For the given five values 18, 25, 20, 36, 49, the three years moving averages are

The integral \(I=\int \frac{e^{5 \log _0 x}-e^{4 \log _0 x}}{e^{3 \log _0 x}-e^{2 \log _0 x}} d x\) is equal to:

The value of the determinant \(D=\) equation \(\left|\begin{array}{lll}x & a & a+x \\ y & b & b+y \\ z & c & c+z\end{array}\right|\) is:

Match List - I with List - II.

LIST - I	LIST - II
(A) \((\hat{i} \times \hat{j})+(\hat{j} \times \hat{i})\)	(I) 1
(B) \(\hat{i} \cdot \hat{i}+\hat{j} \cdot \hat{j}+\hat{k} \cdot \hat{k}\)	(II) \(\hat{k}-\hat{j}\)
(C) \(\hat{i} \times(\hat{i}+\hat{j}+\hat{k})\)	(III) \(\overrightarrow{0}\)
(D) \(\hat{i} \cdot(\hat{i}+\hat{j}+\hat{k})\)	(IV) 3

Choose the correct answer from the options given below :

The value of the integral \(\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x\) is equal to:

If \(\vec{a}=5 \hat{i}+\hat{j}+3 \hat{k}\) then the sum of projections of \(\vec{a}\) on \(x\)-axis, \(y\)-axis and \(z\)-axis is:

The integrating factor of the differential equation \(x \frac{d y}{d x}-y=\sin x\) is :

The Differential Equation representing the family of tangents to the circle \(x^2+y^2=r^2\)is:

Answer the question on the basis of passage given below:
Aldehydes are generally more reactive than ketones in nucleophilic addition reactions due to steric and electronic reasons. Sterically, the presence of two relatively large substituents in ketones hinders the approach of nucleophile to carbonyl carbon more than aldehydes having only one such substituent Electronically aldehydes are more reactive than ketones because two alkyl groups reduce the elctrophilicity of the carbonyl more effectively than in former.
4-Hydroxy-4-methylpentan-2-one and 4-methylpent-3-en-2-one are the products obtained from A by aldol
condensation. \(A\) is:

Based on their rate laws, arrange the following reactions in the decreasing sequence of the reaction order.
(A)Rate \(=k[A]^{3 / 2}[B]^{-1}\)
(B)Rate \(=k\left[ CHCl _3\right]\left[ Cl _2\right]^{1 / 2}\)
(C)Rate \(=k\left[ CH _3 COOC _2 H _5\right]\left[ H _2 O \right]^0\)
(D)Rate \(=k[A]^{1 / 2}[B]^{3 / 2}\)
Choose the correct answer from the options given below:

Match List - I with List - II

List - I (Cell Type)	List - II (Characteristic/Reaction)
A. Fuel Cell	I. Rechargeable
B. Mercury Cell	II. Reaction at anode, \(\text{Zn} \rightarrow \text{Zn}^{2+} + 2\text{e}^{-}\)
C. Leclanche Cell	III. Cell reaction \(2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}\)
D. Ni-Cd Cell	IV. Gives steady potential

Choose the correct answer from the options given below :

The resistance of a wire is \(10 \Omega\). Its length is increased by \(10 \backslash \%\) by stretching. The new resistance of the wire will now be :

Which of the following is more reliable ?