Sudhir had Rs 45,000. He lent a part of it at 4% p.a. and the remaining at 10% p.a. simple interest. He earned a total profit at 8% p.a. on the money lent, what sum did he lend at 10% p.a ?

Which of the following inequalities holds true?
(A) \(\sqrt{5}+\sqrt{3}>\sqrt{6}+\sqrt{2}\).
(B) If \(a>b\) and \(c<0\), then \(\frac{a}{c}<\frac{b}{c}\).
(C) \(\frac{1}{x^2}>\frac{1}{x}>1\), if \(0<x<1\).
(D) If \(a\) and \(b\) are positive integers and \(\frac{a-b}{6.25}=\frac{4}{2.5}\), then \(b>a\).
Choose the correct answer from the options given below:

Match List-l with List-ll

List-l (Differential Equation)	List-ll (Order and degree of differential equation)
(A) \(\frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^2=e^{\frac{d y}{d x}}+1\)	(I) Order = 1, Degree = 2
(B) \(\left(\frac{d^2 y}{d x^2}\right)^2+4\left(\frac{d y}{d x}\right)^3=e^y-1\)	(II) Order = 2, Degree = 1
(C) \(3\left(\frac{d y}{d x}\right)+4 y+e^y=\frac{d x}{d y}\)	(III) Order = 2 , Degree = 2
(D) \(\frac{d^2 y}{d x^2}+3\left(\frac{d y}{d x}\right)=\left(e^y+\frac{d y}{d x}\right)^2\)	(IV) Order = 2, Degree = Not defined

Choose the correct answer from the options given below :

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

If x = a sin t and y = a \(\left(\cos t+\log \tan \frac{t}{2}\right)\) then \(\frac{d^2 y}{d x^2}\) is:

The area of the region bounded by the parabola \(y^2=x\) and the straight line 2y = x is

Out of the given statement, choose the correct statement.
(A) The direction ratios of the vector \(\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}\) is \(3,-1,4\).
(B) If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \cos \theta\).
(C) The unit vector in the direction of vector \(\vec{a}=\hat{i}+2 \hat{j}-2 \hat{k}\) is \(\hat{a}=\frac{1}{3}(\hat{i}+2 \hat{j}-2 \hat{k})\).
(D) If \(\vec{a}=3 \hat{i}\) and \(\vec{b}=4 \hat{j}\) then \(\vec{a} \cdot \vec{b}=12\).
(E) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle then its area is given of \(\frac{1}{2}|\vec{a} \times \vec{b}|\).
Choose the correct answer from the options given below :

What is the full form of ELISA ?

What will happen during the electrolysis of aqueous solution of \(CuSO_4\) by using platinum electrodes?
A. Copper will deposit at cathode.
B. Copper will deposit at anode.
C. Oxygen will be released at anode.
D. Copper will dissolve at anode.
Choose the correct answer from the options given below:

Choose the phenomenon from the following, which shows that light is a transverse wave.

Let \(\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)\). Then \(y\) is :

Read the passage carefully and answer the Questions
The decomposition of \(N_2O_5\ (g)\) is given as
\(N_2O_5(g) \rightarrow 2NO_2(g) + \frac{1}{2}O_2(g)\)
The above reaction is found to be of first order.
Choose the correct statement about the rate of the reaction:

Observe the given diagram and answer the following question :

Genetically engineered insulin was made by Eli Lilly in 1983 by using :