List of top Mathematics Questions

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:

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

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:

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

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:

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

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?

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

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 \(AB\).

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

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

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.

\(BC=a,\; AC=b,\; AB=c\) are sides of \(\triangle ABC\) and \(\angle C\neq \frac{\pi}{2}\). Which of the following is not correct?

Find Mode

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:

Segments of lines \[ 2x+3y=1 \] and \[ 4x-3y=11 \] are diameters of a circle of area \(153.94\) square units. Then the equation of circle with integer radius is:

Find the value of \(n\) if \[ \left(\sum_{k=1}^{n}(-1)^{k-1}k\right)^2 - \sum_{k=1}^{n}(-1)^{k-1}k^2 +2450=0. \]

Find the acute angle at which curves \[ y=(x-2)^2 \] and \[ y=-4+6x-x^2 \] intersect.

In a tuition batch of 2 students, the probability that \(X\) will pass the examination is \(\frac25\) and that of \(Y\) is \(\frac34\). Assuming independence, what is the probability that neither \(X\) nor \(Y\) will pass?

Let \(A_1,A_2,A_3\) be events in a sample space with \(A_1\cap A_2\neq \phi\). Then always:

If \(x,y,z\) satisfy \[ x+y+z=1, \] \[ 4x+9y+16z=25, \] \[ 16x+18y+256z=625, \] find the value of \(x\):

The number of ordered tuples \((p,q,r)\) in truth table for which the statement \((\neg p \lor q)\Rightarrow r\) is true is: