If \(x=2 t^3\) and \(y=3 t^4\), then \(\frac{d^2 y}{d x^2}\) is equal to :

Match List-l with List-ll

List-l	List-ll
(A) \(\int_{-a}^a f(x) d x=0\)	(I) \(0\)
(B) \(\int_0^{2 a} f(x) d x=2 \int_0^a f(x) d x\)	(II) 1
(C) \(\int_{-\pi}^\pi \cos x d x\)	(III) \(f\) is an odd function
(D) \(\int_{-1}^1 x^{101} d x+1\)	(IV) \(f(2 a-x)=f(x)\)

Choose the correct answer from the options given below :

A random variable X has the following probability distribution

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of k/4 is

If \(f(x)=3 x^2+10 x-5\), then by using differentials the appropriate value of \(f(2.03)\) is

The slope of the normal to the curve \(y=2 x^2-4\) at \(P(1,-2)\) is:

Let f : R → R be defined as f(x) = [x], where [x] denotes the greatest integer less than or equal to x. Then which of the following statements are correct?
(A) f is one-one but not onto
(B) f is not onto
(C) f is not one-one
(D) f is one-one and onto
Choose the correct answer from the options given below:

For the given values 27, 35, 42, 45, 51, 34, 43; the five yearly moving averages are:

When aniline is reacted with benzoyl chloride, the correct product is

Read the passage and answer the question : There are thousands of varieties of rice in India alone. The diversity of rice in India is one of the richest in the world. Basmati rice is distinct for its unique aroma and flavour and 27 documented varieties of Basmati are grown in India. There is reference to Basmati in ancient texts, folklore and poetry, as it has been grown for centuries. Several attempts have also been made to patent uses, products and processes based on Indian traditional herbal medicine, e.g. turmeric, neem. There has been growing realisation of the injustice, inadequate compensation and benefit sharing between developed and developing countries. The Indian Parliament has recently cleared a Bill that takes such issues into consideration, including patent terms emergency provisions and research and development initiative.
How many varieties of rice India has?

If \(A\) and \(B\) are non singular square matrices of the same order,
then which of the statements are true ?
(A) \((\operatorname{adj} A)(\operatorname{adj} B)=(\operatorname{adj} B)(\operatorname{adj} A)\)
(B) \((A B)^T=A^T B^T\), if \(A^T\) denotes transpose of \(A\)
(C) \((A B)^{-1}=B^{-1} A^{-1}\)
(D) Multiplication of matrices is not commutative

The projection of \(\hat{i}-\hat{j}\) on the vector \(\hat{i}+\hat{j}\) is :

The value of the integral \(I=\int_{-3}^3|x| d x\) is:

Baker's Yeast is: