List of top Mathematics Questions

For \(x \in \mathbb{R}\), define \[ \langle x \rangle = x-[x] \] where \([x]\) denotes the greatest integer less than or equal to \(x\). Then for any arbitrary pair of real numbers \(x,y \in \mathbb{R}\), which of the following is always true?

Evaluate \[ \int_{0}^{\sqrt{\pi}} x\sin^{2}(x^{2})\,dx \]

Let \(\theta \neq \dfrac{(2n+1)\pi}{2}\), for \(n\in\mathbb{Z}\). Consider the system of equations \[ x\cos\theta+y\sec\theta=0 \] \[ x\sin\theta+y\tan\theta=0 \] This system does not have a unique solution if and only if \(\theta\) belongs to:

The sum of X, Y, W, and Z is 84. The sum of Y, W, and Z is three times X. The sum of X, W, and Z is 320% of Y. W is 20% of the sum of X, Y, and Z. Find the value of Z.

The sum of four numbers A, B, C, and D is 10,600. Without A, the average of B, C, and D is 1,000. Without B, the average of A, C, and D is 3,220. Without C, the average of A, B, and D is 3,180. Find the value of D.

Ten people went out for dinner. Nine of them contributed ₹400 each, while the tenth person contributed an amount that was ₹900 more than the average contribution of the entire group. How much did the tenth person contribute?

The price of LPG increases by \(16\%\). By what percentage should consumption be reduced so that the total expenditure remains the same?

Kritika has three solid objects cone, hemisphere, cylinder. All have same base radius and height. Then the ratio of volume of cylinder : cone : hemisphere is

72, 69, 66, \(\ldots\) Number continue in same pattern as long as they remain positive. What will be the maximum sum of terms?

In a group of people:

• 70 play only Hockey.

• 100 play only Football.

• 30 play both Hockey and Football.

• 150 play neither game.
What percentage of the people play Hockey?

For \(a \in \mathbb{R}\), consider the real valued function defined on \((-1,1)\): \[ f(x)= \begin{cases} \dfrac{(1+x)^{1/3}-(1+2x)^{1/4}}{x}, & x\neq0,\\ a,& x=0. \end{cases} \] If \(f\) is differentiable at \(x=0\), then value of \(a+f'(0)\) is:

For a given sample the computed values of variance and fourth central moment are \(3\) and \(63\) respectively. Then underlying frequency distribution is classified as:

Define relation \(\sim\) on set \(\{1,2,\dots,10\}\) by \(a \sim b\) if \(a-2b\) is divisible by \(3\), then:

Let \((x_0,y_0)\in\mathbb Z^2\) be a point on straight line \(8x-3y=11\) which is equidistant from coordinate axes. Then point \((x_0,y_0)\) will lie only in:

Coefficient of \(x^{10}\) in the expansion of \[ \left(x^2+\frac1x\right)^{12} + \left(x+\frac1{x^2}\right)^{12} \] is:

Let \(x-y\tan35^\circ=\tan25^\circ(y+x\tan35^\circ)\) for some \(x,y\in\mathbb{R}\). Then which of the following is true?

Consider graph of function \(f(x)=2\cos\left(\frac{x}{2}\right)+3\), \(g(x)=4\). The number of points of intersection of two graphs in interval \([0,4\pi]\) is:

An engineer standing at point \(P\) wishes to determine the width of a rectangular pond. She finds distance to westernmost point \(A\) to be \(60\) m and distance to northernmost point \(B\) to be \(80\) m. If angle \(APB=60^\circ\), find \(AB\).

\(x,y,z\) are positive real numbers such that \[ \sqrt{x+y}-3\sqrt{y+z}=2 \] and \[ 4x-5y-9z=8. \] Find \[ \sqrt{\frac{20x+38y+18z+1}{9z+9y+2}}. \]

Which of the following equation represents common tangent to parabola \(y=-x^2\) and \(y=(x-2)^2\)?

\[ \lim_{x\to0} \frac{|x|\log_e(1+|\sin2x|)} {x^2(|x|+3)} \]

Which of the following is not same as \((A\Delta B)\cap C\)?

The distance (in meter) for 7 throws of a shotputter are \(14.5,15.2,16.8,17.1,15.9,16.3,14.7\). Calculate sample mean and sample standard deviation.

Given observations \[ 10,4,11,6,17,15,9,8,x \] and mean = mode = median. Find the value of \(x\).

Let \(X\) and \(Y\) be two independent identically distributed Bernoulli random variables with \[ P(X=1)=\frac12, \qquad P(X=0)=\frac12. \] If \(Z=XY\), then distribution of \(Z\) is: