List of practice Questions

A thief is spotted by a policeman from a distance of 100m. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8 km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken ?

If ⁿC₉ = ⁿC₃. what is n?

Given expression:
\(\frac{(0.682)^2-(0.318)^2}{0.682-0.318}\)

Among P, Q, R, S, T, each having different weight. R is heavier than only P and S is lighter than Q and heavier than T. Who among them is the heaviest?

First two words are related in a certain way in:
Transition: Change:: Immobility: ?
Identify the suitable word in place of? so that third and fourth words also become relatable the some manner.

Sourav completes a journey in \(5\frac12\) hours. If he covers half of the distance at \( 5\ km/h\) and the remaining distance at \(6\  km/h\), then find the total distance covered by him.

Which of the following statements are true for rectangles?
A. All interior angles are right angles.
B. Diagonals are perpendicular to each other.
C. Diagonals are equal.
D. Opposite angles are supplementary
Choose the correct answer from the options given below:

The price of rice increases by 30%. A family reduced its consumption so that the expenditure of the rice is up only by 10%. If the total consumption of the rice before the price rise was 10 kg per month, then the consumption of rice per month at present (in kg) is:

What should replace the question mark ?
\(\frac{854\times 854 × 854-276 × 276 × 276}{854 \times854 + 854×276+276 × 276}=?\)

Area lying between the curves \(y^2 = 9x\) and y = 3x is:

The present value (in ₹.) of a perpetuity of ₹.3600 payable at the end of each quarter, if the interest rate is 9% per annum compounded quarterly, is:

In reference to sampling, match List I with List II

Choose the correct answer from the options given below:

If f(x)= \(\frac{\sqrt{4} + x - 2}{x}, If \ x \neq 0 \\ k \ If \ x \neq 0\) ,is continuous at x = 0, then the value of k is:

The mean of Binomial distribution \(B(4,\frac13) \) is : 

Which of the following can be the probability distribution of a random variable ?

If the objective function for an LPP is \( z=3x-4y \) and corner points for bounded feasible region are \((5, 0) (6, 5) \)and \((4, 10)\), then:
(A) maximum value of \(z\) is \(2\)
(B)minimum value of\( z\) is \(2\)
(C) maximum value of \(z \)is at \((5, 0)\)
(D) no maximum value of\( z\)
(E)maximum value of \(z\) is \(15\)
Choose the correct answer from the options given below:

If f(x) =\(\begin{cases}\frac{x^2-9}{x-3}, x≠3 \\ 5, x=3 \end {cases}\) then f(x):

A, B and C can do a work in 10, 12 and 15 days respectively. In how many days will the work be completed if B is assisted by both A and C on every third day?

The relation R in the set A = {1, 2, 3, 4} is given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} is :

Match List I with List II

List I (Functions)		List II (Derivatives)
A.	f(x)=sin-1x	I.	\(\frac{1}{1+x^2}\), x ∈ R
B.	f(x)=tan-1x	II.	\(\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
C.	f(x)=cos-1x	III.	\(-\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
D.	f(x)=sin-1x	IV.	\(-\frac{1}{1+x^2}\), x ∈ R

Choose the correct answer from the options given below :

Which of the following statements is true ?
A. If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.
B. Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
C. In a LPP, the minimum value of the objective function Z = ax + by (a, b > 0) is always 0 if origin is one of the corner points of feasible region.
D. In a LPP the max value of the objective function Z = ax + by is always finite.
Choose the correct answer from the options given below :

The maximum value of the function y = 2 - |x - 3| is :

For the function f(x) = 2e^5x + 10, which of the following is the most appropriate option.

If x=5t and \(y=\frac5t,\) then \(\frac{d^2y}{dx^2}\) at t=1 is