If \(f(x) = sin\) \(x - cos\) \(x\), \(x \in[0,2 \pi]\) then
(A) f(x) is increasing in \(\left(0, \frac{3 \pi}{4}\right)\)
(B) f(x) is decreasing in \(\left(0, \frac{3 \pi}{4}\right)\)
(C) f(x) is decreasing in \(\left(\frac{3 \pi}{4}, \frac{7 \pi}{4}\right)\)
(D) f(x) is decreasing in \(\left(\frac{7 \pi}{4}, 2 \pi\right)\)
Choose the correct answer from the options given below:

Three partners Ramesh, Suresh and Mahesh shared the profit in a business in the ratio \(5: 4: 7\) respectively. They invested the money for 10 months, 8 months and 6 month

In the context of linear programming, Match List I with List II

List - I	List - II
(A) Z = 250x +75y	I. non-trivial constraints
(B) \(5 x+y \leq 100, x-y \leq 4\)	II. feasible solution
(C) \(x, y \geq 0\)	III. objective function
(D) points within and on the boundary of shaded region	IV. Trivial constraints

The corner points of the feasible region of a LPP are \(P(0, 5), Q(1, 5), R(4, 2)\) and \(S(12, 0)\).
The minimum value of the objective function \(Z = 2x + 5y\) is at the point:

If A and B are two events such that \(P(A) \neq 0\) and \(P(A / B)=1\) then :

If \(y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}\), then

Given that \(\vec{a}=-3 \hat{i}-6 \hat{j}+4 \hat{k}, \quad \vec{b}=9 \hat{i}-\lambda \hat{j}-12 \hat{k}\)
If \(\vec{a} \times \vec{b}=\overrightarrow{0}\), then the value of \(\lambda\) is

If the function
\(f(x)=\left\{\begin{array}{ll}a x+2, & x \leq 1 \\x^2+3 x+b, & x>1\end{array}\right.\)
is differentiable at \(x=1\), then the value of \((2 a+b)\) is

The rate of a first order reaction at a constant temperature

The best reagent for preparing an alkyl chloride from an alcohol is

If \(a , b\) and \(c\) are distinct prime numbers then the value of \(\left|\begin{array}{lll}a-b & b-c & c-a \\ b-c & c-a & a-b \\c-a & a-b & b-c\end{array}\right|\) is equal to

If \(\left|\begin{array}{ccc}x-2 & 1 & 2 \\ 1 & 2 x & 1 \\ -1 & 1 & 1\end{array}\right|=3\) then the values of x are:

Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of CX 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.
Which of the following bromo isomer of butane will react at a faster rate towards SN2 reaction?