List of practice Questions

The number of minterms in an \( n \) variable truth table is:
The reduced form of the Boolean function \( F = xyz + xyz' + x'yz + zy'z \) is

Consider the following Boolean expression for F: \( F(P, Q, R, S) = PQ + PQR + \overline{P}QR \). The minimum sum of products form of F is
 

A CPU generates 32-bit virtual addresses. The page size is 4 KB. The processor has a translation look-aside buffer (TLB) which can hold a total of 128 page table entries and is 4-way set associative. The minimum size of the TLB tag is:
Which of the following reasons according to the passage provide material comforts to people in case of science?
Select the most appropriate preposition to fill in the blank. A baby sister is someone who looks \(\underline{\hspace{1cm}}\) other people's children.
Select the most appropriate preposition to fill in the blank.
We haven't been to Delhi \(\underline{\hspace{1cm}}\) almost five years.
Which of the following statements according to the passage is correct:
Choose the right option which will complete the first word and begin the second word.
E X(....) A C L E 
A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is
The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2, and 6, then the mean deviation from the mean of the data is:
A speaks truth in 60% and B speaks the truth in 50% cases. In what percentage of cases they are likely to contradict each other while narrating some incident?
If \[ \int f(x) \, dx = g(x), \text{ then } \int x^5 f(x^3) \, dx \] is
If \[ \lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^2}{x^2 - k^2}, \text{ then find } k \]

If the equation \[ |x^2 - 6x + 8| = a \] \(\text{has four real solutions, then find the value of \( a \):}\)
 

If A and B are square matrices such that \( B = -A^{-1}BA \), \(\text{ then }\) \( (A + B)^2 \) is

If \( f(x) \) is a polynomial of degree 4, \( f(n) = n + 1 \) and \( f(0) = 25 \), then find \( f(5) \)?

The maximum value of \( f(x) = (x - 1)^2 (x + 1)^3 \) is equal to \[ \frac{2^p 3^q}{3125} \,\, \text{then the ordered pair of} (p, q) \text{ will be} \]

If \( n_1 \) and \( n_2 \) are the number of real valued solutions of \( x = |\sin^{-1} x| \) \(\text{and}\) \( x = \sin(x) \text{ respectively, then the value of} \, n_2 - n_1 \text{ is:}\)

If \( \theta = \cos^{-1} \left( \frac{3}{\sqrt{20}} \right) \) is the angle between \( \mathbf{a} = \hat{i} - 2x\hat{j} + 2y\hat{k} \) and \( \mathbf{b} = x\hat{i} + \hat{j} + y\hat{k} \), then the possible values at \( (x, y) \) that lie on the locus are:

A real valued function \( f \) is defined as \[ f(x) = \begin{cases} -1 & \text{if} \, -2 \leq x \leq 0 \\ x - 1 & \text{if} \, 0 \leq x \leq 2 \end{cases} \] \(\text{Which of the following statements is FALSE?}\)

A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. The tip of the pillar subtends angles \( \tan^{-1}(3) \) and \( \tan^{-1}(2) \) at A and B respectively. Which of the following choices represents the height of the pillar?
A university is offering elective courses in Mathematics, Economics, and Sociology. Each of its 100 undergraduate students has to opt for at least one of these electives. Course enrollment data showed that 47 students enrolled for Mathematics, 47 students enrolled for Economics, and 57 students enrolled for Sociology. If 7 students enrolled for all three courses, how many students enrolled for exactly one course?
Study the diagram and answer the question that follows:
Hemant deposits 10% of his salary in PF. He saves 30% of remaining salary. The ratio of his expenses on medicine and groceries is 3 : 4 of remaining salary after saving. If his expenses in medicine was Rs. 2700, then find his monthly salary.