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

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

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)

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)

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

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

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

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

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)

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

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

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

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

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

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

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.

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

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)

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

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

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

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

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

1.0

2.1

3.-1

4.2

Limxâ†’0 log(1 â€“ x) is equals to

1. 0

2.1

3.1/2

4.None of these

Limxâ†’0 {(ax â€“ bx)/ x} is equal to

1. log a

2. log b

3.log (a/b)

4.log (aÃ—b)

Limyâ†’âˆž {(x + 6)/(x + 1)}(x+4) equals

1. e

2.eÂ³

3.e5

4. e6

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

1. 240

2.280

3.330

4.350

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)

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

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

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)

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)

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)

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

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

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)

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

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

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

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

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

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

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

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

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

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

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€¦..

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

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)

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

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

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

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

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

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

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

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)

The parametric representation (2 + tÂ², 2t + 1) represents

1. a parabola

2. a hyperbola

3.an ellipse

4.a circle

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

1.7

2.8

3.9

4.10

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

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)

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

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

1. a/b

2. -a/b

3.-c/b

4.c/b

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

1. 3557

2.3775

3.3757

4.3575

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

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

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

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

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

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

1.0

2.1

3.2

4.-2

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

1.0

2.1

3.2

4.-2

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

The value of the limit Limxâ†’0 (cos x)cot2 x is

1. 1

2.e

3.e1/2

4. e-1/2

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

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

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

Two lines are perpendicular if the product of their slopes is

1.0

2.1

3.-1

4.None of these

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

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

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

1. -15/4

2.15/4

3.-5

4.5

- MCQ Questions for Class 11 Chemistry sets 1
- MCQ Questions for Class 11 Chemistry sets 2
- MCQ Questions for Class 11 Chemistry sets 3
- MCQ Questions for Class 11 Physics sets 1
- MCQ Questions for Class 11 Physics sets 2
- MCQ Questions for Class 11 Physics sets 3
- MCQ Questions for Class 11 Biology sets 1
- MCQ Questions for Class 11 Biology sets 2
- MCQ Questions for Class 11 Biology sets 3
- MCQ Questions for Class 11 Biology sets 4
- MCQ Questions for Class 11 Maths sets 1
- MCQ Questions for Class 11 Maths sets 2
- MCQ Questions for Class 11 Maths sets 3
- MCQ Questions for Class 11 English sets 1
- Class 11 Sociology MCQs Multiple Choice Questions sets 1
- MCQ Questions for Class 11 Business Studies sets 1
- MCQ Questions for Class 11 Geography
- MCQ Questions for Class 11 Geography sets 2
- MCQ Questions for Class 11 Geography sets 3

Online Exam TestTop Tutorials are Core Java,Hibernate ,Spring,Sturts.The content on Online Exam Testwebsite is done by expert team not only with the help of books but along with the strong professional knowledge in all context like coding,designing, marketing,etc!