In the expansion of (1+x)^{(p+q)} the ratio of coefficients of x^{p} and x^{q} is :
If 1, ω, ω^{2} are cube roots of unity and a + b + c = 0, then (a + bω + cω^{2})^{3} + (a + bω^{2} + cω)^{3} =
The locus of the centre of the circle which cuts circles x^{2}+y^{2}+2g₁x+2f₁y+c₁=0 and x^{2}+y^{2}+2g₂x+2f₂y+c₂=0 orthogonally, is
If circles x^{2}+y^{2}+2ax+c=0 and x^{2}+y^{2}+2by+c=0 touch each other, then
The solution of differential equation (dy/dx)=[(x(2logx+1))/(siny+ycosy)] is
The differential equation corresponding to the family of curves y=c(xc)^{2}, where c is a constant, is :
If f(x)=log_{x2}log(x), then at x=e, f'(x)=
(d/dx)[cos⁻^{1}((xx⁻^{1})/(x+x⁻^{1}))]=
The latus rectum of an ellipse is 1/3 of the major axis. It's eccentricity is
The foci of the hyperbola 9x^{2}  16y^{2} = 144 are
Equation of the tangent to the hyperbola 2x^{2}  3y^{2} = 6 which is parallel to the line y = 3x + 4 is
Given equation of hyperbola is 2x^{2}  3y^{2} = 6
Dividing by 6 we get
Therefore equations are:
y = 3x + 5
and y = 3x  5
In the interval ( 3,3) the function
sin⁻^{1}[2x/(1+x)] = 2tan⁻^{1}x for
The value of the is
Largest value of min (2 + x^{2}, 6  3x) when x > 0 is :
The vertex of the parabola x^{2} + 8x + 12y + 4 = 0 is
The length of the latus rectum of the parabola y^{2} + 8x − 2y + 17 = 0 is
A problem in EAMCET examination is given to 3 students A, B and C whose chances of solving it are respectively. The probability that the problem will be solved is
A person puts three cards addressed to three different people in three envelopes with three different addresses without looking. What is the probability that the cards go into their respective envelopes
Number of ways the letter can be put into envelops = 3! = 6
Probability = 1/6
In a ΔABC , the correct formulae among the following are:
In a ΔABC , is equal to
If the cube roots of unity are 1, ω, ω^{2} then the roots of the equation(x  1)^{3} + 8 = 0, are
If a, b and c are real numbers such that a^{2} + b^{2} + c^{2} = 1, then ab + bc + ca lies in the interval
The absiccae of the points of the curve y = x^{3} in the interval [2, 2], when the slope of the tangent can be obtained by mean value theorem for the interval [2, 2] are
Given that equation of curve y = x 3 = f x
If the sum of the first n terms of a series be 5n^{2} + 2n, then its second term is
If the sum of first n terms of an A.P. be 3n^{2}  n and its common difference is 6, then its first term is
If √3 + i = (a + i b) (c + i d) then tan⁻^{1} (b/a) + tan⁻^{1} (d/c) is equal to
The equation of bisectors between the lines 3x+4y7=0 and 12x+5y+17=0 are
The condition that one root of the equation ax^{2} + bx + c = 0 be reciprocal of other root is___
From given hypothesis take roots α and 1/α then
The locus of the orthocentre of the triangle formed by the lines
(1 + p)x  py + p(1 + p) = 0,
(1 + q)x  qy + q(1 + q) = 0,
and y = 0, where p ≠ q , is
Let
If l is the length of the intercept made by a common tangent to the circle x^{2} + y^{2} = 16 and the ellipse x^{2}/25 + y^{2}/4 = 1, on the coordinate axes, then 81l^{2} + 3 is equal to
equals
In a triangle ABC, let ∠C = π ∕ 2 . If r is the inradius and R is the circumradius of the triangle, then 2(r + R) is equal to
equals
The projections of a vector on the three coordinate axis are 6, 3, 2 respectively. The direction cosines of the vector are:
How many real solutions does the equation x^{7} + 14x^{5} + 16x^{3} + 30x − 560 = 0 have?
f:[1, ∞) → [2, ∞) is given by equals
Let f (x) = then
Tangents are drawn from the point ( 1, 2) to y^{2} = 4x. The length of these tangents with intercept on line x = 2 is
The differential equation (x^{4} − 2xy^{2} + y^{4}) dx − (2x^{2}y − 4xy^{3} + sin y) dy = 0 has its solution as
Let f (x) can be continuous at x = 0
A line is drawn from A( − 2, 0) to intersect the curve y^{2} = 4x in P and Q in the first quadrant such that then slope of the line is always
are noncoplanar nonzero vectors and is any vector in space then,
is equal to
If f(x) = x^{4}(1x)^{2}, x ∈ [0,1], then which of the following is true?
If the points where a, b, c are different from 1, lie on the line lx + my + n = 0, then:
(m + 2) sin θ + 2(m − 1) cos θ = 2m + 1 , if:
Let a, b, c, d real numbers. Suppose that all the roots of the equation z^{4} + az^{3} + bz^{2} + cz + d = 0 are complex numbers lying on the circle z = 1 in the complex plane. The sum of the reciprocals of the roots is necessarily
There exist a triangle ABC satisfying the conditions,
If are any two vectors then the vector bisecting the angle between
is equal to
If a, b, c are non zero real numbers such that 3 (a^{2} + b^{2} + c^{2} + 1) = 2 (a + b + c + ab + bc + ca) , then a, b, c are in
The value of is equal to
Let f (x) = x − 1  − [ x ] , then
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