List of top Mathematics Questions

Let $S$ be the set of all 3-digit numbers containing the digits 3, 5 and 7 without repetition. The sum of all numbers in $S$ is

The A.M. and G.M. of two positive real numbers $a$ and $b$ ($a > b$) are $A$ and $G$ respectively. If $A:G = 5:3$, then $(a^2 + b^2) : ab = $

If $\cos \theta, \sqrt{2}\sin \theta$ and $\sqrt{3}\tan \theta$, where $0 < \theta < \frac{\pi}{2}$, are the second, third and fourth terms of a geometric series, respectively, then the first term of the geometric series is

The sum of four consecutive terms in a geometric progression is 960. If the fourth term is 8 times as large as the first term, then the smallest number in the geometric progression is

The sum of the first two terms of a geometric series is 12 and the third term is 16. Then the common ratio $r > 0$ of the geometric progression is

If $\alpha$ is a real number satisfying $\alpha^2 - \frac{1}{\alpha^2} = 2$, then the value of $(\alpha + \frac{i}{\alpha})^{16}$ is equal to

The complex number $z$ satisfying the equation $\frac{Re(z)}{2+i} + \frac{Im(z)}{1+2i} = \frac{3}{1-2i}$, is

Let $z = 1 + i$, where $i = \sqrt{-1}$. If $z - \frac{24\bar{z}}{z^2} = \lambda z$, then the value of $\lambda$ is equal to

If the complex number $z = x + iy$ satisfies the equation $5z - 2\bar{z} = \frac{7 - 7i}{1 + i}$, then the value of $x + y$ is equal to

Let $f(x) = x^2 - 10x$ and $g(x) = e^x + 5$ for $x \in \mathbb{R}$. Then, for all $x$, $g(2x) - (f \circ g)(x) = $}

Let $f(x) = \frac{10}{7 + 4\sin x + 3\cos x}, x \in \mathbb{R}$. Then the range of the function $f$ is

Let $f(x) = \sin^{-1}x$ and $g(x) = x - 2$. To define the composite function $f \circ g$, the largest domain of $g(x)$ has to be}

Let $A$ and $B$ be two subsets of a universal set $U$. If $n(U) = 116$, $n(A \cup B) = 99$, $n(B) = 61$ and $n(A \cap B) = 28$, then $n(A')$ is equal to

Let \[ f(x)=\sqrt{7-x} \] and \[ g(x)=\sqrt{x-5}. \] Then the domain of the function \[ h(x)=f(x)g(x) \] is:

Let \(A\) be the set of odd integers in \([0,10]\) and let \(B\) be the set of prime numbers in \([0,10]\). If \[ R=\{(a,b)\in A\times B:\ a+b \text{ is odd}\}, \] then \(n(R)\) is equal to:

The value of \[ \left[\frac{5i}{(3+i)(3-i)}\right]^{2026} \] is equal to:

If \[ \sum_{k=1}^{n}\log_{10}(5^k)=66\log_{10}(5), \] then the value of \(n\) is equal to:

Let \[ f(x)= \begin{vmatrix} -1 & x & 3 \\ 0 & 1 & 2x \\ 1 & -1 & 1 \end{vmatrix}. \] Then the value of \(f(-1)\) is equal to:

The value of \[ \tan\!\left(\tan^{-1}(3)+\tan^{-1}(7)\right) \] is equal to:

The latus rectum of the hyperbola \(\frac{(3x - 7)^2}{9} - \frac{(4y + 3)^2}{8} = 1\) is

Let \[ \vec{a} = (\sin^2\alpha)\hat{i} + (\cos 2\alpha)\hat{j} + (\cos^2\alpha)\hat{k}, \qquad 0\leq\alpha\leq\frac{\pi}{2}, \] and \[ \vec{b} = \hat{i} - 2\hat{j} + \hat{k}. \] If \(\vec{a}\) and \(\vec{b}\) are perpendicular to each other, then the value of \(\alpha\) is equal to:

If \[ \{(2,-3,5),\ (1,\alpha,7),\ (3,\beta,3)\} \] is not a basis of the vector space \(\mathbb{R}^3\), then \((\alpha,\beta)\) lies on the locus:

The iterative formula for finding the approximate root of $f(x) = 0$ using Newton-Raphson method is:

Choose a possible probability density function from the given functions: