List of practice Questions

Correct statements regarding Arrhenius equation among the following are:
Factor $e^{-E_a/RT}$ corresponds to fraction of molecules having kinetic energy less than $E_a$.
At a given temperature, lower the $E_a$, faster is the reaction.
Increase in temperature by about $10^\circ\text{C}$ doubles the rate of reaction.
Plot of $\log k$ vs $\dfrac{1}{T}$ gives a straight line with slope $= -\dfrac{E_a}{R}$.
Choose the correct answer from the options given below:

If the image of the point $ P(1, 2, a) $ in the line \[ \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{7 - z}{2} \] is $ Q(5, b, c) $, then $ a^2 + b^2 + c^2 $ is equal to

Let $A$ be the focus of the parabola $y^2=8x$. Let the line $y=mx+c$ intersect the parabola at two distinct points $B$ and $C$. If the centroid of triangle $ABC$ is $\left(\frac{7}{3},\frac{4}{3}\right)$, then $(BC)^2$ is equal to:

A light wave described by E = 60[$\sin(3 \times 10^{15})t + \sin(12 \times 10^{15})t$] (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately)________ eV. (h=$6.6 \times 10^{-34}$ J.s. and e=$1.6 \times 10^{-19}$ C)

Let a point A lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC, where the points B and C lie on the lines $L_1$ and $L_2$, respectively, is:

Decomposition of A is a first order reaction at T(K) and is given by $ A(g) \rightarrow B(g) + C(g) $.
In a closed 1 L vessel, 1 bar A(g) is allowed to decompose at T(K). After 100 minutes, the total pressure was 1.5 bar. What is the rate constant (in $ min^{-1} $) of the reaction ? ($ \log 2 = 0.3 $)

The number of elements in the set $\{x\in[0,180^\circ]: \tan(x+100^\circ)=\tan(x+50^\circ)\tan x\tan(x-50^\circ)\}$ is

Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance ($u$) and image distance ($v$) using same convex lens having power $+5$ D as (25,96), (30,62), (35,37), (45,35) and (50,32) respectively. Identify correct statement.

From the given following (A to D) cyclic structures, those which will not react with Tollen's reagent are :

অনুক্ত কর্তা কাকে বলে?

Let $f: R \to (0, \infty)$ be a twice differentiable function such that $f(3) = 18$, $f'(3)=0$ and $f''(3) = 4$. Then $\lim_{x \to 1} \log_e \left[ \frac{f(2+x)}{f(3)} \right]^{\frac{18}{(x-1)^2}}$ is equal to:

A parallel beam of light travelling in air (refractive index $1.0$) is incident on a convex spherical glass surface of radius of curvature $50 \, \text{cm}$. Refractive index of glass is $1.5$. The rays converge to a point at a distance $x \, \text{cm}$ from the centre of curvature of the spherical surface. The value of $x$ is ___________.

Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to

$X$ is the number of geometrical isomers exhibited by $[\mathrm{Pt(NH_3)(H_2O)BrCl}]$.
$Y$ is the number of optically inactive isomer(s) exhibited by $[\mathrm{CrCl_2(ox)_2}]^{3-}$.
$Z$ is the number of geometrical isomers exhibited by $[\mathrm{Co(NH_3)_3(NO_2)_3}]$. Find the value of $X + Y + Z$. }

The number of relations, defined on the set \{a, b, c, d\}, which are both reflexive and symmetric, is equal to:

From the following, how many compounds contain at least one secondary alcohol?

When 300 J of heat is given to an ideal gas with $ C_p = \frac{7}{2}R $, its temperature rises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) ______ g. (R = 8.314 J/mol K)

Given below are two statements regarding conformations of n-butane. Choose the correct option.

In a meter bridge experiment to determine the value of unknown resistance, first the resistances $2\,\Omega$ and $3\,\Omega$ are connected in the left and right gaps of the bridge and the null point is obtained at a distance $l$ cm from the left end. Now, when an unknown resistance $x\,\Omega$ is connected in parallel to $3\,\Omega$, the null point is shifted by $10\,\text{cm}$ to the right. The value of $x$ is ________ $\Omega$.

A Wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances \[ (R_1=R_2=R_3=R_4). \] When $R_3$ resistance is heated, its resistance value increases by $10%$. The potential difference $(V_a-V_b)$ after $R_3$ is heated is _______ V.

If the line $ ax + 2y = 1 $, where $ a \in \mathbb{R} $, does not meet the hyperbola $ x^2 - 9y^2 = 9 $, then a possible value of $ a $ is:

Let $ PQR $ be a triangle such that \[ \vec{PQ}=-2\hat i-\hat j+2\hat k,\quad \vec{PR}=a\hat i+b\hat j-4\hat k,\ a,b\in\mathbb{Z}. \] Let $ S $ be the point on $ QR $ which is equidistant from the lines $ PQ $ and $ PR $. If \[ |\vec{PR}|=9 \quad \text{and} \quad \vec{PS}=\hat i-7\hat j+2\hat k, \] then the value of $ 3a-4b $ is:

Let $\vec{a}=2\hat{i}-\hat{j}-\hat{k}$, $\vec{b}=\hat{i}+3\hat{j}-\hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}+3\hat{k}$. Let $\vec{v}$ be the vector in the plane of $\vec{a}$ and $\vec{b}$, such that the length of its projection on the vector $\vec{c}$ is $\dfrac{1}{\sqrt{14}}$. Then $|\vec{v}|$ is equal to

In a microscope, the objective has a focal length $f_o=2$ cm and the eye-piece has a focal length $f_e=4$ cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is_____.

Given below are two statements:
Statement I: An object moves from position $ \vec{r}_1 $ to position $ \vec{r}_2 $ under a conservative force field $ \vec{F} $. The work done by the force is \[ W = -\int_{\vec{r}_1}^{\vec{r}_2} \vec{F} \cdot d\vec{r}. \]
Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of the above statements, choose the correct answer from the options given below: