List of top Mathematics Questions

Let \( A = \{x : x = 4n + 1, n \in \mathbb{Z}, 0 \leq n < 4 \} \)
Let \( B = \{x : x = 15n + 4, n \in \mathbb{N}, n \leq 3 \} \)
Let \( C = \{x : x \text{ is a prime number}, x \in A \cup B \} \)
Then the cardinal number of set \( C \) is

If f(x) is a second degree polynomial such that \(f(x) \ge 0 \forall x \in \mathbb{R}>\), \(f(-3) = 0\) and \(f(0) = 18\) then \(f(3) = \)

If $\int \frac{\sqrt{1-\sqrt{x}}}{\sqrt{x(1+\sqrt{x})}}dx = 2f(x)-2\sin^{-1}\sqrt{x}+c$, then $f(x)=$

If \( \frac{2+3i}{i-2} - \frac{4i-3}{3+4i} = x+iy \), then \( 3x+y = \)

If \(\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C\), where C is constant of integration, then f(x) is

If y = 3e2x + 2e3x, then $\frac{d^2y}{dx^2} + 6y$ is equal to

Let AX = B be a system of three linear equations in three variables. Then the system has
(A) a unique solution if |A| = 0
(B) a unique solution if |A| $\neq$ 0
(C) no solutions if |A| = 0 and (adj A) B $\neq$ 0
(D) infinitely many solutions if |A| = 0 and (adj A)B = 0
Choose the correct answer from the options given below:

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:

If $0 \le x \le \frac{3}{4}$, then the number of values of $x$ satisfying the equation $\text{Tan}^{-1}(2x-1) + \text{Tan}^{-1}2x = \text{Tan}^{-1}4x - \text{Tan}^{-1}(2x+1)$ is

The integral domain of which cardinality is not possible:
A. 5
B. 6
C. 7
D. 10

If X is a random variable with probability distribution $P(X=k) = \frac{(2k+3)c}{3^k}$, $k=0,1,2,\dots,\infty$, then $P(X=3) =$

The least non-negative remainder when \(3^{128}\) is divided by 7 is:

If \( x = 2\sqrt{2}\sqrt{\cos 2\theta} \) and \( y = 2\sqrt{2}\sqrt{\sin 2\theta} \), \( 0<\theta<\frac{\pi}{4} \) then the value of \( \frac{dy}{dx} \) at \( \theta = 22\frac{1}{2}^\circ \) is

If \( f(x)=\tan \left(\frac{\pi}{\sqrt{x+1}+4}\right) \) is a real valued function then the range of \( f \) is

Number of all possible words (with or without meaning) that can be formed using all the letters of the word CABINET in which neither the word CAB nor the word NET appear is

There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is

Let $\vec{a} = \hat{i} +2\hat{j}+3\hat{k}$, $\vec{b}=2\hat{i}-3\hat{j}+\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}-2\hat{k}$ be three vectors. If $\vec{r}$ is a vector such that $\vec{r}\cdot\vec{a} = 0$, $\vec{r}\cdot\vec{b} = -2$ and $\vec{r}\cdot\vec{c} = 6$ then $\vec{r}\cdot(3\hat{i}+\hat{j}+\hat{k})= $

Given that: \[ \cot \left( \frac{A + B}{2} \right) \cdot \tan \left( \frac{A - B}{2} \right) \] and the equation involving coordinates: \[ \frac{x}{2} + \frac{y}{3} + \frac{2}{6} - 1 = 0 \] Find the area of \( \Delta ABC = 2 \).

The number of all possible three letter words that can be formed by choosing three letters from the letters of the word FEBRUARY so that a vowel always occupies the middle place is

A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black die resulted in a 5 is

The number of integers lying between 1000 and 10000 such that the sum of all the digits in each of those numbers becomes 30 is

The range of the real valued function \( f(x)=\sin ^{-1}\left(\sqrt{x^{2}+x+1}\right) \) is