List of practice Questions

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
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