Area of a rectangle having vertices A, B, C, D with position vectors \(-\hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}, \hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}, \hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\) and \(-\hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\) respectively is:

If \(A=\left[\begin{array}{ll}1 & -1 \\ 2 & -1\end{array}\right], B=\left[\begin{array}{cc}a & 1 \\ b & -1\end{array}\right]\) and \((A+B)^2=A^2+B^2\) then

If A and B are symmetric matrices, then \(A B-B A\) is

Mr. Jain wishes to purchase a shop for ₹25,00,000 with down payment of ₹2, 00, 000. If he can amortize the balance at 9% per annum compounded monthly for 25 years, what will be his monthly installment if it is given that \(\left(a_{\frac{300}{0.0075}}=119.1616\right)\)?

An automobile dealer wishes to buy four luxury cars of different brands with some down payment and balance in equal monthly instalments for 10 years
The bank charges \(9 \%\) interest per annum compounded monthly
Given \(\frac{0.0075(1.0075)^{120}}{(1.0075)^{120}-1}=0.01266\)

Luxury Car	Price of the Car (in Rs.)	Down payment (in Rs.)
P	25,00,000	5,00,000
Q	35,00,000	12,00,000
R	45,00,000	15,00,000
S	42,00,000	15,00,000

Match List I with List II

List-I (Luxury Car)	List-II (EMI (in Rs.))
(A) P	(i) 34,182
(B) Q	(ii) 37,980
(C) R	(iii) 29,118
(D) S	(iv) 25,320

Choose the correct answer from the options given below :

The sum of the order and degree of the differential equation \(\frac{d^2 y}{d x^2}+\sqrt[3]{\frac{d y}{d x}}+(1+x)=0\) is :

If the matrix \(\left[\begin{array}{ccc}x-y & 1 & -2 \\ 2 x-y & 0 & 3 \\ 2 & -3 & 0\end{array}\right]\) is skew-symmetric, then the values of \(x\) and \(y\) are respectively:

Match List-I with List-II

List-I (Enzymes)	List-II (Products)
(A) RNA polymerase I	(I) hnRNA
(B) RNA polymerase III	(II) hydrolysis of lactose
(C) RNA polymerase II	(III) rRNA
(D) \( eta\)-galactosidase	(IV) tRNA, 5SrRNA, snRNA

Choose the correct answer from the options given below:

An example of inverted ecological pyramid is:

If the total energy is transferred by the electromagnetic waves on a surface be \(U\) in time \(t\), then the total momentum delivered to the surface is

Radiation of frequency \(2 v _0\) incident on a metal with threshold frequency \(v _0\) results in maximum kinetic energy of photoelectrons as :

A line through the points \(A(3,4,1)\) and \(B(5,1,6)\) is drawn.
The coordinates of the points where the line through the points \(A \backslash \& B\) crosses the \(X Y\) plane 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?