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List of top Mathematics Questions

Let α→ = $2\^{i}-\^{j}+5\^{k} and b→= α\^{i}+β\^{j}+2\^{k}. If ((α→×b→)×\^{i}).\^{k} $=$\frac{ 23}{2}$,then $|b→×2\^{j}\| $is equal to

Let ℝ → ℝ be function defined as
f(x) = αsin($(\frac{π[x]}{2})$+[2-x],α∈R
where [t] is the greatest integer less than or equal to t.
If lim x→1 f(x) exists, then the value of$∫_0^4$ f(x)dx
is equal to

Let $a_1, a_2, a_3, \ldots$ be an arithmetic progression with $a_1=7$ and common difference 8. Let $T_1, T_2, T_3, \ldots$ be such that $T_1=3$ and $T_{n+1}-T_n=a_n$ for $n \geq 1$. Then, which of the following is/are TRUE ?

If the coefficients of x and x² in the expansion of (1 + x)^p (1 – x)^q, p, q≤15, are – 3 and – 5 respectively, then coefficient of x³ is equal to ______.

Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAⁿ + mB^m = I} is _______.

$\begin{array}{l}(p \land r )\Leftrightarrow ( p \land (\sim q))\end{array}$is equivalent to (~ p) when r is

Let $\alpha$ and $\beta$ be real numbers such that $-\frac{\pi}{4}<\beta<0<\alpha<\frac{\pi}{4}$ If $\sin (\alpha+\beta)=\frac{1}{3}$ and $\cos (\alpha-\beta)=\frac{2}{3}$, then the greatest integer less than or equal to $\left(\frac{\sin \alpha}{\cos \beta}+\frac{\cos \beta}{\sin \alpha}+\frac{\cos \alpha}{\sin \beta}+\frac{\sin \beta}{\cos \alpha}\right)^2$ is ____.

Considering only the principal values of the inverse trigonometric functions, the value of $\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^2}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^2}+\tan ^{-1} \frac{\sqrt{2}}{\pi}$ is ___

Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A :Cߏ∩B ≠ φ} is _____________.

Let the matrix $A=\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$ and the matrix $B_0=A^{49}+2 A^{98}$ If $B_n=\text{Adj}\left(B_{n-1}\right)$ for all $n \geq 1$, then $\text{det}\left( B _4\right)$ is equal to :

Let $z$ be a complex number with non-zero imaginary part If $\frac{2+3 z+4 z^2}{2-3 z+4 z^2}$ is a real number, then the value of $|z|^2$ is ___ .

Let
$I = ∫^{\frac{π}{3}}_{\frac{π}{4}}(\frac{8sinx-sin2x}{x})dx$
Then

$∫^5_0\,cos(π(x-[\frac{x}{2}]))dx $, where [t] denotes greatest integer less than or equal to t, is equal to

The set of values of $k$, for which the circle $C : 4x^2 + 4y^2 – 12x + 8y + k = 0$ lies inside the fourth quadrant and the point $\bigg(1, -\frac{1}{3}\bigg)$ lies on or inside the circle $C$, is