List of top Questions asked in Andhra Pradesh State Council of Higher Education

\( \frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} - \sqrt{5}} + \frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} + \sqrt{5}} = \)
A coin is tossed 6 times. What is the probability of getting head at least once?
When two dice are thrown, what is the probability of getting the sum 7?
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?
What is the Harmonic Mean of 3, 4, 5, and 6?
What is the Geometric Mean of 12, 30, and 75?
The Standard Deviation of 2, 4, 6, 8, 10 is
The arithmetic mean of some numbers is 18 and their median is 16. Then what is the mode?
The median of 260, 240, 210, 190, 180, 220, 230, 250 is
The mean deviation of 3, 4, 5, 6, 7 is
\[ \lim_{x \to \infty} 5 \left( 1 + \frac{4}{x} \right)^x = \]
If each exterior angle of a regular polygon is \( 36^\circ \), then the number of sides of the polygon is
The equation of the straight line passing through the points \( (1, -5) \) and \( (-2, 4) \) is
If \( y = x(x - 1)(x - 2) \), then the derivative \( \frac{dy}{dx} \) is
The arithmetic mean of 7.6, 6.8, 5.4, 6.4, 7.2, (4)8, 6.6, and 5.8 is
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?
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
\[ \tan \left( -\frac{23}{3} \pi \right) = \]
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
If \( A \) is a non-singular 3x3 matrix, then \( \left| 5A \right| \) is
\[ (1 + \sqrt{2})^4 + (1 - \sqrt{2})^4 \]
If \( x^4 - x^3 + 2x^2 + ax + b \) is exactly divisible by \( x^2 - 3x + 2 \), then \( (a, b) \) is
The solution set of \( x^2 + 6x < 91 \) is
If \( \frac{a}{c} = \frac{c}{d} = \frac{e}{f} \), then
A sum becomes double in 8 years at simple interest. What is the rate percent per annum?