List of top Mathematics Questions

If the ratio of the areas of two squares is 25 : 36, then the ratio of their perimeters is

If the volume of a sphere is divided by its surface area, we obtain 27 cm. The radius of the sphere is

If 0.06% of a number is 84, then 30% of that number is

The least value of $x$, for which the expression $x^2 + x + 17$ will not give a prime number, is

\(P\) sells a table to \(Q\) at a profit of 10% and \(Q\) sells it to \(R\) at a profit of 12%. If \(R\) pays Rs. 246.40 for it, then how much had \(P\) paid for it?

A train 300 metres long is running at a speed of 25 meters per second, it will cross a bridge 200 metres long in

Sultan took a loan from the bank at 8% per annum, and was supposed to pay a sum of Rs.2240 at the end of 4 years. If the same sum is cleared off in four equal annual installments at the same rate, the amount of annual installment will be

The variance of first n odd natural numbers is $\frac{n^{2}-1}{3}$ : The sum of first n odd natural number is $n^2$ and the sum of square of first n odd natural numbers is $\frac{n\left(4n^{2}-1\right)}{3}.$

The equation of straight line through the intersection of the lines $x - 2y = 1 $ and $x + 3y = 2$ and parallel $3x + 4y = 0$ is

The length of the sub-tangent, ordinate and the sub-normal are in

The value of $a$ for which the volume of parallelepiped formed by the vectors $\hat {i}+a\hat{j} + \hat{k} \,\, \hat{j}+a\hat{k} $ and $ a\hat{i}+\hat{k} $ is minimum, is

If mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value atleast one is

A boy is throwing stones at a target. The probability of hitting the target at any trial is $\frac{1}{2}$ .The probability of hitting the target $5^{th}$ time at the $10^{th}$ throw is :

Two dice are thrown together $4$ times. The probability that both dice will show same numbers twice is -

The differential equation whose solution is $Ax^2 + By^2 = 1$ where $A$ and $B$ are arbitrary constants is of

If $A = \begin{bmatrix}1&-5&7\\ 0&7&9\\ 11&8&9\end{bmatrix}$, then trace of matrix $A$ is

The value of integral $\int\limits_0^1 \, \sqrt{\frac{1-x}{1+x}}dx$ is

The tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ at

The value of $\displaystyle\lim_{x\to\infty}\left(\frac{\pi}{2} - \tan^{-1} x\right)^{1/x} $ is

$\int \frac{dx}{\sin x - \cos x + \sqrt{2}} $ equals to

There are $5$ letters and $5$ different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A, its equation is

The coefficient of $x^n$ in the expansion of $\log_a (1 + x)$ is

The maximum value of $4 \, \sin^2 \, x - 12 \sin \, x + 7$ is

Let $x_1 , x_2,...., x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be the variance. Variance of $2x_1, 2x_2, ..., 2x_n$ is $4 \sigma^2$. Arithmetic mean $2x_1, 2x_2, ..., 2x_n $ is 4 $\bar{x}$ .