A 95% confidence interval for a population mean was reported to be 152 to 160. If the standard deviation \(\sigma=15\), then the sample size is (given \(Z_{0.025}=1.96\) ) :

Let \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then \(\left(A^{-1}\right)^T\) equals

The maximum value of \(f(x)=\left(\frac{1}{x}\right)^x\) is

In a 700 m race, the ratio of speeds of two participants A and B is 5: 6. If A has a start of 150 m, then the distance by which A wins the race is :

Let \(X\) denotes the number of hours you study during a randomly selected school day. The random variable \(X\) has the following probability distribution.

X	0	1	2	3	4
P(X)	K	2K	2K	2K	K

Match List - I with List - II.

LIST - I	LIST - II
(A) Value of K	(I) \(\frac{1}{4}\)
(B) Probability you study at least two hours	(II) \(\frac{1}{8}\)
(C) Probability you study exactly two hours	(III) \(\frac{3}{8}\)
(D) Probability you study at most one hour	(IV) \(\frac{5}{8}\)

Choose the correct answer from the options given below:

For the given 5 values \(24,18,33,42,24\); the \(3\) -year moving averages are:

For \(A=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]\) if \(M_{i j}\) and \(A_{i j}\) are the minor and the cofactor of \(a_{i j}\) respectively, then \(|A|\) equals to :
(A) \(a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}\)
(B) \(a_{21} A_{12}+a_{22} A_{22}+a_{23} A_{32}\)
(C) \(a_{11} M_{11}-a_{12} M_{12}+a_{13} M_{13}\)
(D) \(a_{11} M_{11}+a_{12} M_{12}+a_{13} M_{13}\)
Choose the correct answer from the options given below :

Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. Both pipes A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 15 minutes, then time for which the pipe B works is :

A digital signal
A. does not provides a continuous set of values.
B. can utilise binary system
C. represents values as discrete steps
D. can utilise decimal as well as binary system
Choose the correct anser from the options given below:

In the 3d series of transition elements, the element more likely to exhibit +1 oxidation state is :

Match List-I with List-II

List-I (Lines)	List-II (Direction Ratios)
(A) \(\frac{x-1}{2}=\frac{2-y}{1}=z\)	(I) \((1,3,-1)\)
(B) \(\frac{2 x-1}{2}=\frac{y+1}{3}=\frac{1-z}{1}\)	(II) \((2,-2,0)\)
(C) \(\frac{x+1}{2}=\frac{3-y}{2}=z=2\)	(III) \((2,-1,1)\)
(D) \(\frac{2 x-3}{4}=\frac{1-2 y}{2}=\frac{z}{5}\)	(IV) (2, -1, 5)

Choose the correct answer from the options given below:

The S.I unit of mutual inductance, the 'henry' can be written as

Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of C X bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom \(X\) is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
What is chiral carbon ?