List of practice Questions

\( \sin(60^\circ + \theta) - \cos(30^\circ - \theta) \) is equal to :
If \(n\) is a natural number then \(9^{2n} - 4^{2n}\) is always divisible by :
If \(n\) is any natural number then \(6^n - 5^n\) always ends with :
If \( \alpha, \beta \) are the zeroes of the polynomial :
\( f(x) = x^2 - p(x+1) - C \) such that \( (\alpha+1)(\beta+1) = 0 \) then C=
In \( \triangle ABC \) and \( \triangle DEF \), \( \angle A = \angle E = 40^\circ \) and AB : ED = AC : EF and \( \angle F = 65^\circ \) then \( \angle B = ? \)
If \( \tan \theta = \frac{a}{b} \) then \( \frac{a\sin\theta + b\cos\theta}{a\sin\theta - b\cos\theta} = \)
If \( \csc\theta = 2x \) and \( \cot\theta = \frac{2}{x} \) then \( 2\left(x^2 - \frac{1}{x^2}\right) = ? \)
If the mean of 1,3,4,5,7,4 is \(m\) and mean of 3,2,2,4,3,3,\(p\) is \((m-1)\) and median is \(q\) then \( p+q = \)
The length, width and height of a rectangular solid are in the ratio of 3:2:1. If the volume of the solid is 48 cm\(^3\). The total surface area at the solid is :
If the diameter of the base of a closed right circular cylinder be equal to its height, h, then its whole surface area is :
If the radius of the base of a right circular cone is \(3r\) and its height is equal to the radius of the base, then its volume is :
If the ratio of volumes of two spheres is 1:8, then the ratio of their surface area is :
Let \(l\) be the lower class limit of a class-interval in a frequency distribution and \(m\) be the mid point of the class. Then the upper class limit of the class is :
Two coins are tossed simultaneously. The probability of getting atmost one head is :
If two interior angles, on the same side of a transversal intersecting two parallel lines, are in the ratio 2 : 3, then the measure of the larger angle is :
If the bisectors of the acute angles of a right triangle meet at O, then the angle at O, between the two bisectors is :
If \( \triangle ABC \cong \triangle ACB \), then \( \triangle ABC \) is Isosceles with :
The figure formed by joining the mid points of the adjacent sides of a rectangle is :
Diagonals AC and BD of trapezium ABCD, in which AB\(||\)DC intersect each other at O. The triangle which is equal in area of \( \triangle \text{AOD} \) is :
The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle, is :
A square and an equilateral triangle have equal perimeters. If the diagonal of the square is \(12\sqrt{2}\) cm, then area of the equilateral triangle is :
If a,b,c are positive real numbers, then \( \sqrt{a^{-1}b} \times \sqrt{b^{-1}c} \times \sqrt{c^{-1}a} \) is equal to :
Calculate the normality of a solution obtained on mixing 100 ml of $\frac{M}{10} H_2 SO_4 , 50 \, ml$ of $\frac{N}{2} HNO_3$ and $25 \, ml $ of $\frac{N}{5} HCl$ solutions.
if aex+bey=c; pex+qey=d and

 the the value of (x, y) is
A 100 mL flask contained \(H_2\) at 200 torr, and a 200 mL flask contained \(He\) at 100 torr. The two flask were then connected so that each gas filled their combined volume. Assume, no change in temperature, total pressure is