List of practice Questions

\(\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} - \sqrt{5}} + \frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} + \sqrt{5}} \) \(=\)

If \(A = \begin{bmatrix} 1 & 8  0 & 1 \end{bmatrix}\), then \(A^8 =\)

Which term in the expansion of \(( x - \frac{1}{x^3})^{40}\) is independent of \(x\)?

When two dice are thrown, what is the probability of getting the sum 7?
A coin is tossed 6 times. What is the probability of getting head at least once?
What is the Harmonic Mean of 3, 4, 5, and 6?
The median of 260, 240, 210, 190, 180, 220, 230, 250 is
The arithmetic mean of some numbers is 18 and their median is 16. Then what is the mode?
The Standard Deviation of 2, 4, 6, 8, 10 is
The mean deviation of 3, 4, 5, 6, 7 is
P and Q are two sets such that \( n(P) = 3 \) and \( n(Q) = 4 \). A relation from \( P \) into \( Q \) is selected at random. What is the probability that the relation is not a function?
\[ \lim_{x \to \infty} 5 \left( 1 + \frac{4}{x} \right)^x = \]
If \( y = x(x - 1)(x - 2) \), then the derivative \( \frac{dy}{dx} \) is
If each exterior angle of a regular polygon is \( 36^\circ \), then the number of sides of the polygon is
What is the area, in square units, of the triangle formed by the points \( (3, 2), (3, -6) \) and \( (5, 2) \)?
The equation of the straight line passing through the points \( (1, -5) \) and \( (-2, 4) \) is
The arithmetic mean of 7.6, 6.8, 5.4, 6.4, 7.2, (4)8, 6.6, and 5.8 is
What is the Geometric Mean of 12, 30, and 75?
A, B and C start a business with investments of Rs.6,000, Rs.7,000, and Rs.8,000 respectively. The profit at the end of the year is Rs.3,150. Then share of B in the profit is
The father is 7 times older than his son. After 5 years the sum of their ages would be 50 years. The son’s age at present is
\[ \tan \left( -\frac{23}{3} \pi \right) = \]
If the angle of elevation of the top of a tower of height 100 meters from a point to its foot is \( \tan^{-1} \left( \frac{4}{5} \right) \), then what is the distance from the point to its foot in meters?
If \( x^4 - x^3 + 2x^2 + ax + b \) is exactly divisible by \( x^2 - 3x + 2 \), then \( (a, b) \) is
\[ (1 + \sqrt{2})^4 + (1 - \sqrt{2})^4 \]
If \( A \) is a non-singular 3x3 matrix, then \( \left| 5A \right| \) is