List of practice Questions

Both the ends of a metallic solid cylinder are semi-spherical. Its total height is 19 cm and the diameter of the cylinder is 7 cm. Find the weight of the solid if the weight of \(1 \, \text{cm}^3\) of the metal is \(4.5 \, \text{g}\).

A chord of a circle of radius 15 cm subtends an angle of \(60^\circ\) at the centre of the circle. Find the area of the corresponding minor segment. \((\pi = 3.14, \, \sqrt{3} = 1.73)\)

Rational number will be

The shape of the graph of a quadratic equation $y = ax^2 + bx + c$, $a \neq 0$, will be

In the system of equations $\dfrac{x}{a} = \dfrac{y}{b}$, $ax + by = a^2 + b^2$, value of y will be

If the equation $x^2 - 4x + a = 0$ has no real roots, then

If the sum of first \(m\) terms of an A.P. is \(n\) and the sum of first \(n\) terms of the A.P. is \(m\), then find the sum of \((m+n)\) terms.

Prove that the angle between the tangents drawn from an external point to a circle is supplementary to the angle formed by the line segment joining the points of contact at the centre of the circle.

In what ratio does the point \((-4, 6)\) divide the line segment joining the points \(A(-6, 10)\) and \(B(3, -8)\)?

Find the roots of the quadratic equation \(3x^2 - 2\sqrt{6}x + 2 = 0\).

The distance between the two points (2, 3) and (4, 1) will be

Irrational number in the following will be

If the difference of two numbers is 26 and one number be three times the other, then find the numbers.

If \(\cot 2A = \tan (A - 22^\circ)\), where \(2A\) is an acute angle, find the value of \(A\).

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

Find the roots of the quadratic equation \(4x^2 + 9x + 5 = 0.\)

Find the volume of a copper rod of length 8 cm whose diameter is 1 cm.

Total surface area of a solid hemisphere with radius \(r\) will be

The mean and median of a frequency table are 27 and 29 respectively. Then its mode will be

The probability of 53 Mondays in a leap year will be

Two friends were born in 2020. Find the probability that the date of birth of both will be same.

The distance of the point \((-3, -4)\) from the origin will be

If \(\cot A = \dfrac{3}{4}\), then the value of \(\sec A\) will be

If \(\tan \alpha = \sin \alpha\), then the value of \(\alpha\) will be

If the ratio of the length of a rod and its shadow is \(1 : \sqrt{3}\), the elevation angle of the sun will be