List of practice Questions

The greatest number of four digits which is divisible by 15, 25, 40, and 75 is:
If \( x^2 + 2(K+2)x + 36 = 0 \) has equal roots, then \( K = \)

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

If \( x^4 - x^3 + 2x^2 + ax + b \) is exactly divisible by \( x^2 - 3x + 2 \), then \( (a, b) \) is
The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is ?
The roots \(\alpha\), \(\beta\) of the equation \(3x^2 + \lambda x - 1 = 0\), satisfy \( \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15 \). The value of \( (\alpha^3 + \beta^3)^2 \) is
If Rakesh borrows Rs. 36,000 from Sathesh at a rate of interest 6% S.I, at the end of four years, how much interest does Rakesh have to pay?
If $(a + b\sqrt{3})^2 = 52 + 30\sqrt{3}$, where $a$ and $b$ are natural numbers, then $a + b$ equals ?
A, B and C are three partners. They all together invested Rs 42,000 in a business. At the end of the year, A received Rs 377.50, B Rs 1085 and C Rs 637.50 as profit. The difference between the investments of B and C is:
The average age of 5 children is 8 years. If the age of the father is included to the children average becomes 13, then the age of the father is
If \( \frac{a}{c} = \frac{c}{d} = \frac{e}{f} \), then
The Standard Deviation of 2, 4, 6, 8, 10 is
A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is
The greatest number of 5 digits which when divided by 4, 5, 6, 7, and 8 leaves 1, 2, 3, 4, and 5, respectively, as remainders is:
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 \( y = \tan^{-1}(x) \), then \( \frac{dy}{dx} = \)
If each exterior angle of a regular polygon is \( 36^\circ \), then the number of sides of the polygon is
If \[ \frac{28.5}{5} \, \frac{21.5}{15} = \frac{15.5}{30} = \left( \frac{x}{4} \right)^3 - 3, \] then the value of \(x\) 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
Evaluate the following expression: \[ \frac{0.963 \times 0.963 - 0.963 \times 0.037 + 0.037 \times 0.037}{0.963 \times 0.963 \times 0.963 + 0.037 \times 0.037 \times 0.037} \]
If the 5th term of \( \left( 2x^2 + \frac{3}{x} \right)^5 \) is 10, then \( x = \)
Evaluate the limit: \[ \lim_{x \to 2} \left[ \frac{1}{x - 2} - \frac{1}{x^2 - 3x + 2} \right]. \]
If \( A \) is a non-singular 3x3 matrix, then \( \left| 5A \right| \) is
After allowing a discount of 12% on the marked price, a shopkeeper still gains 21%. How much (in percentage) is the marked price above the cost price?
By selling an item at a discount of 20%, the profit is 20%. The profit percentage, if the item is sold at a discount of 10%, is: