List of top Mathematics Questions

Let be a sequence such that a₁ + a₂ +....+ a_n=\(\frac{n^2+3n}{(n+1) (n+2)}\) If  \(28 ∑^{10}_{k=1} \frac{1}{a_k} =  P _1 P_ 2 P _3 . . . P_ m\) , where p₁, p₂, …..p_m are the first m prime numbers, then m is equal to

If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=

For any y∈R, let cot\(^{-1}\)(y) ∈ (0,π) and tan\(^{-1}\)(y) ∈ (\(-\frac{\pi}{2},\frac{\pi}{2}\)). Then the sum of all the solutions of the equation\(tan^{-1}(\frac{6y}{9-y^2})+cot^{-1}(\frac{9-y^2}{6y})=\frac{2\pi}{3}\, for\,0<|y|<3,\) is equal to

The range of f(x) = \(4\sin^{-1}(\frac{x^2}{x^2+1})\) is 

Let the point $P(\alpha, \beta)$ be at a unit distance from each of the two lines $L _1: 3 x -4 y +12=0$, and $L _2: 8 x +6 y +11=0$ If $P$ lies below $L _1$ and above $L _2$, then $100(\alpha+\beta)$ is equal to

Let \(A :\{1,2,3,4,5,6,7\}\). Define \(B=\{T \subseteq A\) : either \(1 \notin T\) or \(2 \in T \}\) and \(C = \{T _{\subseteq} A : T\) the sum of all the elements of \(T\) is a prime number \(\}\). Then the number of elements in the set \(B \cup C\) is _______ .

Given the function \(y(x)=(x+3)(x-2)\), for \(-4<x<4\). What is the value of \(x\) at which the function has a minimum?

Which of the following shapes can be used to tile (completely cover by repeating) a flat plane infinitely in all directions, without leaving gaps or overlaps?

Find the coefficient of \(x^4\) in \((x-1)^3(x-2)^3\).

A line of symmetry divides a figure into two parts that are mirror images. The given figure consists of 16 unit squares. Three are already black. What is the minimum number of additional squares that must be coloured black so that both \(PQ\) (vertical midline) and \(MN\) (diagonal) are lines of symmetry? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}

In the given figure, \(PQRS\) is a parallelogram with \(PS = 7\text{ cm}\), \(PT = 4\text{ cm}\) and \(PV = 5\text{ cm}\). What is the length of \(RS\) (in cm)? (The diagram is representative.) \begin{center} \includegraphics[width=0.5\textwidth]{01.jpeg} \end{center}

The coefficient of \(x^4\) in \((x-1)^3(x-2)^3\) is equal to \underline{\hspace{1cm}}.

A firm needs both skilled labour and unskilled labour. Skilled wage = ₹ 40{,}000 per month; unskilled wage = ₹ 15{,}000 per month. The total wage bill for 100 labourers is ₹ 23{,}75{,}000 in a month. How many skilled labour are employed? {(in Integer)}

The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

Two vertical poles of height 6 m and 18 m are 10 m apart on a flat ground. A string needs to be connected from the top of one pole to a peg on the ground and then on to the top of the other pole. The minimum length (m) of the string is

The area under the curve \( y = x^2 + 2x \) between \( x = 0 \) and \( x = 4 \), using the trapezoidal rule with a step size of one, (in integer) is ____________________.

The value of \( x \) for which the inverse of the following matrix does not exist is \[ \begin{bmatrix} 1 & 3 & 0 \\ 2 & x & 4 \\ -1 & 0 & 2 \end{bmatrix} \]

Let \( X \) be a random variable with probability density function \[ f(x) = \begin{cases} \alpha \lambda x^{\alpha - 1} e^{-\lambda x^\alpha} & \text{if } x > 0, \\ 0 & \text{otherwise} \end{cases} \] where \( \alpha > 0 \) and \( \lambda > 0 \). If the median of \( X \) is 1 and the third quantile is 2, then \( (\alpha, \lambda) \) equals:

Suppose that \( X \) has the probability density function \[ f(x) = \begin{cases} \frac{\lambda^{\alpha}}{\Gamma(\alpha)} x^{\alpha-1} e^{-\lambda x} & \text{if } x > 0, \\ 0 & \text{otherwise}, \end{cases} \] where \( \alpha > 0 \) and \( \lambda > 0 \). \text{Which one of the following statements is NOT true?}

Let \( (X, Y) \) have joint probability density function \[ f(x, y) = \begin{cases} 8xy & \text{if } 0 < x < y < 1, \\ 0 & \text{otherwise.} \end{cases} \] If \( E(X \mid Y = y_0) = \frac{1}{2} \), then \( y_0 \) equals

Suppose that there are 5 boxes, each containing 3 blue pens, 1 red pen and 2 black pens. One pen is drawn at random from each of these 5 boxes. If the random variable \( X_1 \) denotes the total number of blue pens drawn and the random variable \( X_2 \) denotes the total number of red pens drawn, then \( P(X_1 = 2, X_2 = 1) \) equals: