List of top Mathematics Questions

Mean & Variance of 7 observations are 8 & 16 respectively, if number 14 is omitted then a & b are new mean & variance. The value of a + b is

If \(a_n=\frac{-2}{4n^2-16n+15}\) and a₁ + a₂ + …… + a₂₅ = m/n where m and n are coprime, then the value of m + n is

If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three non-zero vectors and \(\hat{\mathbf{n}}\) is a unit vector perpendicular to \(\mathbf{c}\) such that: \(\mathbf{a} = \alpha \mathbf{b} - \hat{\mathbf{n}}, \, (\alpha \neq 0)\) and \( \mathbf{b} \cdot \mathbf{c} = 12 \), then \( \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) \) is equal to:

If [t] denotes the greatest integer \(≤ 1\), then the value of \(3\frac{(e - 1)^2}{e}\) is:

Let the solution curve y = y(x) of the differential equation\(\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1 + x^6)^{3/2}} y = 2x \exp\left(x^3 - \frac{\tan^{-1}(x^3)}{1 + x}\right)^6\)pass through the origin. Then y(1) is equal to:

A straight line cuts off the intercepts OA = a and OB = b on the positive directions of the x-axis and y-axis, respectively. If the perpendicular from the origin O to this line makes an angle of \(\frac{\pi}{6}\) with the positive direction of the y-axis and the area of △OAB is \(\frac{98\sqrt{3}}{3},\) then a² − b² is equal to:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions \(f : S → P(S)\), where \(P(S)\) denotes the power set of S, such that \(f(n) ⊂ f(m)\) where \(n < m,\) is:

Let α be the area of the larger region bounded by the curve y² = 8x and the lines y = x and x = 2, which lies in the first quadrant. Then the value of 3α is equal to:

If $\lambda_1<\lambda_2$ are two values of $\lambda$ such that the angle between the planes $P_1: \vec{r}(3 \hat{i}-5 \hat{j}+\hat{k})=7$ and $P_2: \vec{r} \cdot(\lambda \hat{i}+\hat{j}-3 \hat{k})=9$ is $\sin ^{-1}\left(\frac{2 \sqrt{6}}{5}\right)$, then the square of the length of perpendicular from the point $\left(38 \lambda_1, 10 \lambda_2, 2\right)$ to the plane $P_1$ is _____

Let the lines l₁ :  \(\frac{x+5}{3} =\frac{y+4}{1}=\frac{z−α}{−2}\)  and l₂ :3x+2y+z–2=0=x–3y+2z-13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(-4,-3, 2), then |a| + |b|+|c| is equal to

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 &  3\\ 2 & 7\end{bmatrix}\)

Find out the degree of the differential equation \(\frac {d^2t}{ds^2}+(\frac {dt}{ds})^2+2t=0\)

For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?

The sum of the maximum and minimum values of the function |5x-7|+[x²+2x] is the interval $\left[\frac{5}{4}, 2\right]$, where $[t]$ is the greatest integer $\leq t$ is ______

The value of $12 \int\limits_0^3\left|x^2-3 x+2\right| d x$ is

Let $f:(0,1) \rightarrow R$ be a function defined by $f(x)=\frac{1}{1-e^{-x}}$, and $g(x)=(f(-x)-f(x))$ Consider two statements (I) $g$ is an increasing function in $(0,1)$ (II) $g$ is one-one in $(0,1)$Then,

A box of dimensions 25cm x 30cm x 45cm is to be painted. A container which contains colour has a capacity to paint 1075cm². How many containers are required to paint the box completely?

The average age of three boys is 22 years. Eight times the age of the youngest of them is 3 times the sum of the ages of the other two boys. Find the age of the eldest of them if he is 8 years older to the youngest of them.

The length of a rectangular plot is 30 m more than its breadth. If the cost of fencing the plot @ 25 per meter is Rs. 5000, what is the length of the plot in m?

Let 𝛂 be the remainder (22)\(^{2022}\) + (2022)\(^{22}\) is divided by 3 and ꞵ be the remainder when the same is divided by 7 then 𝛂\(^2\) + ꞵ\(^2\) is?

Let 𝑃 be a 3×3 matrix having the eigenvalues 1,1 and 2. Let (1,−1,2) ^𝑇 be the only linearly independent eigenvector corresponding to the eigenvalue 1. If the adjoint of the matrix 2𝑃 is denoted by 𝑄, then which of the following statements is/are TRUE?

Let the plane P : 4x – y + z = 10 be rotated by an angle \(\frac{π}{2}\) about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is

If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are three non-zero vectors and \(\hat{n}\) is a unit vector perpendicular to \(\vec{c}\) such that \(\vec{a}\)=\(\alpha \vec{b}\)-\(\hat{n}\), \(\alpha \neq 0\) and \(\vec{b}\) .\( \vec{c}\)=12, then |\(\vec{c} \times(\vec{a} \times \vec{b})\)| is equal to:

If, for some 𝛼∈(0, ∞),
\(∫^∞_02^{-x^2}dx=a\sqrt\pi,\) 
then 𝛼 equals (round off to two decimal places)