Mr. Jayesh plans to save amount for higher studies of his daughter, required after 10 years. How much amount should he save at the beginning of each year to accumulate Rs.1,00,000 at the end of 10 years, if rate of interest is 12% compounded annually? [Given \((1.12)^{11}\) = 3.5]

A bag contains 4 red and 6 green balls. A ball is drawn at random, its colour is noted and is returned to the bag.
One additional ball of the colour drawn is put in the bag. Again a ball is then drawn from the bag. The probability of this ball to be of green colour is

Two curves \(x^3-3 x y^2+2=0\) and \(3x^2 y-y^3=2\) :

\(\int_{-\pi}^\pi \frac{e^{\sin x}}{e^{\sin x}+e^{-\sin x}} d x\) is equal to:

The image of the point \((3,-2,1)\) in the plane \(3 x-y+4 z=2\) is:

Let \(P=\left[a_{i j}\right]\) be a \(3 \times 3\) matrix and let \(Q=\left[b_{i j}\right]\) be a \(3 \times 3\) matrix,
where \(b_{i j}=2^{i+j} a_{i j}\) for \(1 \leq i, j \leq 3\).
If the determinant of \(P\) is 2 , then the determinant of the matrix \(Q\) is ___________ .

If \(f(x)=x^3 e^{-x}\), then the value of \(f^{\prime \prime}(1)\) is equal to

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.
Alfred Russel Wallace, a naturalist, arrived at conclusions similar to Darwin while working in:

The partial vapour pressure of an electrolyte at the following concentrations,
decreases in the order
(A) 0.5 M
(B) 0.1 M
(C) 0.05 M
(D) 0.001 M
Choose the correct answer from the options given below:

A \( 14.0 \, \mu\text{F} \) capacitor is connected to a 220 V, 50 Hz source. The value of peak current in the circuit is (Given: \( \pi = \frac{22}{7} \) and \( \sqrt{2} = 1.414 \)):

Match List-I with List-II

List - I	List - II
(A) Point of minima of \(f(x)=|x+1|\)	(I) 1
(B) Minimum value of \(f(x)=|x|\)	(II) -1
(C) Maximum value of \(f(x)=1-x^2\)	(III) 2
(D) Minimum value of \(f(x)=2+\sin ^2 x\)	(IV) 0

Choose the correct answer from the options given below :

Which of the following is an example of nuclear fusion ?

The conductivity of electrolytic (ionic) solution depends on
(A). Nature of electrolyte added
(B). Nature of solvent
(C). Temperature
(D). Size of ions produced
Choose the correct answer from the options given below :