List of top Mathematics Questions

If the matrix \(\begin {bmatrix} x-y&1&-2 \\ 2x-y&0&3 \\ 2&-3&0 \end {bmatrix}\) is skew-symmetric, then values of x and y are respectively

 6 red and 6 black balls are arranged such that no two black balls are together. Find the total number of ways it can be arranged.

For \(x ∈ R\), let \(tan^{-1} (x) ∈ \) (\(-\frac{\pi}{2},\frac{\pi}{2}\)). Then the minimum value of function \(f: R \rightarrow R\) defined by \(f(x) =\) \(\int_{0}^{x\,tan^{-1}x}\frac{e^{(t-cos\,t)}}{1+t^{2023}}dt\)  is

Let f:[1,∞) \(\rightarrow\) R be a differentiable function such that f(1) = \(\frac{1}{3}\) and 3\(\int_{1}^{x}\)f(t)dt=xf(x)-\(\frac{x^3}{3}\),x∈[1,∞). Let e denote the base of the natural logarithm. Then the value of f(e) is

The curved surface area of a right circular cone of height 12 cm and base diameter 10 cm is:

Find the 18^th and n^th term of the A.P. given by :
8, 13, 18,...

If a person travel \(10\frac{1}{5}\) Km in 3h, then the distance covered by him in 5 h will be :

Find the co-ordinate of the mid point of a line which joins P(2,-1) and Q(-3, 4):

How many chords can be drawn through 5 points on a circle ?

Two pipes A and B can fill a tank in 10 h and 15 h Respectively. Find the time taken to fill the tank when both the pipes are turned on simultaneously :

At what rate of interest 1,200 becomes ₹ 1,323 in 2 years where interest gets compounded annually:

Arun invests an amount of ₹4,000 at the rate of 2% simple interest per annum. For how many years did he invest the amount to double his sum?

A bag contains 6 white and 4 black ball. Two balls are drawn at random. Then the probability of getting balls of the same colour is ___.

If \[ \frac{2x^2 + 5x + 6}{(x + 2)^3} = \frac{a}{x + 2} + \frac{b}{(x + 2)^2} + \frac{c}{(x + 2)^3}, \] then \( a \cdot b + b \cdot c + c \cdot a = \)?

If \[ \begin{vmatrix} x & 4 & -1 \\ 2 & 1 & 0 \\ 0 & 2 & 4 \end{vmatrix} = 0, \text{ then find the value of } x. \]

If the slope of the tangent on a curve at any point \((x, y)\) is equal to \[ \frac{y^2 - x^2}{2xy} \] then the equation of the normal at the point \(\left(1, \frac{\sqrt{3}}{2}\right)\) is

A point on the plane passing through the points \((\sqrt{2},1,4), (0,-1,0)\) and \((0,0,1)\) is:

A box contains 5 white balls and 7 black balls. In how many ways can 3 balls be drawn from the box such that at least one black ball is included?}

If \[ \vec{a} = -2\hat{i} + 9\hat{j} - 6\hat{k}, \quad \vec{b} = t\hat{i} - 2\hat{j} + 6\hat{k} \] are vectors such that \(|\vec{a} + \vec{b}| = 25\), then the sum of the values of \(t =\ ?\)

If \( \alpha \) is the modulus of \( z_1 = 4 + 3i \), then a point that does not lie in the region represented by } \[ |z - z_1| \leq \alpha \] is