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
Posted Date:-2021-12-26 08:10:59
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
Posted Date:-2021-12-26 08:25:41
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)
Posted Date:-2021-12-26 08:35:38
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)
Posted Date:-2021-12-26 08:14:04
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
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
Posted Date:-2021-12-26 08:24:51
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
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
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
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
Posted Date:-2021-12-26 09:03:50
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
Posted Date:-2021-12-26 08:48:20
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
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
Posted Date:-2021-12-26 08:38:49
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
Posted Date:-2021-12-26 08:16:54
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
Posted Date:-2021-12-25 15:41:34
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.
Posted Date:-2021-12-25 15:35:17
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
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
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
Posted Date:-2021-12-25 16:48:29
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
Posted Date:-2021-12-26 08:50:58
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
Posted Date:-2021-12-26 08:16:01
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
Posted Date:-2021-12-25 15:32:45
Limx→-1 [1 + x + x² + ……….+ x10] is
1.0
2.1
3.-1
4.2
Posted Date:-2021-12-26 08:53:49
Limx→0 log(1 – x) is equals to
1. 0
2.1
3.1/2
4.None of these
Posted Date:-2021-12-26 08:55:36
Limx→0 {(ax – bx)/ x} is equal to1. log a
2. log b
3.log (a/b)
4.log (a×b)
Posted Date:-2021-12-26 08:57:15
Limy→∞ {(x + 6)/(x + 1)}(x+4) equals
1. e
2.e³
3.e5
4. e6
Posted Date:-2021-12-26 09:00:32
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
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)
Posted Date:-2021-12-25 16:46:51
The angle between the vectors with direction ratios are 4, -3, 5 and 3, 4, 5 is
1. π/2
2.Ï€/3
3.Ï€/4
4.Ï€/6
Posted Date:-2021-12-26 08:42:42
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
Posted Date:-2021-12-26 08:30:23
The center of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is?
1.(2,-3)
2. (-2,3)
3. (-4,6)
4.(4,-6)
Posted Date:-2021-12-26 08:28:54
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)
Posted Date:-2021-12-26 08:11:36
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
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
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
Posted Date:-2021-12-26 09:01:27
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)
Posted Date:-2021-12-26 08:20:25
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
Posted Date:-2021-12-26 08:17:47
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
Posted Date:-2021-12-26 08:22:34
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
Posted Date:-2021-12-26 08:13:06
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
Posted Date:-2021-12-26 08:44:14
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
Posted Date:-2021-12-25 16:38:58
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
Posted Date:-2021-12-25 16:44:48
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
Posted Date:-2021-12-25 16:51:49
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
Posted Date:-2021-12-25 16:40:45
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
Posted Date:-2021-12-25 16:55:28
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
Posted Date:-2021-12-26 08:34:10
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 – ……..
Posted Date:-2021-12-26 09:02:25
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
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)
Posted Date:-2021-12-26 08:31:07
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
Posted Date:-2021-12-25 16:49:07
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
Posted Date:-2021-12-26 08:27:09
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
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
Posted Date:-2021-12-25 16:38:07
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
Posted Date:-2021-12-26 08:09:40
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
Posted Date:-2021-12-26 08:34:51
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
Posted Date:-2021-12-26 08:14:59
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)
Posted Date:-2021-12-26 08:12:19
The parametric representation (2 + t², 2t + 1) represents
1. a parabola
2. a hyperbola
3.an ellipse
4.a circle
Posted Date:-2021-12-26 08:18:38
The perpendicular distance from the point (3, -4) to the line 3x – 4y + 10 = 0
1.7
2.8
3.9
4.10
Posted Date:-2021-12-26 08:10:13
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
Posted Date:-2021-12-26 08:38:09
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
The radius of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is?
1. √57/4
2. √77/4
3.√77/2
4.√87/4
Posted Date:-2021-12-26 08:24:08
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
The sum of AP 2, 5, 8, …..up to 50 terms is
1. 3557
2.3775
3.3757
4.3575
Posted Date:-2021-12-25 15:38:52
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
Posted Date:-2021-12-25 15:30:20
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
Posted Date:-2021-12-25 16:51:03
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
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
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
Posted Date:-2021-12-26 08:53:12
The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²) is1.0
2.1
3.2
4.-2
Posted Date:-2021-12-26 08:54:38
The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²) is1.0
2.1
3.2
4.-2
Posted Date:-2021-12-26 08:54:56
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
Posted Date:-2021-12-26 08:59:20
The value of the limit Limx→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
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
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
Posted Date:-2021-12-25 16:41:27
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
Posted Date:-2021-12-25 16:47:31
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
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
Posted Date:-2021-12-25 16:39:42
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
Posted Date:-2021-12-25 16:52:20
y-intercept of the line 4x – 3y + 15 = 0 is
1. -15/4
2.15/4
3.-5
4.5
Posted Date:-2021-12-25 16:54:04