List of practice Questions

M is a square matrix of order 3. If \[ M(\operatorname{adj} M)= \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}, \] then the value of \[ |M+\operatorname{adj} M| \] is equal to:

The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is:

If \[ f(x)= \begin{cases} \dfrac{x-2}{|x-2|}+a, & x<2, \\[6pt] a+b, & x=2, \\[6pt] \dfrac{x-2}{|x-2|}+b, & x>2, \end{cases} \] is continuous at $x=2$, then

If $ P(A) = \frac{3}{5} $, $ P(\overline{B}) = \frac{4}{7} $, and $ P(A \cup B) = \frac{2}{3} $, which of the following are correct?

(A) $ P(A \cap B) = \frac{17}{105} $
(B) $ P(A \mid B) = \frac{17}{45} $
(C) A and B are independent events
(D) $ P(B \mid A) = \frac{17}{36} $

A sequence of DNA has 300 nitrogenous base pairs, of which 75 are Guanine. What is the number of Thymine in this sequence?

Statement I: Nitrogen in pyridine cannot be estimated by Kjeldahl's method
Statement II: Nitrogen in pyridine changes to ammonium sulphate when heated with conc. H$_2$SO$_4$ in Kjeldahl's method.
Read the above given statements and choose the correct answer from the given options.

Tribal republic of Yaudheyas was located in:

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24t$ and $43.6t - 4.9t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2$ s is _______.

The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is: ____.

Which among $ 2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6} $ and $ 12^{1/12} $ is the largest?

Gyan Prakash left for his college in his car -
(J) He drove 15 km towards the North and then 10 km towards the West.
(K) He then turned South and covered 5 km.
(L) Further, he turned to the East and moved 8 km.
(M) Finally, he turned right and drove 10 km.
How far and in which direction is he from his starting point?

For $n\in\mathbb{N}$, if \[ y=ax^{n+1}+bx^{-n}, \] then \[ x^2\frac{d^2y}{dx^2} \] is equal to:

Fill in the blanks with the appropriate words and complete the given sentence.
A well-known chef, started his career __________________ the age of 15 when the prodigy __________________ cooking under Eric Ripert at the iconic New York restaurant.

Match List-I with List-II (Traditional Textiles):