List of top Mathematical Ability Questions

In triangle ABC, the lengths of the sides are 5 cm, 8 cm and 9 cm. If D, E and F are the midpoints of BC, CA and AB respectively, then the area of triangle DEF, in $cm^2$, is

In an arithmetic progression, the first term is 2 and the sum of its first five terms is one-fourth of the sum of the next five terms. The 20th term of that progression is

Sum of first three terms of a GP is 93 and the product of the first and third terms is 225. Then the 4th term of the GP is

$ax^{2}-bx+c=0$ has roots $\sin60^\circ$ and $\cos60^\circ$. Then \[ \frac{ac}{b^{2}}+\frac{a+c}{b} = \ ? \]}

$(\cos^{2}0^{\circ}+\sin^{2}30^{\circ})(\tan^{2}45^{\circ}+\cot^{2}60^{\circ})(\cos^{2}180^{\circ}+\sin^{2}90^{\circ})=$

$\tan(A+B)=m$ and $\tan(A-B)=n$. Then $\tan(2A)=$

If $\tan\theta,\;2\tan\theta+2,\;3\tan\theta+3$ are in geometric progression and $\tan\theta\neq -1$, then $\tan\theta=$

The equation \(x^3-24x^2+\alpha x-\beta=0\) has positive integral roots \(p,q,r\). If geometric mean of the three roots is 8, then \(\alpha=\)

The polynomial \(4x^3+ax^2+bx+c\) leaves remainders 11, -3 and 41 respectively when divided by \(x+1\), \(x+2\) and \(x-2\). Then the remainder when it is divided by \(x-1\) is

A polynomial \( p(x) \) in x leaves remainder 5 and 6 when the polynomial \( p(x) \) is divided by \( x+1 \) and \( x+3 \) respectively. If it leaves remainder \( ax+b \) when divided by \( x^{2}+4x+3 \), then \( 4a+6b = \)

If \(\frac{48}{x+y}-\frac{6}{x-y}=10\) and \(\frac{15}{x+y}+\frac{4}{x-y}=9\), then \(x^{2}+y^{2}=\)

If \(x, y\) are two real numbers such that \(x+y=23\) and \(x^{2}+y^{2}=289\), then \(x^{3}+y^{3}=\)

A boat sails 27 kms down stream in 3 hours but takes 9 hours to sail back the same distance up stream. Calculate the ratio of speed of boat to speed of stream.

If \(\alpha,\beta\) are the zeroes of the polynomial \(x^2-78x+k\) and if \(\alpha=\beta-6\), then \(k=\)

The floor of hall of dimensions \(18\,m \times 12\,m\) is to be fixed by tiles of size \(45\,cm \times 15\,cm\). The number of tiles required for the floor of the hall is:

Three sets A, B and C are defined as follows:
\(A=\{x|x\text{ is an even integer}\}\),
\(B=\{x|x\text{ is an integer and multiple of 5}\}\),
\(C=\{x|x\text{ is an integer and multiple of 10}\}\).
Then \(A \cap (B \cup C)=\)

A solid metallic sphere of 16 cm diameter is melted and cast into smaller solid spheres of diameter 4 cm. The number of smaller spheres formed is:

If A and B are two non-empty sets, then \((A\cup B)-(A\cap B)=\)

If \(793 \equiv x \pmod{29}\) and \(0 \le x < 29\), then the sum of distinct prime divisors of \(x\) is:

The product of two numbers 13 and \(x\), when divided by 11 leaves remainder 7. The least positive such integer \(x\) is:

If the total surface area of a cone is \(384\pi \, cm^2\) and its height is 16 cm, then volume of the cone, in \(cm^3\) is

160 people are employed to finish the work in 120 days. After 40 days it was found that only \(\frac{1}{5}\) of the work is completed. To complete the work in the scheduled time, how many more people are to be employed?

In triangle ABC, \( AB=26 \) cm, \( AC=24 \) cm and \( \angle C=90^{\circ} \). If \( r_1, r_2, r_3 \) are the areas of the semi-circles with AB, AC, BC as diameters respectively, then \( \frac{1}{\pi}(r_1 + 2r_2 + 3r_3) \) (in \( cm^2 \)) is

The perimeter of the longest circle that can be inscribed in a rectangle of sides \(161 \, \text{cm}\) and \(296 \, \text{cm}\), in cm, is (take \( \pi \approx \frac{22}{7} \)).

The height of a cylinder is 7 cm and the area of its curved surface is 264 sq.cm. Then the volume of the cylinder in cu.cm. is (take value of \( \pi=\frac{22}{7} \))