If \(x=4 t\) and \(y=\frac{4}{t}\), then \(\frac{d^2 y}{d x^2}\) is

Let \(\vec{a}=2 \hat{i}-\hat{j}, \vec{b}=-4 \hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}+2 \hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) such that \(\vec{c} \cdot \vec{d}=34\), then \(|\vec{d}|\) is equal to

The function \(f: R \rightarrow[-1,1]\) defined by f(x) = cos x is:

If A is a 3 × 3 square matrix such that |A| = 2, then |3 adj A| is

\(\text { If } \int \frac{1+x \log x}{x e^{-x}} d x=e^x f(x)+C \text {, }\)
where \(C\) is constant of integration, then \(f(x)\) is

Equation of a line is \(\frac{x-3}{2}=\frac{4-y}{3}=\frac{2-z}{4}\) then its direction cosines are:

If \(m\) and \(n\) are respectively the order and degree of the differential equation
\(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^3+y=4 x\),
then the value of \((m+n)\) is :

Let A be a non-singular matrix of order \(n \times n\)
Then \(|\operatorname{adj}(3 A)|\) is equal to:

A capacitor of capacitance \( C = 10 \text{ } \mu\text{F} \) is charged by connecting it to a battery of emf 12 V. The capacitor is now disconnected and reconnected to the battery with the polarity reversed. The heat developed in the connecting wires will be:

Question based on the following passage: P-Block elements are placed in group 13 to 18 in the periodic table. Group 15 is nitrogen family.
Nitrogen can react with hydrogen, oxygen, halogens etc. It shows multiple oxidation states in its various oxides i.e. \(N_2O, N_2O_3, N_2O_5\) etc. Important allotropic forms of phosphorus are white, red and black phosporus. Various compounds of phosphorus are phosphine, \(PCl_3, PCl_5\) and oxoacids of phosphorus. Oxidation states \(+1\) to \(+5\) are seen in various oxoacids of phosphorus. Group 17 elements are collectively known as halogens. Bond dissociation enthalpy of \(F_2\) is smaller than \(Cl_2\).
The gases present in group 18 are chemically unreactive, they form only few compounds. Neil Bartlett (in 1962) observed the reaction of a noble gas. Since then, many noble gas compounds have been synthesised.
Explosive nature of fluorine (\(F_2\)) is due to:

Which of the following statements about the rate of a chemical reaction are correct?
(A) The rate of reaction is always proportional to the concentration of reactants
(B) An exponential time course is followed by the first order reaction
(C) The unit of rate of reaction in the gaseous state is atm/s
(D) The concentration of reactant decreases exponentially with time for a zero order reaction
Choose the correct answer from the options given below:

Which of the following reactions has a positive \(\Delta S^{\circ}\) value?

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, 3d series (Sc to Zn), 4d series (Y to Cd), 5d series (La and Hf to Hg) and 6d series which has Ac and elements from Rf to Cn. The two series of the inner transition metals; 4f (Ce to Lu) and 5f (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of s and p-block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
Which of the following statements is correct?