List of practice Questions

Area of the sector of an angle $\theta^\circ$ of a circle with radius $r$ will be

The diameter of a solid pipe is 4 cm whose length is 20 cm. Then the volume of the metal used in the pipe will be

Total surface area of a solid hemisphere with radius $r$ will be

10th term of the sequence $\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, \dots$ will be

If in $\triangle ABC$ and $\triangle DEF$, $\dfrac{AB}{DE} = \dfrac{BC}{FD}$, then they will be similar if

The perimeter of a triangle whose vertices are (0, 4), (0, 0), and (3, 0) will be

If $3 \tan A = 4$ then the value of $\sec A$ will be

If $\tan \alpha + \cot \alpha = 5$, then the value of $\tan^2 \alpha + \cot^2 \alpha$ will be

If $\sin \theta = \csc \theta$ and $0 \leq \theta \leq \dfrac{\pi}{2}$, then the value of $\theta$ will be

The angle of elevation of the top of a tower from the top of a house whose height is 15 m is \(30^\circ\). Also, the angle of elevation of the top of the tower from the ground of the same house is \(60^\circ\). Find the height of the tower and the distance of the tower from the house.

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.