List of practice Questions

Find the value of \( 4\tan^2 45^\circ + \cos^2 30^\circ - \sin^2 60^\circ \).
Find the roots of the equation \( x + \frac{1}{x} = 3, \quad x \neq 0 \).
Find the mean of the following data:
\[ \begin{array}{c|c|c|c|c|c} \text{Variable} & 4 & 6 & 8 & 10 & 12 \\ \hline \text{Frequency} & 4 & 8 & 14 & 11 & 3 \end{array} \]
A circle has a radius of 6 cm. Find the length of that chord which is at a distance of 4 cm from the center.
If one zero of the polynomial \( (a+2)x^2 - 3ax -2 \) is negative of the other, then find the polynomial.
The sum of the digits of a two-digit number is 9. If 9 is added to the number, the digits of the number are reversed. Write the equation for these statements.
Solve the pair of equations \( \sqrt{2} x + \sqrt{3}y = 0 \) and \( \sqrt{3}x - \sqrt{8}y = 0 \) by the method of substitution or elimination.
The length, breadth, and height of a cuboid are 26 m, 14 m, and 6.5 m, respectively. Find the lateral surface area of the cuboid.
The curved surface area and volume of a cylinder are 264 m\(^2\) and 396 m\(^3\) respectively. Find the radius and height of the cylinder.
The base radius of a cone is \( 7\sqrt{7} \) cm and its height is 21 cm. Find the volume of the cone.
If \( q \) is a positive integer, which of the following is an odd positive integer?
The H.C.F. of two consecutive odd numbers is:
Find the area of the triangle whose vertices are \( (0,4) \), \( (3,6) \), and \( (-8,-2) \).
Evaluate: \( \csc 39^\circ \cos 51^\circ + \tan 21^\circ \cot 69^\circ - \sec^2 21^\circ \)
Prove that \( \sec^4 \theta - \tan^4 \theta = 1 + 2\tan^2 \theta \).
Find the zeroes of the quadratic polynomial \( x^2 - 3 \) and verify the relationship between the zeroes and the coefficients.
Divide polynomial \( x^4 - 2x^3 - x + 2 \) by the polynomial \( x^2 - 3x + 2 \).
Using Euclid division algorithm, find the HCF of 252 and 594.
The simplest form of \( 0.\overline{3} + 0.\overline{4} \) is:
If \( 156 = 2^x \times 3^y \times 13^z \), then \( x + y + z = \)?
\( \sqrt{10} \times \sqrt{15} \) is:
In the form of \( \frac{p}{2^n \times 5^m} \), 0.105 can be written as:
If H.C.F. of two numbers is 25 and L.C.M is 50, then the product of numbers will be:
If in the division algorithm \( a = bq + r \), given \( b = 61 \), \( q = 27 \), and \( r = 32 \), then the value of \( a \) is:
Which of the following is an arithmetic progression (A.P.)?