List of top Mathematics Questions

The value of k for which the system of linear equations \(\frac{x}{2} + \frac{y}{3} = 5\) and \(2x + ky = 7\) is inconsistent, is
In the given figure, a circle is centred at (1, 2). The diameter of the circle is
Observe the graph of polynomial p(x). Number of zeroes of p(x) is
It is given that \(\Delta ABC \sim \Delta EDF\). Which of the following is not true ?
If PQ and PR are tangents to the circle with centre O and radius 4 cm such that \(\angle QPR = 90^\circ\), then the length OP is
The \(n^{\text{th}}\) term of an A.P. is \(\sqrt{2}n + 1\). Its common difference is
If the quadratic equation \(9x^2 + 8kx + 16 = 0\) has real and equal roots, then the value of k is
From a solid cylinder whose height is 2.8 cm and radius 2.1 cm, a conical cavity of the same height and same radius is hollowed out. Find the volume and the total surface area of the remaining solid.
Two poles of equal heights are standing opposite to each other on either side of the road which is 90 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30\(^\circ\) and 60\(^\circ\) respectively. Find the height of the poles and the distances of the point from the poles. [Use \(\sqrt{3}\) = 1.732]
Find the mean of the following distribution :
If \(\cos A + \sin A = \sqrt{2} \cos A\), prove that \(\cos A - \sin A = \sqrt{2} \sin A\).
Two numbers are in the ratio 3 : 5 and their LCM is 180. Find the HCF of these two numbers.
Find a relation between x and y such that the point P(x, y) is equidistant from the points A(5, 3) and B(1, 7).
Find the quadratic polynomial the sum of whose zeroes is 1 and their product is –12. Hence find the zeroes of the polynomial.
Prove that \(\frac{2 + 3\sqrt{5}}{7}\) is an irrational number, given that \(\sqrt{5}\) is an irrational number.
A circle is inscribed in a right triangle ABC, right angled at B. If the lengths of the two sides containing the right angle are 8 cm and 15 cm, find the radius of the incircle.
Assertion (A) : If the Mode and Mean of a data are 12 k and 15 k, then Median of the data is 14 k.
Reason (R) : The relation between the Mean, Mode and Median of a data is : Mean = 3 Median – 2 Mode.
Assertion (A) : In a circle of radius 21 cm, an arc of length 22 cm subtends an angle of 60\(^\circ\) at the centre.
Reason (R) : The length of arc of a sector of a circle of radius r and central angle \(\theta\) is \(\frac{2\pi r\theta}{360}\).
The number of conical bottles of radius 2 cm and height 1.2 cm that can be filled from a cylindrical bottle of radius 6 cm and height 8 cm, full of liquid, is
If HCF of 66 and 99 is expressible in the form of \(55m - 132\), then the value of m is :
Two dice are thrown simultaneously. The probability of getting a sum of 7 is :
One ticket is drawn at random from a bag containing 50 tickets numbered 1 to 50. The probability that the drawn ticket has a number which is a multiple of 7 is :
\(\sin 2 \theta = 2 \sin \theta\) is true, when \(\theta\) is equal to
The perimeter of sector of a circle of radius 21 cm and central angle 60\(^\circ\), is
From a point P, tangents PQ and PR are drawn to a circle with centre O and radius 6 cm. If OP = 10 cm, then area of quadrilateral PQOR is :