List of top Mathematics Questions

One-third of one-fourth of a number is 12. Then the number is

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

\(P\) 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?

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

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

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

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

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

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

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

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

If $\sin^2 \theta + \sin^2 \phi = 1/2, \cos^2 + \cos^2 \phi = 3/2$, then $\cos^2 (\theta - \phi)$ is equal to

For the function $f\left(x\right)= \frac{x^{100}}{100} + \frac{x^{99}}{99} + ... \frac{x^{2}}{2} + x + 1 , $ f ' (1) = mf' (0), where m is equal to

In how many ways can $5$ prizes be distributed among $4$ boys when every boy can take one or more prizes ?

The number of positive integral solution of $abc = 30$ is

The value of the determinant $\begin{vmatrix}265&240&219\\ 240&225&198\\ 219&198&181\end{vmatrix}$ is

Let $x$ and $y$ be two natural numbers such that $xy = 12(x + y)$ and $x \le y$. Then the total number of pairs $(x, y)$ is

Let $T(k)$ be the statement $1 + 3 + 5 + ... + (2k - 1)= k^2 +10$ Which of the following is correct?

What is the value of n so that the angle between the lines having direction ratios $(1, 1, 1)$ and $(1, -1, n)$ is $60^{\circ}$ ?