List of practice Questions

If $\sin A = \cos A$, then the value of $A$ will be:
If \( A = 30^\circ \), then the value of \( \frac{1 + \tan^2 A}{1 + \cot^2 A} \) will be:
If the radius of a sphere is doubled, then the increase in percentage of its surface area will be:
The ratio between the diameters of two circles is \( 4 : 9 \). The ratio between their circumferences will be:
The mean of a frequency distribution is \( 24.1 \) and the mode is \( 28 \). Its median will be:
One third of any number is equal to 21. Then the number will be:
If one root of the quadratic equation $x^2 + 2x - p = 0$ is $-2$, then the value of $p$ will be:
The ratio of the areas of two triangles is equal to the square of the ratio of their corresponding sides. Then these triangles will be:
The coordinate of the point on the $x$-axis and equidistant from the points $(2, -5)$ and $(-2, 9)$ will be:
If \( \triangle ABC \) is an isosceles triangle with \( AB = AC \), then:
In $\triangle ABC$, if $AB = 6\sqrt{3}$ cm, $AC = 12$ cm, and $BC = 6$ cm, then $\angle B$ will be:
For any two positive integers ‘a’ and ‘b’:
The quotient of a non-zero rational and irrational number will be:
If \( m = 5 \) and \( n = m + 7 \), then the value of \( \sqrt{m^2 + n^2} \) will be:
The equivalent rational numbers of any rational number will be:
If $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ are two linear equations, and if $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$, then:

On decreasing the 𝑝H from 7 to 2, the solubility of a sparingly soluble salt (MX) of a weak acid (HX) increased from 10−4 mol L−1 to 10−3 mol L−1. The 𝑝Ka of HX is

Let \( \alpha, \beta \) be the roots of the equation \( x^2 - \sqrt{2}x + 2 = 0 \), then \( \alpha^{14} + \beta^{14} \) is equal to:
The commercial unit of electric energy is commonly known as ‘unit’. Write its actual name and establish the relationship between this unit and the SI unit of energy.
What factors forced Gorbachev to reform the Soviet Union? What were its consequences?
The Shah Commission was appointed by Janata Party in 1977. Why was this commission appointed and what were its finding?
What is Shock Therapy? And what were its results? Discuss.
What changes took place in Indian Politics after the emergency? Discuss.
What were the main steps decided in 2005 to make the United Nation Organisation more relevant?
What was the 'Two Nations Theory'? What was its result?