List of top Mathematics Questions

Prove that : \(\tan^2 \theta + \cot^2 \theta + 2 = \sec^2 \theta \csc^2 \theta\)

If \(\sin \theta = \frac{1}{\sqrt{11}}\text{, then } \cot \theta\) equals

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

If \(\frac{-20}{9}, \frac{-2}{9}, \frac{16}{9}, \ldots\) are in A.P., then next term of the sequence is

In the given figure, \(\Delta ODC \sim \Delta OBA\). If \(\angle BOC = 110^\circ\), \(\angle ODC = 45^\circ\) and \(AB = 2 CD\), then find (i) \(m\angle OAB\) (ii) \(OB : OD\).

The distance between the points \(P(-4, 5)\) and \(Q(-1, 2)\) is

If the zeroes of the polynomial \(p(x) = 2x^2 - 7x + 6\) are \(\alpha\) and \(\beta\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is

In a circular museum hall of radius 14 m, some statues are displayed. Statues are kept inside the inner concentric circle of radius 7 m. One such statue lying in sector OAB, is fenced along line segments OA, AP, PB and BO where P is a point on outer circle. Based on above information, answer the following questions :

(i) Find m\(\angle\)AOP.

Find mean and mode of the following data :

Seema daily goes to a park to exercise on machines available there. When Seema spent 15 minutes on exercise bicycle and 30 minutes on double cross walker, she received a message of burning 435 calories on her fitness watch. When she spent 30 minutes on exercise bicycle and 40 minutes on double cross walker, she received a message of burning 690 calories. To find the number of calories burned per minute on each machine, answer the following :

(i) Represent the above situation in terms of a pair of linear equations in two variables.

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 ?

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are \(60^\circ\) and \(30^\circ\) respectively. Find the height of the poles and the distance of the point from the poles.

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

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

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

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.

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

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 \(\frac{MN}{QR} = \frac{1}{4}\).

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 \(\cos \theta = \frac{\text{Base}}{\text{Hypotenuse}}\).

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.

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

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.

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

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