List of top Mathematical Ability Questions

If the mean of the following data is \(12.5\), find the value of \(k\).

\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Class interval} & 0\text{-}5 & 5\text{-}10 & 10\text{-}15 & 15\text{-}20 & 20\text{-}25 \\ \hline \text{Frequency} & 2 & k & 6 & 4 & 1 \\ \hline \end{array} \]

Median of the following frequency distribution is

Find the mean of the numbers \[ 5^2,\;6^2,\;7^2,\;8^2,\;9^2,\;10^2. \]

Consider the quadratic equation \[ x^2+ax+b=0, \] where \(a,b\in\{1,2,3,4\}\). What is the probability that the equation has real roots?

Two dice are rolled. What is the probability of getting a total of \(9\)?

The weights of \(14\) children (in kg) are given below. Find the median weight of the children (in kg). \[ 47,\;39,\;46,\;32,\;50,\;43,\;44,\;45,\;37,\;36,\;48,\;42,\;41,\;40 \]

Calculate the arithmetic mean (approximately) from the following data

The arithmetic mean of \(4^2,\,8^2,\,12^2,\ldots,32^2\) is

If the median of the following classified data is \(11\), find the value of \(a\) in the table.

Equation of a straight line which makes an angle \(150^\circ\) with the positive direction of X-axis and an intercept \(4\) units on the Y-axis is

The straight line \(5x+3ay+k=0\) with the slope \(\dfrac{10}{9}\) passing through the point \((4,8)\), then \(k=\)

ABCD is a quadrilateral with \(A(3,5)\), \(B(5,9)\) and \(C(3,7)\). If the line \(y=3x\) meets the sides \(AB\) and \(BC\) in points \(P\) and \(Q\) respectively, then \(PQ^2=\)

The equation of the line passing through the origin and perpendicular to the line joining the points \(A(4,-3)\) and \(B(6,3)\) is

The equation of a straight line whose slope is \(\frac13\) and which divides the line joining the points \(A(0,2)\) and \(B(5,-3)\) in the ratio \(4:7\) is

A line cuts the positive axes \(OX\), \(OY\) in the points \(A\), \(B\) respectively. If the point \(P(3,5)\) divides the line \(AB\) in the ratio \(2:1\) internally, then the equation of the line is

A line passing through the point \(P(2,1)\) meets the coordinate axes in \(A\) and \(B\). If \(P\) divides \(AB\) in the ratio \(4:3\), then the equation of \(AB\) is

Let \(A(7,2)\), \(B(0,1)\) be any two points. If the distance of \(P(x,5)\) from \(A\) is same as the distance from \(B\), then the value of \(x\) is

In a trapezium, the two non-parallel sides are of length \(13\) cm each. The distance between the parallel sides is \(12\) cm. If the smaller of the parallel sides is \(11\) cm, then the sum of the lengths of the two diagonals, in cm, is

In the adjacent figure \(PT\) is a tangent drawn from an external point \(P\) touching the circle at \(T\). \(PAB\) is a secant cutting the circle at \(A\) and \(B\). If \(PT=5\) cm and \(PA=4\) cm, then \(AB\) (in cm) is

\(P,Q,R\) are points on a circle with centre \(O\) as shown in the figure. If \(\angle PQR=100^\circ\), then \(\angle OPR=\)

In a triangle \(PQR\), \(PS\) is the angle bisector of \(\angle P\). \(PQ=3\), \(QS=2\) and \(SR=3\), then \(PR=\)

\(ABCD\) is a cyclic quadrilateral whose diagonals intersect at \(E\). If \(\angle DBC=70^\circ\), \(\angle BAC=30^\circ\) and \(AB=BC\), then \(\angle ECD=\)

If \[ \csc\theta+\cot\theta=5 \] then \[ 11+12\tan\theta= \]

If the angles of depression of the top and bottom of an 8 meter tall building from the top of a multistoried building are \(30^\circ\) and \(45^\circ\) respectively, then the height (in meters) of that multistoried building is