The degree of the differential equation \(\left(2+\left(\frac{d y}{d x}\right)^2\right)^{\frac{3}{2}}=a^2 \frac{d^2 y}{d x^2}\) is :

Given that the function \(f(x)\) is continuous on \(R\). Match \(List - I\) with \(List - II\) .

\(List - I\)	\(List - II\)
(A) \(f(x)=\left\{\begin{array}{ll}k x^2, & x<3 \\ 3, & x \geq 3\end{array}\right.\)	(I) \(k=\frac{5}{4}\)
(B) \(f(x)=\left\{\begin{array}{ll}k x+1, & x \geq 4 \\ x+2, & x<4\end{array}\right.\)	(II) \(k=-1\)
(C) \(f(x)=\left\{\begin{array}{ll}\frac{5+x}{2}, & x \neq 0 \\ 3 k, & x=0\end{array}\right.\)	(III) \(k=\frac{1}{3}\)
(D) \(f(x)=\left\{\begin{array}{ll}x+k, & x>-2 \\ -3, & x \leq-2\end{array}\right.\)	(III) \(k=\frac{5}{8}\)

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Match List-I with List-II

List-I	List-II
(A) \(f(x)=|x|+1\)	(I) Not differentiable at \(x=3\) only
(B) \(f(x)=|x-3|\)	(II) Not differentiable at \(x=-3\) only
(C) \(f(x)=|x+3|\)	(III) Not differentiable at \(x=3\), \(-3\) only
(D) \(f(x)=\left|x^2-9\right|\)	(IV) Not differentiable at \(x=0\) only

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Area of the region bounded by the curve \(y=\cos (x)\) and x -axis between \(x=0\) and \(x=\pi\) is :

If the matrix \(A=\left[\begin{array}{ccc}0 & -3 & x+y \\ 3 & x-2 y & 5 \\ -6 & -5 & 0\end{array}\right]\) is skew-symmetric then values of \(x\) and \(y\) respectively are :

The probability distribution of a random variable X is given below:
\(\begin{array}{lllll} X & 0 & 1 & 2 & 3 \\ P ( X ) & k & & \\ & & \frac{k}{2} & \frac{k}{4} & \frac{k}{8}\end{array}\)
then the value of \(P(X \leq 2)+P(X>2)\) is :

The area of the region bounded by the curves \(y=x^2+2, y=-x, x=0\) and x = 1 is :

Read the paragraph given below and answer the question.
Sutton and Boveri argued that the pairing and separation of a pair of chromosomes would lead to the segregation of a pair of factors they carried. Sutton united the knowledge of chromosomal segregation with Mendelian principles and called it the chromosomal theory of inheritance. Following this synthesis of ideas, experimental verification of the chromosomal theory of inheritance by Thomas Hunt Morgan and his colleagues, led to discovering the basis for the variation that sexual reproduction produced. Morgan worked with the tiny fruit files, which were found very suitable for such studies. They could be grown on simple synthetic medium in the laboratory. They complete their life cycle in a short span of time and a single mating could produce a large number of progeny flies. Also, there was a clear differentiation of the sexes - the male and female flies are easily distinguishable. Also, it has many types of hereditary variations that can be seen with low power microscopes.
Drosophila melanogaster complete their life cycle in

The magnetisation at the centre of a bar magnet (magnetic length 10 cm), having pole strength 6.3 A m, and area of cross-section \(A = 0.70 \text{ cm}^2\) is

Which one of the following statements is not correct
A. D (-) fructose exists in furanose structure
B. D (+) glucose exists in pyranose structure
C. In sucrose the two monosaccharides are held together by peptide linkage
D. Maltose is a reducing sugar
E. Pentaacetate of glucose does not react with hydroxylamine
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Match List-l with List-II

List-l (Complex)	List-II (Property)
(A) Fuel Cell	(I) Anode: \(Zn (s) \rightarrow Zn ^{2+}+2 e^{-}\) Cathode: \(MnO _2+ NH _4^{+}+e^{-} \rightarrow MnO ( OH )+ NH _3\)
(B) A secondary cell	(II) Cathode: \(O _2(g)+2 H _2 O (l)+4 e^{-} \rightarrow 4 OH ^{-}(a q)\) Anode: \(2 H _2(g)+4 OH ^{-}(a q) \rightarrow 4 H _2 O (l)+4 e^{-}\)
(C) Mercury cells	(III) \(Pb (s)+ PbO _2(s)+2 H _2 SO _4(a q) \rightarrow 2 PbSO _4(s)+2 H _2 O (l)\)
(D) Leclanche cell (Simplified)	\((I V) Zn ( Hg )+ HgO (s) \rightarrow ZnO (s)+ Hg (l)\)

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Arrange the given organisms involved in a food chain in correct sequence ?
(A) Fish
(B) Phytoplankton
(C) Man
(D) Zooplankton
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If \(A\) is a square matrix such that \(A^2=A\) and \(I\) is the identify matrix of the same order as \(A\) then \((I+2 A)^3-6 A\) is equal to