List of top Mathematics Questions

There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylinderical). The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm. Considering mushroom a solid object, answer the following questions :

(i) What is the total height of a mushroom ?

In the given figure, \(\triangle\)ABC is right angled triangle with \(\angle\)A = \(90^\circ\). AD is perpendicular to BC.

(a)(i) Prove that \(\triangle\)DBA \(\sim\) \(\triangle\)DAC

Prove that \(\sqrt{2}\) is an irrational number.

Points P(6, 0), Q(2, 8) and R(\(-2\), 4) are vertices of \(\triangle\)PQR. It is given that MN $\parallel$ QR such that \(\frac{PM}{MQ} = \frac{1}{3}\). Using distance formula and ratio formula, show that \(\frac{MN}{QR} = \frac{1}{4}\).

Prove that \(\sqrt{\frac{1 - \sin A}{1 + \sin A}} = \frac{1}{\sec A + \tan A}\).

Chord AB of a circle subtends an angle of \(120^\circ\) at the centre O of the circle. Find the length of arc AB, if radius of the circle is 21 cm.

In the given figure, AB $\parallel$ DC. If OB = 3OD and CD = 1.8 cm, then find the length AB.

Assertion (A) : Median of a data is the value of \(\frac{N}{2}\), where N represents sum of all frequencies.
Reason (R) : Median divides the whole distribution in two equal parts.

If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B when joined, then establish a relation between a and b.

Find the H.C.F. and L.C.M. of 1530 and 2040.

Assertion (A) : For an acute angle \(\theta\), \(\cos \theta\) is always less than 1.
Reason (R) : In a right-angled triangle, hypotenuse is the longest side and \(\cos \theta = \frac{\text{Base}}{\text{Hypotenuse}}\).

The total surface area of a solid cone of radius 7 cm and slant height 25 cm, is

The length of a pendulum is 70 cm and it describes an arc of length 88 cm when swings. The angle subtended by the arc at the centre is

PQ is tangent to a circle at a point P on the circle. The number of tangents which can be drawn to the circle parallel to PQ, is

The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is

A bag contains some red and some white balls. A ball is drawn at random from the bag. If the probability of getting a red ball is \(\frac{2}{7}\), then the probability of getting a white ball is

A card is drawn from a well-shuffled deck of 52 playing cards. The probability of getting a queen of spade is

In the given figure, DE $\parallel$ BC. If AD : AB = 1 : 3 and AE = 2.5 cm, then AC equals

If \(-26\), x, 2 are in A.P., then the value of x is

The graph of a polynomial \(p(x)\) is shown here. The number of zeroes of the polynomial \(p(x)\) is

\(n^{\text{th}}\) term of the A.P. : \(-\frac{1}{3}, \frac{4}{3}, 3, \ldots\) is

If value of \(\cot \theta\) is \(\sqrt{5}\), then \(\sin \theta\) equals

A chord \(QR\) subtends an angle of \(105^\circ\) at the centre \(O\) of the circle. The measure of \(\angle RQP\) is

The probability of getting sum greater than 10, when two dice are rolled together, is

Which of the following statements is not always true?