List of practice Questions

Let A and B be sets. \[A \cap X = B \cap X = \varnothing \quad \text{and} \quad A \cup X = B \cup X \quad \text{for some set } X,\ \text{find the relation between } A \text{ and } B.\]
 

Find foci of the equation \( x^2 + 2x - 4y^2 + 8y - 7 = 0 \)
A bag contains different kinds of balls in which there are 5 yellow, 4 black, and 3 green balls. If 3 balls are drawn at random, then find the probability that no black ball is chosen.
Number of points at which \( f(x) \) is not differentiable, where \[ f(x) = |\cos x| + 3 \text{in} [-\pi, \pi] \]
A point \( P \) in the first quadrant, lies on \( y^2 = 4ax \), \( a > 0 \), and keeps a distance of \( 5a \) units from its focus. Which of the following points lies on the locus of \( P \)?
If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the sum of the magnitude of the projections on each of the axis is
P, Q, R, S, T, U, V are sitting around a table in the same order, for group discussion at equal distances. Their positions are clockwise. If V sits in the north, then what will be the position of 'S'?
Which of the following can be formed from "RECOMMENDATION" word letters?
Ritu purchased 20 dozen bananas at the rate of Rs. 375 per dozen. She sold each one of them at the rate of Rs. 33. What was the percentage profit?
In the half yearly exam, only 60% of the students were passed. Out of these (passed in half-yearly), only 70% students are passed in annual exam. Out of remaining students (who fail in half-yearly exam) 80% passed in annual exam. What percent of the students passed the annual exam?
On Monday, Akash ran 4 km less than the distance he ran on Tuesday. Sanjay, who ran the same distance on Monday and Tuesday, ran 5 km more on Tuesday than the distance Akash ran on Monday. Find the difference between the distance covered by Akash and Sanjay over the two days.
If 'E' stands for +, 'F' stands for –, 'M' stands for ×, 'N' stands for ÷, then 19 M 5 E 39 N 3 F 8 = ?
The time required for fetching and execution of one machine instruction is

Consider the circuit shown below and find the minimum number of NAND gates required to design it. 

How many 32K × 1 RAM chips are needed to provide a memory capacity of 256 K?
What is a potential problem of 1's complement representation of numbers?

Consider the following minterm expression for \( F \): \[ F(P, Q, R, S) = \Sigma(0, 2, 5, 7, 8, 10, 13, 15) \] \(\text{The minterms 2, 7, 8, and 13 are don't care terms. The minimal sum of products form for F is}\)

Suppose we have a 10-bit computer that uses 10-bit 2's complement representation. The number representation of -35 is

Equivalent of the decimal number \( (25.375)_{10} \) in binary form

I have \(\underline{\hspace{1cm}}\) umbrella. I bought it \(\underline{\hspace{1cm}}\) year ago.
A computer producing factory has only two plants \(T_1\) and \(T_2\). Plant \(T_1\) produces 20% and plant \(T_2\) produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that \( P(\text{computer turns out to be defective given that it is produced in plant } T_1) = 10P(\text{computer turns out to be defective given that it is produced in plant } T_2)\), where \( P(E) \) denotes the probability of an event \(E\). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant \(T_2\) is

If \[ \mathbf{a} = \hat{i} - \hat{k}, \mathbf{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k}, \mathbf{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k}, \] \(\text{then }\) [\(\mathbf{a}\)  \(\mathbf{b}\)  \(\mathbf{c}\)] \(\text{ depends on:}\)
 

The graph of the function \( f(x) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right) \) is symmetric about:
Largest value of \( \cos^2 \theta - 6 \sin \theta \cos \theta + 3 \sin^2 \theta + 2 \)
Given two events \( A \) and \( B \) such that the odds in favour of \( A \) are 2:1 and the odds in favour of \( A \cup B \) are 3:1. Consistent with this information, the smallest and largest value for the probability of event \( B \) are given by