List of practice Questions

The angle of elevation of a tower PQ from a point A on the ground is observed as $30^\circ$. After walking 12 m towards the foot of the tower, the angle of tower is observed as $60^\circ$. Then the height of the tower in meter is

If ABC is an isosceles triangle with $AB=AC$ and $\angle BAC=70^\circ$, then the external angle at C is

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

ABCD is a quadrilateral whose diagonal BD is of length 26 cm. The lengths of the perpendiculars drawn from A and C on BD are 14 cm and 8 cm respectively. The area of the quadrilateral in sq. cm. is

In the adjoining figure, \(AD \parallel BC\). What is the perimeter of the quadrilateral \(ABCD\)?

Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle (in cm) 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 \( 4a+6b = \)

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 \(\frac{48}{x+y}-\frac{6}{x-y}=10\) 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 \(x^{3}+y^{3}=\)

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:

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:

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

If \(793 \equiv x \pmod{29}\) and \(0 \le x < 29\), then the sum of distinct prime divisors of \(x\) 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 \(A \cap (B \cup C)=\)

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

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