List of top Mathematics Questions

A circle has radius 3 and its centre lies on the line $y = x -1$ . The equation of the circle, if it passes through $(7, 3)$, is

If $\left(\vec{a}\times\vec{b}\right)^{2}+\left(\vec{a}.\vec{b}\right)^{2}=676$ and $\left|\vec{b}\right|=2,$ then $\left|\vec{a}\right|$ is equal to

The system of linear equations : $x + y + z = 0, 2x + y - z = 0, 3x + 2y = 0$ has :

The area under the curve $y = | cos\, x - sin \,x |, 0 \le x\le\frac{\pi}{2}$, and above x-axis is :

If vector equation of the line$\frac{x-2}{2}=\frac{2y-5}{-3}=z+1,$ is $\vec{r}=\left(2\hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2\hat{i}-\frac{3}{2} \hat{j}+p\hat{k}\right)$ then $p$ is equal to

If \(log_8 x+log_4 x+log_2 x=11,x=?\)

If a²-b² = 8 and a*b = 2, find a⁴+b⁴.

In $\triangle ABC$, $\angle CAB=60^\circ$, $BC=a$, $AC=b$, $AB=c$. Which relation is correct? \includegraphics[width=0.5\linewidth]{image83.png}

In a regular hexagon, ropes are tied to connect every pair of vertices (all sides and all diagonals). How many distinct intersection points do the ropes create?

The inverse of the function \(f(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}+2\) is given by

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

If $I_{n} = \int \frac{\sin nx}{\sin x} dx $ for $n = 1, 2 , 3,...,$ then $I_6$ =

A tangent is drawn from an external point P to a circle of 8 cm radius. If the length of the tangent is 15 cm then the distance between the centre of the circle and point P is

f \(\int_0 ^a3x^2dx=8\) then find the value of a

Find the value of log_y(x⁴) if log_x(y³) = 2

How many terms are in the Arithmetic Progression 20, 25, 30,..., 135, 140?

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole workalone?

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Sarthak bought 7 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Sarthak start with ?

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is :

If \(tan ^{-1}(sinx)=\frac{\pi}{4}\),then the value of \(x\) is:

If \(cos2\theta+sin\theta= \sqrt{2}cos \theta,Then \ cos\theta-sin \theta=? \)

If log₁₀10=1, log₁₀100=2, what is the value of log₅125?