List of practice Questions

Simplest form of \(\frac{\sec A}{\sqrt{\sec^2 A - 1}}\) is

The line segment joining the points \(P(-4, -2)\) and \(Q(10, 4)\) is divided by y-axis in the ratio

A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as \(60^{\circ}\). If \(AB = 5\sqrt{3}\) m, then length of the wire is

In the given figure, \(AB \parallel EF\). If \(AB = 24\) cm, \(EF = 36\) cm and \(DA = 7\) cm, then \(AE\) equals

Devansh proved that \(\triangle ABC \sim \triangle PQR\) using SAS similarity criteria. If he found \(\angle C = \angle R\), then which of the following was proved true?

While calculating mean of a grouped frequency distribution, step deviation method was used \(u = \frac{x-a}{h}\). It was found that \(\bar{x} = 64\), \(h = 5\) and \(a = 62.5\). The value of \(\bar{u}\) is

For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is

Which of the following can not be the probability of an event?

The value of \(m\) for which the quadratic equation \(3x^2 - 7x + m = 0\) has real and equal roots, is

If the zeroes of a polynomial \(p(x)\) are \(-3\) and \(8\), then \(p(x)\) equals

The value of \(p\) for which roots of the quadratic equation \(x^{2} - px + 6 = 0\) are rational, is

An arc of length \(2.2\) cm subtends an angle \(\theta\) at the centre of the circle with radius \(2.8\) cm. The value of \(\theta\) is

Two dice are rolled together. The probability of getting an outcome \((x, y)\) where \(x>y\), is

Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

Assertion (A) : The system of linear equations \(3x - 5y + 7 = 0\) and \(-6x + 10y + 14 = 0\) is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Evaluate : \(\frac{\sin^3 60^{\circ} - \tan 30^{\circ}}{\cos^2 45^{\circ}}\)

For acute angles A and B and \(A + 2B\) and \(2A + B\) are acute if \(\tan (A + 2B) = \sqrt{3}\) and \(\sin (2A + B) = \frac{1}{\sqrt{2}}\), then find the measures of angles A and B.}

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is \(3/5\), then find the number of yellow balls.

In the given figure, \(AB \parallel DE\) and \(AC \parallel DF\). Show that \(\triangle ABC \sim \triangle DEF\). If \(BC = 10\) cm, \(EB = CF = 5\) cm and \(AB = 7\) cm, then find the length DE.

Prove that \(14 - 2\sqrt{3}\) is an irrational number, given that \(\sqrt{3}\) is irrational.

A circle centered at (2, 1) passes through the points A(5, 6) and B(-3, K). Find the value(s) of K. Hence find length of chord AB.

Prove that the point P dividing the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 3 : 2, lies on the line \(x - 3y = -1\). Also find length of PA and PB.

Use graphical method to solve the system of linear equations : \(x = -3\) and \(5x - 2y = -5\).

The sum of first n terms of an A.P. is \(2n^{2} + 13n\). Find its \(n^{th}\) term and hence \(10^{th}\) term.

Prove that :
\(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).