List of practice Questions

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
The arithmetic mean of 7.6, 6.8, 5.4, 6.4, 7.2, (4)8, 6.6, and 5.8 is
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
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
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
The distance between the lines \( 3x + 4y + 1 = 0 \) and \( 6x + 8y - 1 = 0 \) 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?
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 \( x^2 + 2(K+2)x + 36 = 0 \) has equal roots, then \( K = \)
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
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