\(\int \frac{d x}{\sqrt{5-4 x-x^2}}\) is equal to :

Which of the following are linear first order differential equations?
(A) \(\frac{d y}{d x}+P(x) y=Q(x)\)
(B) \(\frac{d x}{d y}+P(y) x=Q(y)\)
(C) \((x-y) \frac{d y}{d x}=x+2 y\)
(D) \(\left(1+x^2\right) \frac{d y}{d x}+2 x y=2\)
Choose the correct answer from the options given below:

Which of the following is a correct statement?

Which of the following is NOT correct about the Central Limit Theorem?

If the function
\(f(x)=\left\{\begin{array}{ll}a x+2, & x \leq 1 \\x^2+3 x+b, & x>1\end{array}\right.\)
is differentiable at \(x=1\), then the value of \((2 a+b)\) is

If the lines \(\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{\lambda}\) and \(\frac{x}{1}=\frac{y}{2 \lambda}=\frac{z}{3}\) are perpendicular to each other, then \(\lambda\) is equal to

Let \(P\) and \(Q\) be any two invertible matrices of the same order. Then Match List-I with List-II

List - I (Matrix)	List - II (Equivalent matrix)
(A) \((P Q)^{-1}\)	(I) \(Q^{-1} P\)
(B) \(\left(P^{-1} Q\right)^{-1}\)	(II) \(Q P^{-1}\)
(C) \(\left(P Q^{-1}\right)^{-1}\)	(III) \(Q^{-1} P^{-1}\)
(D) \(\left(P^{-1} Q^{-1}\right)^{-1}\)	(IV) \(Q P\)

Choose the Correct answer from the options given below :

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders.
What is the probability of having a daughter to a couple expecting their first child?

If \(\int_0^1 \frac{e^x}{1+x} d x=K\), then \(\int_0^1 \frac{e^x}{(1+x)^2} d x\) is equal to:

Identify the correct sequence of events for the technique of DNA fingerprinting.
(A) Hybridization using labelled VNTR probe, followed by detection of hybridized DNA fragments by autoradiography
(B) Transfer of separated DNA fragments to synthetic membranes, such as nitrocellulose or nylon
(C) Isolation and digestion of DNA by restriction endonucleases
(D) Separation of DNA fragments by electrophoresis
Choose the correct answer from the options given below:

Grignard's reagent synthesis is always carried out in dry ether because

Consider the following data

Year (X)	2014	2016	2018	2020	2022	2024
Profit(in Rs. Thousand) (Y)	7	9	10	12	14	14

Then for the above data the equation of straight line trend by method of least square is given by:

Arrange the following in the decreasing order of their wavelengths.
(A) microwaves
(B) ultraviolet rays
(C) infrared rays
(D) gamma rays
Choose the correct answer from the options given below: