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List of top Mathematics Questions

If : $|z + 1| = αz + ß(i + 1)$ and $z = \frac 12 - 2i$, find $α + ß$.

If $4 cos\ θ + 5 sin\ θ = 1$, then all possible values of $tan\ θ$, is/are
Where, $θ∈(-\frac \pi2,\frac \pi2)$

If $\frac {dy}{dx} - \frac {(sin2x)}{(1+cos^2x)}y = \frac {sinx}{1+cos^2x }$and $y(0) =0$ then $y(\frac \pi2)$ is ………..

If in a G.P. of64terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P., then the common ratio of the G.P. is equal to:

Let

$ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix} $

and $|2A|^3 = 2^{21}$ where $\alpha, \beta \in \mathbb{Z}$. Then a value of $\alpha$ is:

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning, and these words are arranged as in a dictionary. The serial number of the word "GTWENTY" is:

Evaluate the limit : $\lim_{x \to \frac{\pi}{2}} \left( \frac{1}{\left( x - \frac{\pi}{2} \right)^3} \int_{\frac{\pi}{2}}^x \cos \left( \frac{1}{t^3} \right) \, dt \right)$

For $ 0 < a < 1 $, the value of the integral \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1 - 2a \cos x + a^2} \] is:

The 20^th term from the end of the progression \[ 20, 19, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \ldots, -129 \frac{1}{4} \] is:

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

If $ 2 \tan^2 \theta - 5 \sec \theta = 1 $ has exactly 7 solutions in the interval $\left[ 0, \frac{n\pi}{2} \right],$ for the least value of $ n \in \mathbb{N} $ then $\sum_{k=1}^{n} \frac{k}{2^k}$ is equal to:

The integral $$ \int \frac{x^8 - x^2}{(x^{12} + 3x^6 + 1) \tan^{-1}\left( \frac{x^3 + 1}{x^3} \right)} \, dx $$ is equal to:

Coefficient of x²⁰¹² in (1-x)²⁰⁰⁸(1+x+x²)²⁰⁰⁷ is equal to ___

Four distinct points $ (2k, 3k), (1, 0), (0, 1) $ and $ (0, 0) $ lie on a circle for $ k $ equal to:

The number of common terms in the progressions 4, 9, 14, 19, ...,up to 25th term and 3, 6, 9, 12, ..., up to 37th term is:

If $ (a, b) $ be the orthocenter of the triangle whose vertices are $ (1, 2) $, $ (2, 3) $, and $ (3, 1) $, and $ I_1 = \int_a^b x \sin(4x - x^2) dx $, $ I_2 = \int_a^b \sin(4x - x^2) dx $, then $ 36 \frac{I_1}{I_2} $ is equal to:

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

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

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

If the shortest distance of the parabola $y^{2}=4x$ from the centre of the circle $x² + y² - 4x - 16y + 64 = 0$ is d, then d²is equal to:

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

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 $AB^3$ = ____.

The portion of the line $ 4x + 5y = 20 $ in the first quadrant is trisected by the lines $ L_1 $ and $ L_2 $ passing through the origin. The tangent of an angle between the lines $ L_1 $ and $ L_2 $ is:

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

How many times 3 comes from 1 to 1000?