If \(X\) is a random variable and \(a, b\) are real numbers, which statements are TRUE?
(A) \(\operatorname{Var}(a X+b)=a^2 \operatorname{Var}(X)\)
(B) \(E(a X+b)=a E(X)+b\)
(C) \(E(a X+b)=a E(X)-E(b)\)
(D) \(\operatorname{Var}(a X+b)=a \operatorname{Var}(X)+b\)
Choose the correct answer :

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

The angle between 2 vectors \(\vec{a}\) and \(\vec{b}\) with magnitude 1 and 2 respectively when \(\vec{a} \cdot \vec{b}=1\) is:

Match List-l with List-ll

List-l	List-ll
(A) \(\int_{-a}^a f(x) d x=0\)	(I) \(0\)
(B) \(\int_0^{2 a} f(x) d x=2 \int_0^a f(x) d x\)	(II) 1
(C) \(\int_{-\pi}^\pi \cos x d x\)	(III) \(f\) is an odd function
(D) \(\int_{-1}^1 x^{101} d x+1\)	(IV) \(f(2 a-x)=f(x)\)

Choose the correct answer from the options given below :

The system of linear equations \(k x+5 y=5,2 x+3 y=5\) will be consistent if

Solution of \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is :

Let \(A=\left[a_{i j}\right]\) be a square matrix, where \(a_{i j}=\left\{\begin{array}{ll}0, & \text { when } i=j \\ 1, & \text { otherwise }\end{array}\right.\)
If \(|\operatorname{adj} A|=|A|^2\), then which of the following statements are correct?
(A) A is a skew-symmetric matrix.
(B) A is a non-singular matrix.
(C) A is a square matrix of order 4.
(D) A is a symmetric matrix.
Choose the correct answer from the options given below :

Read the passage carefully and answer the questions based on the passage:
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. In the rate equation Rate \(=k[\mathrm{~A}]^x[\mathrm{~B}]^y\)
\(x\) and \(y\) indicate how sensitive the rate is to the change in concentration of A and B, respectively. Sum of these exponents, i.e., \(x +y\) gives the overall order of a reaction where \(x\) and \(y\) represent the order with respect to the reactants A and B respectively. Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. For a first order reaction, the concentration of the reactant varies as \([\mathrm{R}]=[\mathrm{R}]_0 e^{-k t}\)
Which of the following is a zero order reaction?

Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
What will be the products formed in the following equation?

Which one of the following statements is correct for a first order reaction?

Glucose reacts with Tollen's reagent (ammoniacal silver nitrate) due to the presence of

The kinetic energy of a moving electron is 180 eV, its linear momentum is about : (mass of 1 electron = \( 9 \times 10^{-31} \text{ kg} \))

Reaction of Chloroethane with ethanolic ammonia will result in :