The measured value of the length of a simple pendulum is $20 \mathrm{~cm}$ with $2 \mathrm{~mm}$ accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $\mathrm{N} \%$. The value of $\mathrm{N}$ is:

The temperature $T(t)$ of a body at time $t=0$ is $160^{\circ} \mathrm{F}$ and it decreases continuously as per the differential equation $\frac{d T}{d t}=-K(T-80)$, where $K$ is a positive constant. If $T(15)=120^{\circ} \mathrm{F}$, then $T(45)$ is equal to

The oxidation number of iron in the compound formed during brown ring test for NO$_3^-$ iron is ________.

Alkyl halide is converted into alkyl isocyanide by reaction with

$\left|\begin{array}{ccc}x+1 & x & x \\ x & x+\lambda & x \\ x & x & x+\lambda^{2}\end{array}\right|=\frac{9}{8}(103 x+81)$, then $\lambda, \frac{\lambda}{3}$ are the roots of the equation :

The shortest distance between the lines ${{x + 2} \over 1} = {y \over { - 2}} = {{z - 5} \over 2}$ and ${{x - 4} \over 1} = {{y - 1} \over 2} = {{z + 3} \over 0}$ is :

If the boiling points of two solvents X and Y (having same molecular weights) are in the ratio $2: 1$ and their enthalpy of vaporizations are in the ratio $1: 2$, then the boiling point elevation constant of $\mathrm{X}$ is $\underline{\mathrm{m}}$ times the boiling point elevation constant of Y. The value of m is ____________ (nearest integer)

Given below are two statements

Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time.

Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time.

In the light of given statements, choose the correct answer from the options given below.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : $\mathrm{Cu^{2+}}$ in water is more stable than $\mathrm{Cu^{+}}$.

Reason (R) : Enthalpy of hydration for $\mathrm{Cu^{2+}}$ is much less than that of $\mathrm{Cu^{+}}$.

In the light of the above statements, choose the correct answer from the options given below :

An electron of a hydrogen like atom, having $Z=4$, jumps from $4^{\text {th }}$ energy state to $2^{\text {nd }}$ energy state. The energy released in this process, will be :

(Given Rch = $13.6~\mathrm{eV}$)

Where R = Rydberg constant

c = Speed of light in vacuum

h = Planck's constant

Among following compounds, the number of those present in copper matte is ___________.

A. $\mathrm{CuCO_{3}}$

B. $\mathrm{Cu_{2}S}$

C. $\mathrm{Cu_{2}O}$

D. $\mathrm{FeO}$

Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be :

The enthalpy change for the conversion of $\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{~g})$ to $\mathrm{Cl}^{-}$(aq) is ($-$) ___________ $\mathrm{kJ} \mathrm{mol}^{-1}$ (Nearest integer)

Given : $\Delta_{\mathrm{dis}} \mathrm{H}_{\mathrm{Cl}_{2(\mathrm{~g})}^{\theta}}^{\ominus}=240 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_{\mathrm{eg}} \mathrm{H}_{\mathrm{Cl_{(g)}}}^{\ominus}=-350 \mathrm{~kJ} \mathrm{~mol}^{-1}$,

${\mathrm{\Delta _{hyd}}H_{Cl_{(g)}^ - }^\Theta = - 380}$ $\mathrm{kJ~mol^{-1}}$

The energy of one mole of photons of radiation of frequency $2 \times 10^{12} \mathrm{~Hz}$ in $\mathrm{J} ~\mathrm{mol}^{-1}$ is ___________. (Nearest integer)

[Given : $\mathrm{h}=6.626 \times 10^{-34} ~\mathrm{Js}$

$\mathrm{N}_{\mathrm{A}}=6.022 \times 10^{23} \mathrm{~mol}^{-1}$]

Suppose $f: \mathbb{R} \rightarrow(0, \infty)$ be a differentiable function such that $5 f(x+y)=f(x) \cdot f(y), \forall x, y \in \mathbb{R}$. If $f(3)=320$, then \sum_\limits{n=0}^{5} f(n) is equal to :

The constant term in the expansion of ${\left( {2x + {1 \over {{x^7}}} + 3{x^2}} \right)^5}$ is ___________.

For independent process at 300 K

The number of non-spontaneous process from the following is __________

Let $y = y(x)$ be the solution of the differential equation ${x^3}dy + (xy - 1)dx = 0,x > 0,y\left( {{1 \over 2}} \right) = 3 - \mathrm{e}$. Then y (1) is equal to

From the photoelectric effect experiment, following observations are made. Identify which of these are correct.

A. The stopping potential depends only on the work function of the metal.

B. The saturation current increases as the intensity of incident light increases.

C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light.

D. Photoelectric effect can be explained using wave theory of light.

Choose the correct answer from the options given below :

An unpolarised light beam of intensity $2 I_{0}$ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of $30^{\circ}$ relative to that of P. The intensity of the emergent light is

Dinitrogen and dioxygen, the main constituents of air do not react with each other in atmosphere to form oxides of nitrogen because :

Let $x_{1}, x_{2}, x_{3}, \ldots, x_{20}$ be in geometric progression with $x_{1}=3$ and the common ratio $\frac{1}{2}$. A new data is constructed replacing each $x_{i}$ by $\left(x_{i}-i\right)^{2}$. If $\bar{x}$ is the mean of new data, then the greatest integer less than or equal to $\bar{x}$ is ____________.

In the given circuit the input voltage V_in is shown in figure. The cut-in voltage of p-n junction diode (D₁ or D₂) is 0.6 V. Which of the following output voltage (V₀) waveform across the diode is correct?

Two elements A and B which form 0.15 moles of A₂B and AB₃ type compounds. If both A₂B and AB₃ weigh equally, then the atomic weight of A is _____________ times of atomic weight of B.

If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

Given below are two statements :

Statement I : The law of gravitation holds good for any pair of bodies in the universe.

Statement II : The weight of any person becomes zero when the person is at the centre of the earth.

In the light of the above statements, choose the correct answer from the options given below.

A bar magnet having a magnetic moment of 2.0 $\times$ 10⁵ JT^$-$1, is placed along the direction of uniform magnetic field of magnitude B = 14 $\times$ 10^$-$5 T. The work done in rotating the magnet slowly through 60$^\circ$ from the direction of field is :

If $\{ {a_i}\} _{i = 1}^n$, where n is an even integer, is an arithmetic progression with common difference 1, and $\sum\limits_{i = 1}^n {{a_i} = 192} ,\,\sum\limits_{i = 1}^{n/2} {{a_{2i}} = 120}$, then n is equal to :