\(x\) speaks truth in \(60 \%\) and \(y\) in \(50 \%\) of the cases.
The probability that they contradict each other while narrating the same fact is:

\(\int_0^1 \tan ^{-1}\left(\frac{2 x-1}{1+x-x^2}\right) d x\) is equal to :

The slope of the normal to the curve \(x=a \cos ^3 \theta, y=a \sin ^3 \theta\) at \(\theta=\frac{\pi}{4}\) is :

The function f defined by \((x)=\left\{\begin{array}{ll}a x+1, & x \leq 3 \\ b x+3, & x>3\end{array}\right.\) is continuous at x = 3 if

The probability distribution of a random variable \(x\) is, \(P(x)=\frac{k}{2^x}, x=0,1,2,3\). Then
Match List-I with List-II

List-I	List-II
(A) k	(I) \(\frac{2}{15}\)
(B) \(P ( x =1)\)	(II) \(\frac{1}{5}\)
(C) \(P (1<x<3)\)	(III) \(\frac{8}{15}\)
(D) \(P(x \geq 2)\)	(IV) \(\frac{4}{15}\)

Choose the correct answer from the options given below :

The value of \(\int_{-3}^2 x^2|2 x| d x\) is :

The matrix \(A = \begin{bmatrix} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0 \end{bmatrix}\) is a

Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
Which of the following is non-reducing sugar?

Match List - I with List - II.

List - I	List - II
(A) Somaclone	(I) Pomato
(B) Totipotency	(II) Virus free regions in plant
(C) Meristem	(III) Genetically identical to original plant used in tissue culture
(D) Somatic hybrid	(IV) Stem cells

Choose the correct answer from the options given below :

If an electrolyte on dissociation gives \(\nu_{+}\) cations and \(\nu_{-}\) anions, then its limiting molar conductivity is given by

An airliner is flying due east from the USA to France. The Earth's magnetic field acts at \( 60^{\circ} \) to the horizontal and has a strength of \( \sqrt{3} \times 10^{-4} \, \text{T} \), and the aircraft speed is \( 300 \, \text{ms}^{-1} \). The wing span of the aircraft is 60 m. The potential difference induced between the tips of the wings is :

Identify the correct sequence of structures formed during spermatogenesis in humans?
(A) Spermatozoa
(B) Secondary spermatocytes
(C) Spermatogonia
(D) Spermatid
Choose the correct answer from the options given below:

The function \(f(x)=x^3, x \in R\), has: