius of the circle 4xÂ² + 4yÂ² â€“ 8x + 12y â€“ 25 = 0 is?`

1. âˆš57/4

2. âˆš77/4

3.âˆš77/2

4.âˆš87/4

Posted Date:-2021-12-26 08:24:08

## Question: `The slope of the line ax + by + c = 0 is`

1. a/b

2. -a/b

3.-c/b

4.c/b

Posted Date:-2021-12-25 16:45:21

## Question: `The sum of AP 2, 5, 8, â€¦..up to 50 terms is`

1. 3557

2.3775

3.3757

4.3575

Posted Date:-2021-12-25 15:38:52

## 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

Posted Date:-2021-12-25 15:30:20

## 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

Posted Date:-2021-12-25 16:51:03

## Question: `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

Posted Date:-2021-12-25 15:34:27

## Question: `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

Posted Date:-2021-12-25 15:31:55

## Question: ```The value of limit Limxâ†’0 {sin (a + x) â€“ sin (a â€“ x)}/x is ```

1. 0

2.1

3.2 cos a

4.2 sin a

Posted Date:-2021-12-26 08:53:12

## Question: `The value of Limxâ†’01 (1/x) Ã— sin-1 {2x/(1 + xÂ²) is`

1.0

2.1

3.2

4.-2

Posted Date:-2021-12-26 08:54:38

## Question: `The value of Limxâ†’01 (1/x) Ã— sin-1 {2x/(1 + xÂ²) is`

1.0

2.1

3.2

4.-2

Posted Date:-2021-12-26 08:54:56

## 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

Posted Date:-2021-12-26 08:59:20

## Question: `The value of the limit Limxâ†’0 (cos x)cot2 x is`

1. 1

2.e

3.e1/2

4. e-1/2

Posted Date:-2021-12-26 08:52:29

## 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

Posted Date:-2021-12-26 08:31:57

## 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

Posted Date:-2021-12-25 16:41:27

## 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

Posted Date:-2021-12-25 16:47:31

## Question: ```Two lines are perpendicular if the product of their slopes is ```

1.0

2.1

3.-1

4.None of these

Posted Date:-2021-12-25 16:53:09

## 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

Posted Date:-2021-12-25 16:39:42

## 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

Posted Date:-2021-12-25 16:52:20

## Question: `y-intercept of the line 4x â€“ 3y + 15 = 0 is`

1. -15/4

2.15/4

3.-5

4.5

Posted Date:-2021-12-25 16:54:04

## More MCQS

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