List of top Mathematics Questions

If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( |\vec{a}| = \sqrt{14} \), \( |\vec{b}| = \sqrt{14} \), and \( \vec{a} \cdot \vec{b} = -7 \), then \[ \frac{|\vec{a} \times \vec{b}|}{|\vec{a} \cdot \vec{b}|} \] is:

Let A=\(\begin{bmatrix} 1 & \frac{1}{51} \\ 0 & 1\end{bmatrix}\). If B=\(\begin{bmatrix} 1 & 2 \\ -1 & -1\end{bmatrix}\)A \(\begin{bmatrix} -1 & -2 \\ 1 & 1\end{bmatrix}\), then the sum of all the elements of the matrix \(\sum^{50}_{n=1}B^n\) is equal to

The C.P. of two shirts taken together is ₹910. If by selling one at a profit of 16% and and the other at a loss of 12%, there is no loss or gain in the whole transaction, then the C.P. of the two shirts are respectively:

The Curved Surface Area of a right circular cylinder of base radius r is obtained by multiplying its volume:

Match List I with List II

List-I		List-II
(A)	Volume of cone	(I)	\(\frac{1}{3}\pi h(r_1^2+r_2^2+r_1r_2)\)
(B)	Volume of sphere	(II)	\(\frac{1}{3}\pi r^2h\)
(C)	Volume of Frustum	(III)	\(\pi r^2h\)
(D)	Volume of cylinder	(IV)	\(\frac{4}{3}\pi r^3\)

Choose the correct answer from the options given below:

At what rate of simple interest, a sum of ₹1,800 will become ₹2,700 in 10 years?

If P, R, T are the areas of parallelogram. a rhombus and a triangle standing on the same base and between the same parallel lines, then which of the following is true?

The number \(0.4\overline{23}\) converted to a fraction, then it is equal to:

If you are head of your office, some media people come to your office and request you brief them about the pension plan of your office, you will:

\(tan^{-1}(\frac {1+\sqrt 3}{3+\sqrt 3})+sec^{-1}(\sqrt {\frac {8+4\sqrt 3}{3+3\sqrt 3})}\) is equal to:

Let S = {1, 2, 3, 4, 5}
if f : S → P(S), where P(S) is power set of S. Then number of one-one functions f can be made is

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:

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

Let $𝑆={𝑤_1,𝑤_2,…….}$ be the sample space associated to a random experiment. Let $𝑃(𝑤_𝑛)= \frac{𝑃(𝑤_{𝑛−1})}{2} ,𝑛≥2.$ Let 𝐴=${(2𝑘+3𝑙:k,𝑙∈ℕ)}$ and $𝐵={𝑤_𝑛:𝑛∈𝐴}$. Then 𝑃( 𝐵) is equal to

The statement B⇒((∼A) ∨ B) is equivalent to :

Consider a function f:N→R, satisfying
$ f(1)+2f(2)+3f(3)+⋯+xf(x)=x(x+1)f(x);x≥2 with f(1)=1.$
Then $\frac{1}{f(2022)} + \frac{1}{f(2028)}$ is equal to $

Let 𝐾 be the sum of the coefficients of the odd powers of 𝑥 in the expansion of $(1+𝑥)^{99}$. Let 𝑎 be the middle term in the expansion of \((2+\frac{1}{\sqrt 2} )^{200}\). If $\frac{⁡^{200}𝐶_{99} 𝐾}{𝑎} =\frac{2^𝑙 𝑚}{𝑛} $, where 𝑚 and 𝑛 are odd numbers, then the ordered pair (𝑙, 𝑛) is equal to

The shortest distance between the lines $\frac{x−1}2 =\frac{y−2}1 =\frac{z−6}{-3} $ and $\frac{x−1}2 =\frac{y+8}{-7} =\frac{z−4}{5} $ is

The value of the integral \(\int^2_1\bigg(\frac{t^4+1}{t^6+1}\bigg)\)dt is 

Let R be a relation defined on N as a ⁡R⁡b if 2a+3b is a multiple of 5 ,a , b∈N. Then R is

If the tangent at a point 𝑃 on the parabola \(𝑦^2=3𝑥\) is parallel to the line \(𝑥+2𝑦=1\) and the tangents at the points 𝑄 and 𝑅 on the ellipse \(\frac{𝑥^2}{ 4} +\frac{𝑦^2}{ 1} =1\) are perpendicular to the line 𝑥−𝑦=2, then the area of the triangle PQR is : 

If \(\overrightarrow a =\hat i+2\hat k,\overrightarrow b =\hat i+\hat j+\hat k,\overrightarrow c =7\hat i−3\hat j+4\hat k,r ×\hat b +\hat b ×\overrightarrow c =\overrightarrow0\) and \(\overrightarrow r .\overrightarrow a =0\). Then \(\overrightarrow r. \overrightarrow c\)  is equal to 

If the lines \(\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{1}\)  and \(\frac{x-a}{2}=\frac{y+2}{3}=\frac{z-3}{1}\) intersect at the point 𝑃, then the distance of the point 𝑃 from the plane 𝑧=𝑎 is : 

The value of the integral \(∫_{\frac 12}^2 \frac{tan^{-1}x}{x}dx\) is equal to