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

If \( A \) is a non-singular 3x3 matrix, then \( \left| 5A \right| \) is
If \( 8^{2x - 4} = 16^{x - 2} \), then \( x = \)
The volumes of two cones of equal height are in the ratio \( 1849 : 961 \). What is the ratio of their radii?
A sum becomes double in 8 years at simple interest. What is the rate percent per annum?
If \( \frac{a}{c} = \frac{c}{d} = \frac{e}{f} \), then
The solution set of \( x^2 + 6x < 91 \) is
If the area of a square field is 7200 sq. m, then the length of its diagonal in meters is
Three numbers in the ratio 2:3:4 have their sum 270. Then the L.C.M. is
The G.C.D. and L.C.M of two numbers are 12 and 252 respectively. If one number is 36, then the other number is
The cost price of 16 pens is the same as the selling price of 12 pens. The percentage of profit is
Evaluate the limit: \[ \lim_{x \to 2} \left[ \frac{1}{x - 2} - \frac{1}{x^2 - 3x + 2} \right]. \]
The distance between the lines \( 3x + 4y + 1 = 0 \) and \( 6x + 8y - 1 = 0 \) is
If the 5th term of \( \left( 2x^2 + \frac{3}{x} \right)^5 \) is 10, then \( x = \)
The equation of the line passing through the point \( (2, -3) \) and perpendicular to the segment joining the points \( (1, 2) \) and \( (-1, 5) \) is
If \( y = \tan^{-1}(x) \), then \( \frac{dy}{dx} = \)
If a flag of 6 meters height, placed on top of a tower, throws a shadow of \( 2\sqrt{3} \) meters along the ground, then the angle in degrees that the sun makes with the ground is
If \( \sin(\theta) = \frac{15}{17} \), then for \( 0^\circ < \theta < 90^\circ \), \[ \frac{15 \cot(\theta) + 17 \sin(\theta)}{8 \tan(\theta) + 16 \sec(\theta)} \]
Evaluate the limit: \[ \lim_{x \to 0} \frac{\sqrt[3]{8 + x} - 2}{x}. \]
If \( x^2 + 2(K+2)x + 36 = 0 \) has equal roots, then \( K = \)
A, B and C can do a piece of work in 4, 5 and 7 days respectively. If they get Rs.415 for working together to complete the job, then A's share is
If \[ \left( \frac{2}{1} \right)^x \left( \frac{-1}{1} \right)^y = \left( \frac{4}{5} \right), \] then find the value of \( 2x - 3y \).
A bag contains 3 red balls, 4 white balls, and 7 black balls. The probability of drawing a red or a black ball is
If \( y = x + \frac{1}{x} \) then \( x^4 + x^3 - 4x^2 + x + 1 = \)
If \( K + 2, 4K - 6, 3K - 2 \) are three consecutive terms of an arithmetic progression, then the value of \( K \) is
The ratio of the sides of a rectangle is 4 : 9 and the area is equal to 144 sq.m. The perimeter in meters is