List of practice Questions

Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to

A thin convex lens of focal length $ 5 $ cm and a thin concave lens of focal length $ 4 $ cm are combined together (without any gap), and this combination has magnification $ m_1 $ when an object is placed $ 10 $ cm before the convex lens.

Keeping the positions of the convex lens and the object undisturbed, a gap of $ 1 $ cm is introduced between the lenses by moving the concave lens away. This leads to a change in magnification of the total lens system to $ m_2 $.

The value of $ \dfrac{m_1}{m_2} $ is

Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E. The energy stored in B, when spring constants $k_A, k_B$ of A and B, respectively satisfy the relation $4k_A = 3k_B$, is :

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 $X + Y + Z$. }

Two circular discs of radius $10$ cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is $30$ cm and its mass is $600$ g. The mass of each disc is also $600$ g. If the applied torque between the two discs is $43\times10^{-7}$ dyne·cm, then the angular acceleration of the system about the given axis $AB$ is ________ rad s$^{-2}$.

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 ________ $\Omega$.

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $ P_1 $ to $ P_2 $ is $ \alpha $ Joule $(P_1 = 21.7 \text{ Pa}, P_2 = 30 \text{ Pa}, C_v = 21 \text{ J/K mol}, R = 8.3 \text{ J/mol K})$. The value of $ \alpha $ is ________.

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.