A person invested ₹ \(10000\) in a stock of a company for \(6\) years.
The value of his investment at the end of each year is given below:

2018	2019	2020	2021	2022	2023
₹11000	₹11500	₹13000	₹11800	₹12200	₹14000

The compound annual growth rate (CAGR) of his investment is:
[Given (1.4) \({ }^{\frac{1}{8}}=1.058\) ]

The number of all onto functions from the set \(\{1,2, \ldots, n\}\) to itself is

The value of \(k\) for which the function \(f(x)=\left\{\begin{array}{ll}\frac{1-\cos 8 x}{16 x^2} & , \text { if } x \neq 0 \\ k & , \text { if } x=0\end{array}\right.\) is continuous at \(x=0\) is :

The product of the order and degree of the following differential equation :
\(x \left( \frac{d^2y}{dx^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + y^2 = 0\)

Two persons A and B throw a die alternately till one of them gets a six and wins the game. If A begins, then the probabilities of winning of A and B respectively are

Pipe A can fill a tank in 24 hours and pipe B in 32 hours. If both the pipes are opened in an empty tank at the same time, then the time taken to fill the tank is:

If the probability distribution of a random variable X is as given below :

X	-1	0	1	2	3
P(X)	K	\(\frac{1}{5}\)	2K	\(\frac{3}{10}\)	K

Then the value of K is:

\(\int_1^2 \frac{1}{x(x+1)} d x, x>0\) equals

Match List-l with List-II:

List-I (Scientists)	List-II (Discovery)
(A) Sutton and Boveri	(I) X-Body
(B) Sturtevant	(II) Chromosomal Theory of Inheritance
(C) Henking	(III) Transformation in bacteria
(D) Griffith	(IV) Genetic maps

Choose the correct answer from the options given below:

Match List-I with List-II

List-I	List-II
(A) Electric Field	(I) [ LTA ]
(B) Electric Flux	(II) \( [ L^2 ] \)
(C) Electric Dipole Moment	(III) \( [ M L T^{-3} A^{-1} ] \)
(D) Area Vector Element	(IV) \( [ M L^3 T^{-3} A^{-1} ] \)

Choose the correct answer from the options given below :

Two similar coils of radius r are placed concentrically with their planes at right angles to each other. The currents flowing in them are I and 3I, respectively. The resultant magnetic induction at the centre is

Read the passage carefully and answer the given questions.
Recombinant DNA Technology Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
Which one of the following techniques is used to amplify a specific DNA sequence?

Consider the following statements
(A) Corpuscular model predicted that if the ray of light bends towards the normal after refraction then the speed of light would be greater in the second medium
(B) In optical fibre, the refractive index of the core is kept higher than cladding.
(C) Diffraction due to clouds is efficient in equal measures for all wavelengths
(D) Light travels faster in glass than in air.
(E) When light reflects from an air glass plate interface, the reflected wave suffers a phase change of \( \pi \).
Choose the correct answer from the options given below :