If x = a (θ + sinθ), y = a(1  cosθ), then at θ = π/2, the length of the normal is
The area of the figure bounded by the curves y = cos x and y = sin x and the ordinates x = 0 and x = π/4 is
The value of f(0) so that f (x) = sinx / x is continuous at x = 0 is
The centroid of a triangle formed by the points (0, 0), (cosθ, sinθ) and (sinθ  cosθ) lies on th line y = 2x. Then, θ is
The term independent of x in the expansion of [x^{2}(1/3x)]^{9} is
The pole of the line 9x+y28=0 with respect to the circle 2x^{2}+2y^{2}3x+5y7=0 is
At which point of the parabola y^{2}=4x is a normal drawn so that it makes equal angles with the axes?
If z = 2/(1 + √3i),then the value of arg (z) is
A singular solution of the differential equation y^{2}[1+(dy/dx)^{2}]=R^{2} is :
(d/dx)(log tanx)=
cos(sin⁻^{1}3/5)+sin⁻^{1}(5/13))=
The inverse of a matrix
The maximum value of x^{3}3x in the interval [0,2] is
Mean of a set of values is based on:
One series containing 3 numbers has mean 8, variance 24 and the second series containing 5 numbers has mean 8, variance 18. Then the variance of the combined data is
If angle between the lines 2x^{2}+5xy+3y^{2}+6x+7y+4=0 is tan⁻^{1}m, the value of m is
In how many different ways can the letters of the word RUMOUR be arranged?
What is the chance of getting multiple of 2 on one and multiple of 3 on the other in a single throw of two dice?
In a Δ ABC , A : B : C = 3 : 5 : 4 . Then a + b + c√2 is equal to
The value of λ for which one root of 3x^{2}  (1 + 4λ)x + λ^{2} + 2 = 0 may be onethird of the other is
In Rule Method the null set is represented by
If p, q, r are in A.P. and x, y, z are in G.P., then x^{qr} y^{rp} z^{pq} is equal to
p, q, r are in A.P. Let d be the c.d.
∴ q = p + d and r = p + 2d
Also, x, y, z are in G.P. Let R be the c.r.
∴ y = xR and z = xR^{2}
Putting the values of q, r, y, z in x^{qr} y^{rp} z^{pq}, we get
= x^{qr} y^{rp} z^{pq} = x^{(p + d)  (p + 2d)} (xR)^{(p + 2d)  p} (xR^{2})^{p  (p + d)}
= x^{d} (xR)^{2d} (xR^{2})^{d} = x^{d}. x^{2d}R^{2d} . x^{d}R^{2d}
= x^{d + 2d  d} . R^{2d  2d} = x^{0}R^{0} = 1 x 1 = 1
The derivative of sin^{2} x with respect to (log x)^{2} is
The equation of bisectors between the lines 3x+4y7=0 and 12x+5y+17=0 are
The equation of the tangent to the curve y=2 sin x+sin 2x at x=π/3 is equal to
The equation sinx + siny + sinz = 3 for 0≤x≤2π, 0≤y≤2π, 0≤z≤2π, has
If A lies in the 2nd quadrant and 3 tan A+4=0 then the value of 2 cot A5 cos A+sinA is equal to
A variable has Poisson distribution with mean m. The probability that the variable takes any of the values 0 or 2 is
If a=i+2j2k, b=2ij+k, c=i+3jk, then ax(bxc)=
If vectors i3j+2k, i+2j represent the diagonals of a parallelogram, then its area is
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