Math miscellaneous Questions

If a ∈ R and the equation -3(x - [x])2 + 2 (x - [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval...

If α, β ≠ 0, and f(n) = αn + βn and = K(1 - α)2 (1 - β)2 (α - β)2, then K is equal to...

If the coefficients of x3 and x4 in the expansion of (1 + ax + bx2) (1 - 2x)18 in powers of x are both zero, then (a, b) is equal to...

If (10)9 + 2(11)1 (10)8 + 3(11)2 (10)7+ ... + 10(11)9 = k(10)9, then k is equal to

is equal to

If x = -1 and x = 2 are extreme points of f(x) = α log |x| + βx2 + x then

The integral is equal to

The integral equals

The image of the line in the plane 2x - y + z + 3 = 0 is the line

The variance of first 50 even natural numbers is

If then λ is equal to

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same...

Coefficient of x11 in the expansion of (1 + x2)4(1 + x3)7(1 + x4)12 is

The integral∫2x12+5x9(x5+x3+1)3 dx is equal to :...

Let a1, a2, a3, ..... , a49 be in A.P. such that ∑k=012a4k+1 = 416 and a9 + a43 = 66. If a12+a22+....+a172 = 140m, then m is equal to-...

For each t ∈R, let [t] be the greatest integer less than or equal to t. Then limx→0+x1x+2x+.....+15x...

The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, x + y + z = 7 is :

The Boolean expression ~ (p ∨ q) ∨ (~ p ∧ q) is equivalent to :...

If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), then xzy2 is equal to :...

From a point P(λ, λ, λ) perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = - x, z = - 1. If P is such that ∠QPR is a right angle, then the possible ...