List of practice Questions

Evaluate \[ \int \frac{1+x+\sqrt{x+x^{2}}}{\sqrt{1+x}+\sqrt{x}}dx \]

Which of the following set of constraints represents the feasible region (shaded portion) in the figure given below?

Value of the determinant \(\begin{vmatrix} \log_{3}512 & \log_{4}3 \\ \log_{3}8 & \log_{4}9 \end{vmatrix}\) is:

General solution of the differential equation \[ \frac{dy}{dx}=e^{x-y}+3x^{2}e^{-y} \] is:

Particular solution of the differential equation \[ \frac{dy}{dx}+2y^{2}=0,\quad y(1)=1 \] is:

Matrix $A=[a_{ij}]_{3\times3}$ where } \[ a_{ij}= \begin{cases} i+j, & i \ne j \\ i-j, & i=j \end{cases} \] Find matrix $A$.

If \( y = \sqrt{x} + \frac{1}{\sqrt{x}} \), then \( 2x \frac{dy}{dx} \) is equal to

10 people went to a restaurant to have a meal as a group. Of these, 9 had already contributed Rs 400 each, while the 10th person had to give the entire additional amount required to honour the restaurant's bill. How much did this person pay if he had to pay Rs 900 more than the group's average?

The ratio of alcohol to water in two containers, A and B, is 5:3 and 1:3, respectively, with both containers having infinite capacity. Suppose that the aim is to obtain 2.1 litres of liquid, which is composed of equal quantities of alcohol and water. How much liquid should be drawn from A (in litres)?

Rajan invests an amount of INR 15,860 in the names of his three sons Rohan, Sohan and Mohan in such a way that they get the same amount after two, three and four years respectively. If the rate of simple interest is 5% then the ratio of amounts invested among Rohan, Sohan and Mohan will be

Seven people of a family P1, P2, P3, P4, P5, P6 & P7 go on a picnic in a sports utility vehicle. P4 is the sister of P7, P2 is the mother of P6's wife. P6 is the son-in-law of P3. P5 and P7 are the grandsons of P3. Two people in that group of 7 are fathers; two are brothers; and two are mothers, and one is a sister. What is the relationship between P1 and P4?

Five boxes P, Q, R, S, T are stacked one above the other. R is above S but below Q. T is at the bottom. P is just above T. Which box is at the top?

Pointing to a woman, Arun says: She is the daughter of my father's only son. How is the woman related to Arun?

Five years ago, A was three times as old as B. Now, A is twice as old as B. What is A's current age?

A train crosses Park Street every forty-five minutes. About 15 minutes ago, one train has crossed Park Street, and the next train will be crossing Park Street by 9.45 am. What is the time now?

X,Y,W,Z jointly purchased an office space for Rs 84 lakhs. The amount contributed by Y, W and Z put together is three times of X. The amount contributed by X, W and Z put together is 320% of Y. Further, the amount contributed by W is 20% of X, Y and Z put together. What is the contribution of Z?

Suppose the price of liquefied petroleum gas (LPG) increases by 16%, by how much percentage should the consumption of LPG be reduced by the household in order to keep the expenditure on LPG at the same level? (Rounded to two decimals)

There are three products A, B and C and its composition of micronutrients are given below. Ranveer is very health conscious and wants to pick a diet that is highest in protein and lowest in fat. From the options given, which diet should he choose?

Crossroads, a wellness centre allows a member to spend a maximum of one hour in a meditation hall. Shailaja has been in a meditation hall for at least one and a half hours. Which of the following is a valid conclusion if only the above information is used?

In a class a student ranked 35th from top and 32nd from bottom. How many students are there in the class?

A hand-held gaming device takes X and Y as two input values. These values get updated as X=XY/2 and Y=Y+1 at each iteration and the game stops when X is greater than or equal to N. For X=2, Y=4 and N=3008, what would be the final value of X when the game stops?

Let W, X, Y, Z be some entities. Statements: a) All Zs are Ys. b) No Y is a X. c) Every X is a W. Conclusions: I. Some Ws are Zs. II. Zs are not Xs.

Kartik has three solid objects — a cone, a hemisphere, and a cylinder. All three have the same base radius and the same height. He completely immerses each solid in a bucket full of water. What is the ratio of the volumes of the cylinder: cone: hemisphere?