List of top Mathematics Questions

If \(lim_{x\rightarrow 0} \frac{\sqrt 1 + \sqrt{1+x^4}-\sqrt 2}{x^4}=A\) and \(lim_{x \rightarrow 0} \frac{sin^2x}{\sqrt 2 - \sqrt{1+cosx}}=B\), then \(AB^3\) = ____.

Which of the following functions represents a cumulative distribution function?

If \(f(x)=\frac {4x+3}{6x-4}\), \(x≠\frac 23 \)and \((fof)(x)=g(x)\), where \(g:R-[\frac 23→R→{\frac 23}]\). Then \((gogog)(4)\) is equal to

How many times 3 comes from 1 to 1000?

\(3, a, b, c\) are in Ap and \(3, a-1, b+1, c+9\) are in GP. Then AM of \(a, b, c\) is

If \(f(x)\) = \(\begin {bmatrix} Cos x& -sinx & 0\\sinx & cos x& 0\\0&0&1 \end {bmatrix} \)Statement I \(⇒ f(x).f(y) = f(x+y)\) Statement II \(⇒f(-x) =0 \) is invertible

Let S = {1, 2, 3, 4, 5, 6} and X be the set of all relations R from S to S that satisfy both the following properties :
i. R has exactly 6 elements.
ii. For each (a, b) ∈ R, we have |a - b| ≥ 2.
Let Y = {R ∈ X : The range of R has exactly one element} and
Z = {R ∈ X : R is a function from S to S}.
Let n(A) denote the number of elements in a set A.

Let \(f:[0,\frac{\pi}{2}]→[0,1]\) be the function defined by \(f(x)=\sin^2x\) and let \(g:[0,\frac{\pi}{2}]→[0,\infin)\) be the function defined by \(g(x)=\sqrt{\frac{\pi x}{2}=x^2}\).

Let S = {1,2,3,..., 20}, R₁ = {(a, b): a divide b}, R₂ = {(a, b): a is integral multiple of b} and a, b ∈ S. n(R₁ - R₂) = ?

\(\int^1_0\frac{1}{\sqrt{3+x}+\sqrt{1+x}}dx=a+b\sqrt2+c\sqrt3\) then \(2a-3b-4c\) is equal to _____.

let \(S\) be the set of positive integral values of a for which \(\frac {ax^2+2(a+1)x+9a+4}{x^2+8x+32}< 0,\) \(∀x∈R\). Then, the number of elements in \(S\) is

\(f(y - 2)^2 = (x - 1)\) and \(x - 2y + 4 = 0\) then find the area bounded by the curves between the coordinate axis in first quadrant (in sq. units).

If \(cos 2x-a \sin x=2a-7\) then range of \(a\) is:

If \(\frac{dy}{dx}\)= \(\frac{(x+y-2)}{(x-y)}\), and y(0) = 2, find y(2)

In the expansion of \((1 + x)(1 - x^2) (1 + \frac 3x + \frac {3}{x^2}+ \frac {1}{x^3})^5\) the sum of coefficients of \(x^3\) and \(x^{-13}\) is

If \(å= î+2ĵ + k, b = 3(î - ĵ + k), å · c = 3\) and \(å \times č = b\), then \(å·((xb)-b-č)\)=

Let the system of equations \(x+2y+3z = 5\), \(2x+3y+z = 9\), \(4x+3y+λz = μ\) have an infinite number of solutions. Then \(λ + 2μ\) is equal to

The number of solution of the equation \(4sin^2 x-4cos^3 x+9-4cos x = 0\), \(x ∈ [-2\pi, 2\pi]\)

If \(n-1C_r= (k^2-8)^nC_r+1\) Find \(k\).

If \(f(x) = (x - 2)^2 (x - 3)^3\) and \(x ∈ [1, 4]\) and If \(M\) and \(m\) denotes maximum and minimum values respectively, then \(M - m\) is

A = {1, 2, 3, 4} , R = {(1, 2), (2, 3), (2, 4)} R ⊆ S and S is an equivalence relation then the minimum number of elements to be added to R is n, then the value of n is?

An equation of a plane parallel to the plane \(x-2y+2z-5=0\) and at a unit distance from the origin is?

Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).

The value of integral \(∫_0^{\frac \pi4} \frac {xdx}{cos^42x+sin^42x}\).

\(3, 7, 1,......., 404\) and \(4, 7, 10,......, 403\). Find sum of common terms.