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List of top Mathematics Questions

Verify that $\sin 2A = \frac{2 \tan A}{1 + \tan^2 A}$ for $A = 30^\circ$.

Evaluate : $\frac{\cos 45^\circ}{\tan 30^\circ + \sin 60^\circ}$

The line $2x - 3y = 6$ intersects x-axis at

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

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

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

A quadratic polynomial having zeroes 0 and -2, is

15th term of the A.P. $ \frac{13}{3}, \frac{9}{3}, \frac{5}{3}, \dots $ is

In $\triangle ABC, \angle B = 90^\circ$. If $ \frac{AB}{AC} = \frac{1}{2} $, then cos C is equal to

Gurveer and Arushi built a robot that can paint a path as it moves on a graph paper. Some co-ordinate of points are marked on it. It starts from graph paper. Some co-ordinate of points are marked on it. It starts from (0, 0), moves to the points listed in order (in straight lines) and ends at (0, 0).

A triangular window of a building is shown above. Its diagram represents a $\triangle ABC$ with $\angle A = 90^\circ$ and $AB = AC$. Points P and R trisect AB and $PQ \parallel RS \parallel AC$.

A hemispherical bowl is packed in a cuboidal box. The bowl just fits in the box. Inner radius of the bowl is 10 cm. Outer radius of the bowl is 10.5 cm.

The following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find the values of $x$ and $y$.

Marks	Number of Students
10 -- 20	12
20 -- 30	30
30 -- 40	$x$
40 -- 50	65
50 -- 60	$y$
60 -- 70	25
70 -- 80	18

From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid.
Use $\pi = \dfrac{22}{7}, \sqrt{5} = 2.2$

If a line drawn parallel to one side of triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to third side. State and prove the converse of the above statement.

Find the smallest value of $p$ for which the quadratic equation $x^2 - 2(p + 1)x + p^2 = 0$ has real roots. Hence, find the roots of the equation so obtained.

In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.

Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

If the points $A(6, 1)$, $B(p, 2)$, $C(9, 4)$ and $D(7, q)$ are the vertices of a parallelogram $ABCD$, then find the values of $p$ and $q$. Hence, check whether $ABCD$ is a rectangle or not.

Find the zeroes of the polynomial $p(x) = 3x^2 - 4x - 4$. Hence, write a polynomial whose each of the zeroes is 2 more than the zeroes of $p(x)$.

Prove that $\sqrt{5}$ is an irrational number.

The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

P is a point on the side BC of $\triangle ABC$ such that $\angle APC = \angle BAC$. Prove that $AC^2 = BC \cdot CP$.

Use the identity: $\sin^2A + \cos^2A = 1$ to prove that $\tan^2A + 1 = \sec^2A$. Hence, find the value of $\tan A$, when $\sec A = \dfrac{5}{3}$ where A is an acute angle.

In a pair of supplementary angles, the greater angle exceeds the smaller by $50^\circ$. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.