\(\int_1^4|x-2| d x\) is equal to:

If \(\vec{a}=2 \hat{i}+m \hat{j}-n \hat{k}\) and \(\vec{b}=\hat{l} \hat{i}-3 \hat{j}+4 \hat{k}\) such that \(\vec{a}=2 \vec{b}\), then the value of \(14 l+m+n\) is :

The interval, on which the function \(f(x)=x^2 e^{-x}\) is increasing, is equal to:

The integrating factor of the linear differential equation \(\frac{d y}{d x}+P(x) y=Q(x)\) is:

If \(\vec{a}\) and \(\vec{b}\) are two unit vectors and \(\vec{a}+\vec{b}\) is also a unit vector, the magnitude of \(\vec{a}-\vec{b}\) is

Let A = {1, 2, 3} Consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} Then R is:

A startup company invested ₹ \(5,00,000\) in shares for 4 years. The value of the investment was: ₹ \(5,50,000\) at the end of first year, ₹ \(5,25,000\) at the end of third year, and on maturity, the final value stood ₹ \( 6,25,000\). The CAGR on the investment will be : [Given : \((1.25)^{\frac{1}{4}}=1.06\)]

Choose the correct products formed in acidic medium.
\(5 \mathrm{SO}_3^{2-}+2 \mathrm{MnO}_4^{-}+6 \mathrm{H}^{+} \rightarrow ?\)

Let \(A\) and \(B\) be \(3 \times 3\) matrices such that \(A \neq B\). If \(A^3=B^3\) and \(A^2 B=B^2 A\), then the determinant of \(A^2+B^2\) is :

Which of the following are first order linear differential equations?
(A)\(\frac{d x}{d y}+P_1(y) x=Q_1(y): P_1(y)\) and \(Q_1(y)\) are functions of y or constant functions
(B)\(\frac{d y}{d x}+P_2(x) y=Q_2(x): P_2(x)\) and \(Q_2(x)\) are functions of a or constant functions
(C)\((x+y) \frac{d y}{d x}=x-2 y\)
(D)\(\left(1+x^2\right) \frac{d y}{d x}-2 x y=x^2+3\)
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ccc}5 & 1 & 0 \\ 6 & 2 & -1\end{array}\right], B^T=\left[\begin{array}{cc}2 & 1 \\ -2 & 0 \\ 1 & 3\end{array}\right]\), then \(B A^T\) is :

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
Which of the following compounds will undergo nucleophilic addition readily?

The electric field intensity produced by the radiations coming from a 200 W bulb at 6 m distance is E . What is the electric field intensity produced by the radiations coming from 100 W bulb at the same distance?