List of top Mathematics Questions

In the adjoining figure, \(PQ \parallel XY \parallel BC\), \(AP=2\ \text{cm}, PX=1.5\ \text{cm}, BX=4\ \text{cm}\). If \(QY=0.75\ \text{cm}\), then \(AQ+CY =\)

Find the least value of ‘a’ so that $f(x) = 2x^2 - ax + 3$ is an increasing function on $[2, 4]$.
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).
The radius of a cylinder is decreasing at a rate of 2 cm/s and the altitude is increasing at a rate of 3 cm/s. Find the rate of change of volume of this cylinder when its radius is 4 cm and altitude is 6 cm.
Find the value of \( x \) in the following equation: \[ \frac{2}{x} + \frac{3}{x + 1} = 1 \]
In the given figure, PA is tangent to a circle with centre O. If \(\angle APO = 30^\circ\) and OA = 2.5 cm, then OP is equal to
PA is tangent to a circle with centre O
If the sum of first n terms of an A.P. is given by \( S_n = \frac{n}{2}(3n+1) \), then the first term of the A.P. is
The value of k for which the system of equations \(3x - 7y = 1\) and \(kx + 14y = 6\) is inconsistent, is
Assertion (A) : \(\triangle ABC \sim \triangle PQR\) such that \(\angle A = 65^\circ\), \(\angle C = 60^\circ\). Hence \(\angle Q = 55^\circ\).
Reason (R) : Sum of all angles of a triangle is \(180^\circ\).
In two concentric circles centred at O, a chord AB of the larger circle touches the smaller circle at C. If OA = 3.5 cm, OC = 2.1 cm, then AB is equal to
In two concentric circles centred at O

In \(\triangle ABC\), \(DE \parallel BC\). If \(AE = (2x+1)\) cm, \(EC = 4\) cm, \(AD = (x+1)\) cm and \(DB = 3\) cm, then the value of \(x\) is

To calculate mean of grouped data, Rahul used assumed mean method. He used \(d = (x - A)\), where \(A\) is the assumed mean. Then \(\bar{x}\) is equal to

Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

OAB is sector of a circle with centre O and radius 7 cm. If length of arc \( \widehat{AB} = \frac{22}{3} \) cm, then \( \angle AOB \) is equal to
Assertion (A) : \((a + \sqrt{b})(a - \sqrt{b})\) is a rational number, where a and b are positive integers.
Reason (R) : Product of two irrationals is always rational.
22nd term of the A.P.: \(\frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots\) is
ABCD is a rectangle with its vertices at (2, --2), (8, 4), (4, 8) and (--2, 2) taken in order. Length of its diagonal is
Which of the following cannot be the unit digit of $8^n$, where $n$ is a natural number?

In the adjoining figure, TS is a tangent to a circle with centre O. The value of $2x^\circ$ is

For a circle with centre O and radius 5 cm, which of the following statements is true?
P: Distance between every pair of parallel tangents is 10 cm.
Q: Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
R: Distance between every pair of parallel tangents is 5 cm.
S: There does not exist a point outside the circle from where length of tangent is 5 cm.

In the adjoining figure, PA and PB are tangents to a circle with centre O such that $\angle P = 90^\circ$. If $AB = 3\sqrt{2}$ cm, then the diameter of the circle is

If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are
If the maximum number of students has obtained 52 marks out of 80, then
If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of cone hollowed out is
$\sqrt{0.4}$ is a/an