List of top Mathematical Ability Questions

If \( (675)^4 \times (240)^6 \times (864)^5 = 2^m \times 3^n \times 5^p \), then \( m+n^2+p^3 = \)

The mean of 13 numbers is 47. The mean of the first 3 numbers is 39, and that of the next 7 numbers is 49.  

The \(11^{\text{th}}\) number is 2 times the \(12^{\text{th}}\) number, and the \(12^{\text{th}}\) number is 3 less than the \(13^{\text{th}}\) number. 

Then the mean of the \(11^{\text{th}}\) and \(13^{\text{th}}\) numbers is:

If the mode of the following classified grouped data is $26$, then find the value of the missing frequency $k$ in the given table:
The mode of the continuous frequency distribution given in the following table is:
When a single number is drawn at random from the first 20 positive natural numbers, the probability that it is a multiple of 4 but NOT a multiple of 6 is equal to:
Consider the quadratic equation $x^{2}+bx+c=0$ where the coefficients $b,c\in\{2,6,8,9\}$. Find the probability that the equation has real and equal roots:}
A bag contains 5 Red, 4 White, and 6 Black balls. If one ball is drawn completely at random, then the probability that it is either a Red or a White ball is:
If \(m\) and \(c\) denote the slope and the \(y\)-intercept of the line \(3x-5y-6=0\), then \((m,c)=\)
If the equation of the line passing through the point \((-4,3)\) and having a slope \(\left(-\frac{2}{3}\right)\) is \(ax+by=c\), then \(a^2+b^2-c^2=\)
The mean of nine distinct numbers is \(20\). If each of the largest four numbers is increased by \(\frac{2}{3}\) and each of the smallest four numbers is reduced by \(\frac{8}{3}\), then the mean of the resultant numbers is
If the arithmetic mean of the frequency distribution given below is $\frac{22}{5}$ and $\sum_{i=1}^{6}f_{i}=35$, then find the value of $a^{2}+b^{3}$:}
Find the median of the following classified frequency data distribution table:
(Note: Assuming a symmetrical balanced continuous representation where the middle median interval applies clearly)
If the median of the data observations $7,13,48,12,19,54,61,x$ is $25$ and it is given that $29<x<42$, then find the value of $x$:
If the point $P(x,y)$ is equidistant from the points $(3,7)$ and $(5,-1)$, then $4y-x=$
$A(3,2)$ and $B$ are two points in the $xy$-plane. If the points $C\left(\frac{9}{2},\alpha\right)$ and $D(\beta,8)$ divide $AB$ in the ratio $3:1$ internally and externally respectively, then the coordinates of point $B$ are:
The inclination of the line joining the points $A(-2,3)$ and $B(-1,4)$ with the positive direction of the $X$-axis is
The lines $3x-2y=-6$ and $x+y=3$ meet the $Y$-axis at the point $A$ and meet the $X$-axis at the points $B$ and $C$. Then the area of $\triangle ABC$ (in sq. units) is
If the line $5y=7x$ divides the line segment joining the points $(3,5)$ and $(-5,2)$ in the ratio $m:n$ (where $\gcd(m,n)=1$), then the least value of $m^{2}+n^{2}$ is}
If the angle between the lines $7x+3py+5=0$ and $3x-14py+11=0$ is $\frac{\pi}{2}$, then a value of $p$ is}
In the adjacent figure of $\triangle ABC$, $AD$ is the internal bisector of $\angle A$. If $AB=6$ cm, $BD=3$ cm and $DC=2$ cm, then $AC=$
In the following figure it is given that $AB$ is parallel to $ED$, the distance between $AB$ and $ED$ is 10 cm, $\angle BCD=90^\circ$, $BC=9$ cm, $CD=8$ cm, $AB=18$ cm, and $ED=12$ cm. Find the area of the figure $ABCD$.
The figure given below shows a field with the measurements given in meters. Find the area of the field $ABCDE$.
A chord of a circle of diameter 24 cm subtends an angle $60^\circ$ at the centre of the circle. Then, the length of the chord, in cm, is
In the adjacent figure, $O$ is the center of the circle and $BC$ is a tangent drawn from $B$. If the radius of the circle is 8 cm and $BA=AO$, then (in cm) $BC=$
ABC is a right-angled triangle with right angle at B. If \(AB = 2\) and \(AC = 5\), then \(\tan C + \sec C =\)