The solution of the differential equation \(\frac{d y}{d x}=\frac{6}{x^2} ; y(1)=3\) is :

The maximum value of \(f(x)=\frac{\log x}{x}\) for \(x\) in \([2, \infty]\) is

The area bounded by \(y=3 x+1, x=0, y=0\) and \(x=a\) is 8 Sq.units. Then value of \(a\) (where \(a>0\) ) is

The value of the expression \(\sin[\cot^{-1}(\cos(\tan^{-1} 1))]\) is:

The angle between the vectors \(\hat{i}-2 \hat{j}+\hat{k}\) and \(3 \hat{i}+2 \hat{j}+\hat{k}\) is:

The value of a washing machine purchased two years ago depreciates at the annual rate of 10%. If its present value is ₹ 50,000, then its value after two years will be :

If \(x, y\) and \(z\) are non zero real numbers, the inverse of matrix \(A=\left[\begin{array}{lll}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right]\) is:

The essential condition for total internal reflection to occur is :

Match List-l with List-II

List-l (Compound/Elements)	List-II (Uses)
(A) Magnesium based alloy is constituent of	(I) Bullets
(B) Lanthanoid oxide	(II) Petroleum cracking
(C) Mixed oxides of Lanthanoids are employed in	(III) Television screen
(D) Misch metal	(IV) Lanthanoid metal and iron

Choose the correct answer from the options given below :

(A) The degree of differential equation \(\frac{d^2 y}{d x^2}+\sin \left(\frac{d y}{d x}\right)=0\) is 2
(B) The degree of differential equation \(\frac{d}{d x}\left(\frac{d y}{d x}\right)+\left(\frac{d y}{d x}\right)^3+\sin x=0\) is 1
(C) The order of differential equation \(2 x^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+y=0\) is 2
(D) The number of arbitrary constants in a particular solution of a differential equation of third order are 3
(E) The integrating factor of the differential equation \(\frac{d y}{d x}-y=\cos x\) is \(e^{-x}\)
Choose the correct answer from the options given below:

Which of the following statements are correct?
A. p-Nitroaniline is a stronger base than aniline
B. Aniline is weaker basic than o-nitro aniline
C. Aniline is a weaker base than ethylamine
D. p-methyoxyaniline is stronger base than aniline
E. Aniline is weaker base than ammonia
Choose the correct answer from the options given below:

The magnetic flux density at a point on the axis of a long solenoid having 1000 turns \(/ m\) when it is carrying a current of 3.4 A is nearly,

Read the following passage carefully and answer the given questions.
Theory of Evolution
The evolution of life is a gradual process through which simple organisms are transformed into complex life forms over billions of years. It involves genetic changes, adaptation to the environment, and the emergence of diversity in species. Fossil records provide evidence of extinct life forms and transitional stages. Evolution is influenced by factors such as mutation, genetic recombination, and environmental pressure, shaping the biodiversity we see today. Charles Darwin and Alfred Russel Wallace were pioneering naturalists who developed the theory of evolution by natural
selection. The voyage of the H.M.S. Beagle was significant in the development of Darwin's theory of evolution as-