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List of top Mathematics Questions

Let $ \alpha, \beta $ be the roots of the equation $ x^2 - \sqrt{2}x + 2 = 0 $, then $ \alpha^{14} + \beta^{14} $ is equal to:

If $\frac{1}{6}$sinθ.cosθ.tanθ are in G.P, then the solution set θ is

Let 𝑀 be a 3×3 real matrix. If 𝑃=𝑀+𝑀^𝑇 and 𝑄=𝑀-𝑀^𝑇, then which of the following statements is/are always TRUE?

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then how many received medals in exactly two of three events?

Let f(x) = $\displaystyle\sum_{k=1}^{10} kx^k$ , x ∈ R. If 2f(2) + f(2) = 190(2)ⁿ + 1 then n is equal to____.

\[ f(x) = \log_e \left( 4x^2 + 11x + 6 \right) + \sin^{-1} \left( 4x + 3 \right) + \cos^{-1} \left( \frac{10x + 6}{3} \right) \]then $ 36|\alpha + \beta| $ is equal to:

Let $P(S)$ denote the power set of $S = \{1, 2, 3, \ldots, 10\}$. Define the relations $R_1$ and $R_2$ on $P(S)$ as $A R_1 B$ if \[(A \cap B^c) \cup (B \cap A^c) = ,\]and $A R_2 B$ if\[A \cup B^c = B \cup A^c,\]for all $A, B \in P(S)$. Then:

Let $y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)$ Then, at $x=1$

Let $ X $ and $ Y $ be the set of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then $ n(X \cap Y) $ is equal to

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to

Let R=$\begin{pmatrix}a&3&b\\c&2&d\\0&5&0\end{pmatrix}$: a,b,c,d ∈ {0,3,5,7,11,13,17,19}. Then the number of invertible matrices in R is

If the value of real number a> 0 for which $x^2$-5ax+1-0 and $x^2-a x-5-0$ have a common real root is $\frac{3}{\sqrt{2 \beta}}$ then $ \beta$ is equal to_______

Let $A=$ [$a_{ij}$]$_{2\times2}$ be a matrix and $A^2 = I$ where $a_{ij} \neq0$. If a sum of diagonal elements and b=det(A), then $3a^2+4b^2$ is

Let $\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}$ be two vectors Then which one of the following statements is TRUE ?

If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___

Three dice are thrown. The probability of getting a sum of numbers which is a perfect cube, is:

If f(x) = [a+13 sinx] & x ε (0, $\pi$), then number of non-differentiable points of f(x) are [where 'a' is integer]

The tangent to the curve $x=cost(3-2cos^2t),y=sint(3-2sin^2t)$ at $t=\frac{\pi}{4}$,makes with the $x-axis$ an angle:

Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______

Let S = (0,1) ∪ (1,2) ∪ (3,4) and T = {0,1, 2,3} . Then which of the following statements is(are) true?

Let P be a point on the parabola y² = 4ax, where a > 0. The normal to the parabola at P meets the x -axis at a point Q. The area of the triangle PFQ where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive integers, then the pair (a, m) is

f domain of the function \[ f(x) = \log_e \left(\frac{6x^2 + 5x + 1}{2x - 1}\right) + \cos^{-1}\left(\frac{2x^2 - 3x + 4}{3x - 5}\right) \] is $ (\alpha, \beta) \cup (\gamma, \delta) $, then $ 18(\alpha^2 + \beta^2 + \gamma^2 + \delta^2) $ is equal to __________.

If \[ \cos \alpha = k \cos \beta \] then \[ \cot \left( \frac{\alpha + \beta}{2} \right) \] is equal to

Let the equation of the tangent at a point $ P $ on the parabola $ x^2 - 4x - 4y + 16 = 0 $ be $ 2x - y - 5 = 0 $. If the equation of the normal drawn at $ P $ to this parabola is $ ax + y + c = 0 $, then find $ ac $:

If $ \theta $ is the acute angle between the tangents drawn from the point $ (2, 3) $ to the hyperbola $ 5x^2 - 6y^2 - 30 = 0 $, then $ \tan \theta $ is: