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 [x2-(1/3x)]9 is
The pole of the line 9x+y-28=0 with respect to the circle 2x2+2y2-3x+5y-7=0 is
At which point of the parabola y2=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 y2[1+(dy/dx)2]=R2 is :
The inverse of a matrix
The maximum value of x3-3x 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 2x2+5xy+3y2+6x+7y+4=0 is tan⁻1m, 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 3x2 - (1 + 4λ)x + λ2 + 2 = 0 may be one-third 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 xq-r yr-p zp-q 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 = xR2
Putting the values of q, r, y, z in xq-r yr-p zp-q, we get
= xq-r yr-p zp-q = x(p + d) - (p + 2d) (xR)(p + 2d) - p (xR2)p - (p + d)
= x-d (xR)2d (xR2)-d = x-d. x2dR2d . x-dR-2d
= x-d + 2d - d . R2d - 2d = x0R0 = 1 x 1 = 1
The derivative of sin2 x with respect to (log x)2 is
The equation of bisectors between the lines 3x+4y-7=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 A-5 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+2j-2k, b=2i-j+k, c=i+3j-k, then ax(bxc)=
If vectors i-3j+2k, -i+2j represent the diagonals of a parallelogram, then its area is