Q1
MATHS
Unit 1: Sets Relations and Functions
An organization awarded 48 medals in event $A$, 25 in event $B$ and 18 in event $C$. If these medals went to total 60 men and only five men got medals in all the three events, then how many received medals in exactly two of three events?
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2023 (1 set)
- A. 15
- B. 9
- C. 10
- D. 21
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Q2
MATHS
Unit 12: Vector Algebra
Let $(\alpha, \beta, \gamma)$ be the image of the point $P(2, 3, 5)$ in the plane $2x + y - 3z = 6$. Then $\alpha + \beta + \gamma$ is equal to
- A. 12
- B. 10
- C. 9
- D. 5
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Q3
MATHS
Unit 10: Co-ordinate Geometry
Consider ellipses $E_k: kx^2 + k^2 y^2 = 1$, $k=1,2,\ldots,20$. Let $C_k$ be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse $E_k$. If $r_k$ is the radius of the circle $C_k$, then the value of $\sum_{k=1}^{20} \frac{1}{r_k^2}$ is
↻ Repeated question — also appeared in
2023 (1 set)
- A. 2870
- B. 3080
- C. 3210
- D. 3320
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Q4
MATHS
Unit 4: Permutations and Combinations
The number of triplets $(x,y,z)$, where $x,y,z$ are distinct non negative integers satisfying $x+y+z=15$, is
↻ Repeated question — also appeared in
2023 (1 set)
- A. 136
- B. 114
- C. 92
- D. 80
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Q5
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
The number of integral solutions $x$ of $\log_{\left(x+7\right)/2}\!\left(\frac{(x-7)^2}{2x-3}\right) \ge 0$ is
↻ Repeated question — also appeared in
2023 (1 set)
- A. 8
- B. 7
- C. 6
- D. 5
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Q6
MATHS
Unit 3: Matrices and Determinants
Let $A$ be a $2\times 2$ matrix with real entries such that $A^\prime = \alpha A + I$, where $\alpha \in \mathbb{R} - \{-1,1\}$. If $\det(A^2-A)=4$, then the sum of all possible values of $\alpha$ is equal to
↻ Repeated question — also appeared in
2023 (1 set)
- A. $\frac{5}{2}$
- B. $\frac{3}{2}$
- C. 2
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Q7
MATHS
Unit 7: Limit Continuity and Differentiability
Let $f(x) = [x^2-x] + [-x+[x]]$, where $x\in\mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is
↻ Repeated question — also appeared in
2023 (1 set)
- A. not continuous at $x=0$ and $x=1$
- B. continuous at $x=0$ and $x=1$
- C. continuous at $x=0$, but not continuous at $x=1$
- D. continuous at $x=1$, but not continuous at $x=0$
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Q8
MATHS
Unit 10: Co-ordinate Geometry
If equation of the plane that contains the point $(-2,3,5)$ and is perpendicular to each of the planes $2x+4y+5z=8$ and $3x-2y+3z=5$ is $\alpha x+\beta y+\gamma z+97=0$ then $\alpha+\beta+\gamma$ =
↻ Repeated question — also appeared in
2023 (1 set)
- A. 15
- B. 16
- C. 17
- D. 18
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Q9
MATHS
Unit 8: Integral Calculus
Area of the region $\{(x,y): x^2+(y-2)^2\le 4,\ x^2\ge 2y\}$ is
↻ Repeated question — also appeared in
2023 (1 set)
- A. $\pi-\frac{8}{3}$
- B. $2\pi-\frac{16}{3}$
- C. $\pi+\frac{8}{3}$
- D. $2\pi+\frac{16}{3}$
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Q10
MATHS
Unit 7: Limit Continuity and Differentiability
Let $f:[2,4]\to \mathbb{R}$ be a differentiable function such that
$$(x\log_e x)\,f'(x)+(\log_e x)f(x)+f(x)\ge 1,\ x\in[2,4]$$
with $f(2)=\frac{1}{2}$ and $f(4)=\frac{1}{4}$.
Consider the following two statements :
(A) : $f(x)\le 1$, for all $x\in[2,4]$
(B) : $f(x)\ge \frac{1}{8}$, for all $x\in[2,4]$
Then,
↻ Repeated question — also appeared in
2023 (1 set)
- A. Only statement (A) is true
- B. Only statement (B) is true
- C. Both statements (A) and (B) are true
- D. Neither statement (A) nor statement (B) is true
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Q11
MATHS
Unit 12: Vector Algebra
Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j},\ \hat{i}+\hat{k}$ and $\hat{i}-\hat{j},\ \hat{j}-\hat{k}$. If $\theta$ is the angle between the vector $\vec{a}$ and the vector $\vec{b}=2\hat{i}-2\hat{j}+\hat{k}$, and $\vec{a}\cdot\vec{b}=6$, then the ordered pair $(\theta, |\vec{a}\times\vec{b}|)$ is equal to
↻ Repeated question — also appeared in
2023 (1 set)
- A. $(\pi/4,\ 3\sqrt{6})$
- B. $(\pi/3,\ 6)$
- C. $(\pi/3,\ 3\sqrt{6})$
- D. $(\pi/4,\ 6)$
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Q12
MATHS
Unit 12: Vector Algebra
For any vector $\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$, with $10|a_i|<1$, $i=1,2,3$, consider the following statements :
(A) : $\max\{|a_1|,|a_2|,|a_3|\}\le |\vec{a}|$
(B) : $|\vec{a}|\le 3\max\{|a_1|,|a_2|,|a_3|\}$
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2023 (1 set)
- A. Only (A) is true
- B. Only (B) is true
- C. Both (A) and (B) are true
- D. Neither (A) nor (B) is true
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Q13
MATHS
Unit 6: Sequence and Series
Let $x_1,x_2,\ldots,x_{100}$ be in an arithmetic progression, with $x_1=2$ and their mean equal to $200$. If $y_i=i(x_i-i)$, $1\le i\le 100$, then the mean of $y_1,y_2,\ldots,y_{100}$ is
↻ Repeated question — also appeared in
2023 (1 set)
- A. 10051.50
- B. 10049.50
- C. 10101.50
- D. 10100
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Q14
MATHS
Unit 2: Complex Numbers and Quadratic Equations
Let $w_1$ be the point obtained by the rotation of $z_1=5+4i$ about the origin through a right angle in the anticlockwise direction, and $w_2$ be the point obtained by the rotation of $z_2=3-5i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $w_1-w_2$ is equal to
↻ Repeated question — also appeared in
2023 (1 set)
- A. $\pi-\tan^{-1}\!\left(\frac{33}{5}\right)$
- B. $-\pi+\tan^{-1}\!\left(\frac{33}{5}\right)$
- C. $\pi-\tan^{-1}\!\left(\frac{8}{9}\right)$
- D. $-\pi+\tan^{-1}\!\left(\frac{8}{9}\right)$
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Q15
MATHS
Unit 8: Integral Calculus
The value of the integral
$$\int_{-\log_e 2}^{\log_e 2}\log_e\!\left(e^x+\sqrt{1+e^{2x}}\right)dx$$
is equal to
↻ Repeated question — also appeared in
2023 (1 set)
- A. $\log_e\!\left(\dfrac{(2+\sqrt5)^2}{\sqrt{1+\sqrt5}}\right)+\dfrac{\sqrt5}{2}$
- B. $\log_e\!\left(\dfrac{\sqrt2(2+\sqrt5)^2}{\sqrt{1+\sqrt5}}\right)-\dfrac{\sqrt5}{2}$
- C. $\log_e\!\left(\dfrac{2(2+\sqrt5)}{\sqrt{1+\sqrt5}}\right)-\dfrac{\sqrt5}{2}$
- D. $\log_e\!\left(\dfrac{\sqrt2(3-\sqrt5)^2}{\sqrt{1+\sqrt5}}\right)+\dfrac{\sqrt5}{2}$
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Q16
MATHS
Unit 14: Trigonometry
The number of elements in the set
$$S=\{\theta\in[0,2\pi]:3\cos^4\theta-5\cos^2\theta-2\sin^6\theta+2=0\}$$ is
↻ Repeated question — also appeared in
2023 (1 set)
- A. 8
- B. 9
- C. 10
- D. 12
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Q17
MATHS
Unit 13: Statistics and Probability
Let $S = \{M = [a_{ij}],\ a_{ij} \in \{0,1,2\},\ 1 \le i,j \le 2\}$ be a sample space and $A = \{M \in S : M \text{ is invertible}\}$ be an event. Then $P(A)$ is equal to
↻ Repeated question — also appeared in
2023 (1 set)
- A. $\frac{47}{81}$
- B. $\frac{16}{27}$
- C. $\frac{49}{81}$
- D. $\frac{50}{81}$
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Q18
MATHS
Unit 13: Statistics and Probability
Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively. A new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding $2$ to each element of $B$. Then the sum of the mean and variance of the elements of $C$ is _____________.
↻ Repeated question — also appeared in
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- A. 38
- B. 32
- C. 36
- D. 40
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Q19
MATHS
Unit 10: Co-ordinate Geometry
Let $R$ be a rectangle given by the lines $x = 0$, $x = 2$, $y = 0$ and $y = 5$. Let $A(a,0)$ and $B(0,b)$, $a \in [0,2]$ and $b \in [0,5]$, be such that the line segment $AB$ divides the area of the rectangle $R$ in the ratio $4:1$. Then the mid-point of $AB$ lies on a
↻ Repeated question — also appeared in
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- A. straight line
- B. parabola
- C. hyperbola
- D. circle
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Q31
PHYSICS
Unit 16: Optics
A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at $4\,\text{km}$ distance from it is $x \times 10^{-2}\,\text{m}$. The value of $x$ is ________.
(Let, radius of earth $R = 6400\,\text{km}$)
- A. 1.25
- B. 12.5
- C. 125
- D. 1250
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Q32
PHYSICS
Unit 19: Electronic Devices
The logic performed by the circuit shown in figure is equivalent to:
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- A. OR
- B. NAND
- C. AND
- D. NOR
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Q33
PHYSICS
Unit 18: Atoms and Nuclei
Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $\lambda_A$ and $\lambda_B$ are decay constants of A and B respectively, then choose the correct relation from the given options.
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- A. $\lambda_A \ln 2 = \lambda_B$
- B. $\lambda_A = \lambda_B \ln 2$
- C. $\lambda_A = \lambda_B$
- D. $\lambda_A = 2\lambda_B$
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Q34
PHYSICS
Unit 17: Dual Nature of Matter and Radiation
A metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is $V_0$. If the same surface is illuminated with radiation of wavelength $2\lambda$, the stopping potential becomes $\frac{V_0}{4}$. The threshold wavelength for this metallic surface will be
↻ Repeated question — also appeared in
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- A. $4\lambda$
- B. $\frac{3}{2}\lambda$
- C. $3\lambda$
- D. $\frac{\lambda}{4}$
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Q35
PHYSICS
Unit 16: Optics
The critical angle for a denser-rarer interface is $45^\circ$. The speed of light in rarer medium is $3 \times 10^8$ m/s. The speed of light in the denser medium is:
↻ Repeated question — also appeared in
2023 (1 set)
- A. $2.12 \times 10^8$ m/s
- B. $3.12 \times 10^7$ m/s
- C. $5 \times 10^7$ m/s
- D. $\sqrt{2} \times 10^8$ m/s
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Q36
PHYSICS
Unit 14: Electromagnetic Induction and Alternating Currents
As per the given graph, choose the correct representation for curve A and curve B.
Where $X_C$ = reactance of pure capacitive circuit connected with A.C. source
$X_L$ = reactance of pure inductive circuit connected with A.C. source
$R$ = impedance of pure resistive circuit connected with A.C. source
$Z$ = impedance of the LCR series circuit
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- A. $A = X_C,\ B = X_L$
- B. $A = X_L,\ B = Z$
- C. $A = X_C,\ B = R$
- D. $A = X_L,\ B = R$
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Q37
PHYSICS
Unit 15: Electromagnetic Waves
The electric field in an electromagnetic wave is given as
$\vec{E} = 20\sin\omega\left(t - \dfrac{x}{c}\right)\hat{j}$ N$^{-1}$ C
where $\omega$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5 \times 10^{-4}$ m$^3$ will be
(Given $\varepsilon_0 = 8.85 \times 10^{-12}$ C$^2$/Nm$^2$)
↻ Repeated question — also appeared in
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- A. $8.85 \times 10^{-13}$ J
- B. $88.5 \times 10^{-13}$ J
- C. $28.5 \times 10^{-13}$ J
- D. $17.7 \times 10^{-13}$ J
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Q38
PHYSICS
Unit 13: Magnetic Effects of Current and Magnetism
The free space inside a current carrying toroid is filled with a material of susceptibility $2 \times 10^{-2}$. The percentage increase in the value of magnetic field inside the toroid will be
↻ Repeated question — also appeared in
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- A. 2%
- B. 0.2%
- C. 1%
- D. 0.1%
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Q39
PHYSICS
Unit 12: Current Electricity
The current sensitivity of moving coil galvanometer is increased by 25%. This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be:
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- A. +25%
- B. -25%
- C. Zero
- D. -50%
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Q40
PHYSICS
Unit 4: Work Energy and Power
Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:
- A. 1 : 4
- B. 4 : 1
- C. 1 : 2
- D. 2 : 1
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Q41
PHYSICS
Unit 12: Current Electricity
A parallel plate capacitor of capacitance $2$ F is charged to a potential $V$. The energy stored in the capacitor is $E_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_2$. The ratio $E_2/E_1$ is:
- A. 1 : 2
- B. 2 : 1
- C. 2 : 3
- D. 1 : 4
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Q42
PHYSICS
Unit 4: Work Energy and Power
The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $(x)$ starting from mean position to extreme position $(A)$ is given by
- A. Graph rising linearly from $0$ to maximum at $A$
- B. Graph constant with $x$
- C. Graph rising nonlinearly from $0$ to maximum at $A$
- D. Graph falling from maximum at $x=0$ to $0$ at $A$
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Q43
PHYSICS
Unit 9: Kinetic Theory of Gases
Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed ($v_{\text{rms}}$) and choose the correct answer from the options given below:
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- A. $v_{\text{rms}}$(mono) > $v_{\text{rms}}$(dia) > $v_{\text{rms}}$(poly)
- B. $v_{\text{rms}}$(mono) < $v_{\text{rms}}$(dia) < $v_{\text{rms}}$(poly)
- C. $v_{\text{rms}}$(mono) = $v_{\text{rms}}$(dia) = $v_{\text{rms}}$(poly)
- D. $v_{\text{rms}}$(dia) < $v_{\text{rms}}$(poly) < $v_{\text{rms}}$(mono)
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Q44
PHYSICS
Unit 8: Thermodynamics
1 kg of water at 100$^\circ$C is converted into steam at 100$^\circ$C by boiling at atmospheric pressure. The volume of water changes from $1.00 \times 10^{-3}\ \text{m}^3$ as a liquid to $1.671\ \text{m}^3$ as steam. The change in internal energy of the system during the process will be
(Given latent heat of vaporisation = 2257 kJ/kg, Atmospheric pressure = $1 \times 10^5\ \text{Pa}$)
↻ Repeated question — also appeared in
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- A. $-2090\ \text{kJ}$
- B. $+2090\ \text{kJ}$
- C. $-2426\ \text{kJ}$
- D. $+2476\ \text{kJ}$
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Q45
MATHS
Unit 14: Trigonometry
On a temperature scale 'X', the boiling point of water is 65$^\circ$X and the freezing point is $-15^\circ$X. Assume that the X scale is linear. The equivalent temperature corresponding to $-95^\circ$X on the Fahrenheit scale would be:
- A. $-48^\circ$F
- B. $-63^\circ$F
- C. $-112^\circ$F
- D. $-148^\circ$F
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Q46
PHYSICS
Unit 6: Gravitation
The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $\rho$ and $\rho/3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_A : g_B)$ will be:
↻ Repeated question — also appeared in
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- A. 3 : 16
- B. 4 : 3
- C. 3 : 4
- D. 1 : 16
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Q47
PHYSICS
Unit 2: Kinematics
From the $v$ - $t$ graph shown, the ratio of distance to displacement in 25 s of motion is:
↻ Repeated question — also appeared in
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- A. 1
- B. $\frac{1}{2}$
- C. $\frac{5}{3}$
- D. $\frac{3}{5}$
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Q48
PHYSICS
Unit 5: Rotational Motion
A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of ____ from the centre :
- A. 1 cm
- B. 2 cm
- C. 4 cm
- D. 8 cm
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Q49
PHYSICS
Unit 4: Work Energy and Power
An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m/s to keep it in position. The number of bullets fired per second by the machine gun is:
- A. 5
- B. 100
- C. 50
- D. 25
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Q50
PHYSICS
Unit 1: Units and Measurements
Given below are two statements :
Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.
Statements II : Au < Parsec (Pc) < ly
In the light of the above statements, choose the most appropriate answer from the options given below:
- A. Both Statements I and Statements II are correct
- B. Both Statements I and Statements II are incorrect
- C. Statements I is correct but Statements II is incorrect
- D. Statements I is incorrect but Statements II is correct
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Q61
CHEMISTRY
Unit 12: Coordination Compounds
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: In the photoelectric effect, the electrons are ejected from the metal surface as soon as the beam of light of frequency greater than threshold frequency strikes the surface.
Reason R: When the photon of any energy strikes an electron in the atom, transfer of energy from the photon to the electron takes place.
In the light of the above statements, choose the most appropriate answer from the options given below:
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- A. Both A and R are correct and R is the correct explanation of A
- B. Both A and R are correct but R is NOT the correct explanation of A
- C. A is correct but R is not correct
- D. A is not correct but R is correct
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Q62
CHEMISTRY
Unit 3: Chemical Bonding and Molecular Structure
Match List-I with List-II:
List-I Species
A. $\mathrm{H_3O^+}$
B. Acetylide anion
C. $\mathrm{NH_4^+}$
D. $\mathrm{ClO_2^-}$
List-II Geometry/Shape
I. Tetrahedral
II. Linear
III. Pyramidal
IV. Bent
Choose the correct answer from the options given below:
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- A. A-III, B-II, C-I, D-IV
- B. A-III, B-I, C-II, D-IV
- C. A-III, B-IV, C-I, D-II
- D. A-III, B-IV, C-II, D-I
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Q63
CHEMISTRY
Unit 6: Equilibrium
$25\ \mathrm{mL}$ of silver nitrate solution $(1\ \mathrm{M})$ is added dropwise to $25\ \mathrm{mL}$ potassium iodide $(1.05\ \mathrm{M})$ solution. The ion(s) present in very small quantity in the solution is/are
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- A. $\mathrm{I^-}$ only
- B. $\mathrm{Ag^+}$ and $\mathrm{I^-}$ both
- C. $\mathrm{K^+}$ only
- D. $\mathrm{NO_3^-}$ only
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Q64
CHEMISTRY
Unit 9: Classification of Elements and Periodicity in Properties
For elements B, C, N, Li, Be, O and F, the correct order of first ionization enthalpy is
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- A. $\mathrm{Li < Be < B < C < N < O < F}$
- B. $\mathrm{Li < B < Be < C < O < N < F}$
- C. $\mathrm{B > Li > Be > C > N > O > F}$
- D. $\mathrm{Li < Be < B < C < O < N < F}$
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Q65
CHEMISTRY
Unit 11: d- and f-Block Elements
In the extraction process of copper, the product obtained after carrying out the reactions
(i) $2\mathrm{Cu_2S} + 3\mathrm{O_2} \rightarrow 2\mathrm{Cu_2O} + 2\mathrm{SO_2}$
(ii) $2\mathrm{Cu_2O} + \mathrm{Cu_2S} \rightarrow 6\mathrm{Cu} + \mathrm{SO_2}$
is called
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- A. Copper matte
- B. Copper scrap
- C. Blister copper
- D. Reduced copper
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Q66
CHEMISTRY
Unit 7: Redox Reactions and Electrochemistry
Given below are two statements:
Statement-I: Methane and steam passed over a heated Ni catalyst produces hydrogen gas.
Statement-II: Sodium nitrite reacts with $\mathrm{NH_4Cl}$ to give $\mathrm{H_2O}$, $\mathrm{N_2}$ and $\mathrm{NaCl}$.
In the light of the above statements, choose the most appropriate answer from the options given below:
- A. Both the statements I and II are correct
- B. Both the statements I and II are incorrect
- C. Statement I is correct but Statement II is incorrect
- D. Statement I is incorrect but Statement II is correct
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Q67
CHEMISTRY
Unit 11: d- and f-Block Elements
Match List-I with List-II:
List-I
A. K
B. KCl
C. KOH
D. Li
List-II
I. Thermonuclear reactions
II. Fertilizer
III. Sodium potassium pump
IV. Absorbent of $\mathrm{CO_2}$
Choose the correct answer from the options given below:
- A. A-IV, B-I, C-III, D-II
- B. A-IV, B-III, C-I, D-II
- C. A-III, B-IV, C-II, D-I
- D. A-III, B-II, C-IV, D-I
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Q68
CHEMISTRY
Unit 10: p-Block Elements
For compound having the formula $\mathrm{GaAlCl_4}$, the correct option from the following is
- A. Oxidation state of Ga in the salt $\mathrm{GaAlCl_4}$ is $+3$.
- B. Ga is coordinated with Cl in $\mathrm{GaAlCl_4}$
- C. Ga is more electronegative than Al and is present as a cationic part of the salt $\mathrm{GaAlCl_4}$
- D. Cl forms bond with both Al and Ga in $\mathrm{GaAlCl_4}$
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Q69
CHEMISTRY
Unit 12: Coordination Compounds
Which of the following complex has a possibility to exist as meridional isomer?
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- A. [Co(NH$_3$)$_3$(NO$_2$)$_3$]
- B. [Co(en)$_3$]
- C. [Co(en)$_2$Cl$_2$]
- D. [Pt(NH$_3$)$_2$Cl$_2$]
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Q70
CHEMISTRY
Unit 13: Purification and Characterisation of Organic Compounds
The set which does not have ambidentate ligand(s) is
- A. $\mathrm{EDTA}^{4-},\ \mathrm{NCS}^-,\ \mathrm{C_2O_4^{2-}}$
- B. $\mathrm{NO_2^-},\ \mathrm{C_2O_4^{2-}},\ \mathrm{EDTA}^{4-}$
- C. $\mathrm{C_2O_4^{2-}},\ \text{ethylene diamine},\ \mathrm{H_2O}$
- D. $\mathrm{C_2O_4^{2-}},\ \mathrm{NO_2^-},\ \mathrm{NCS}^-$
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Q71
CHEMISTRY
Unit 20: Principles Related to Practical Chemistry
Given below are two statements:
Statement I: If BOD is 4 ppm and dissolved oxygen is 8 ppm, then it is a good quality water.
Statement II: If the concentration of zinc and nitrate salts are 5 ppm each, then it can be a good quality water.
In the light of the above statements, choose the most appropriate answer from the options given below:
↻ Repeated question — also appeared in
2023 (1 set)
- A. Both the statements I and II are correct
- B. Both the statements I and II are incorrect
- C. Statement I is correct but Statement II is incorrect
- D. Statement I is incorrect but Statement II is correct
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Q72
CHEMISTRY
Unit 13: Purification and Characterisation of Organic Compounds
Thin layer chromatography of a mixture shows the following observation:
The correct order of elution in the silica gel column chromatography is
↻ Repeated question — also appeared in
2023 (1 set)
- A. B, C, A
- B. A, C, B
- C. C, A, B
- D. B, A, C
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Q73
CHEMISTRY
Unit 16: Organic Compounds Containing Halogens
Arrange the following compounds in increasing order of rate of aromatic electrophilic substitution reaction
- A. c, a, b, d
- B. b, c, a, d
- C. d, b, c, a
- D. d, b, a, c
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Q74
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
Where $\mathrm{Nu} =$ nucleophile, find out the correct statement from the options given below for the above 2 reactions.
- A. Reaction (I) is of 1st order and reaction (II) is of 2nd order
- B. Reactions (I) and (II) both are of 1st order
- C. Reactions (I) and (II) both are of 2nd order
- D. Reaction (I) is of 2nd order and reaction (II) is of 1st order
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Q75
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
$A$ and $B$ in the above reactions are:
- A. $A = \mathrm{CO_2H}$-terminated keto acid; $B = \mathrm{CO_2H}$-terminated alkane
- B. A dicarboxylic acid derivative and B a hydrazone-containing product
- C. $A$ is a keto acid and $B$ is the corresponding open-chain acid after Wolff-Kishner reduction
- D. $A$ is a keto acid and $B$ is the corresponding hydrocarbon with one carbonyl reduced to $\mathrm{CH_2}$
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Q76
CHEMISTRY
Unit 12: Coordination Compounds
The complex that dissolves in water is
↻ Repeated question — also appeared in
2023 (1 set)
- A. $[\mathrm{Fe_3(OH)_2(OAc)_6}]\,\mathrm{Cl}$
- B. $\mathrm{K_3[Co(NO_2)_6]}$
- C. $\mathrm{Fe_4[Fe(CN)_6]_3}$
- D. $\mathrm{(NH_4)_3[As(Mo_3O_{10})_4]}$
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Q77
CHEMISTRY
Unit 18: Organic Compounds Containing Nitrogen
o-Phenylenediamine reacts with $\mathrm{HNO_2}$ to give 'X'. 'X' is major product.
-
A.
Benzotriazole (benzene ring fused with a five-membered ring containing three nitrogens)
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B.
Benzotriazole tautomer with one $\mathrm{N-H}$ group
-
C.
o-Diazoniobenzene-type intermediate with two diazonium groups
-
D.
Indazole-like fused bicyclic compound with $\mathrm{NH}$
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Q78
CHEMISTRY
Unit 15: Hydrocarbons
The polymer $X$ consists of linear molecules and is closely packed. It is prepared in the presence of triethylaluminium and titanium tetrachloride under low pressure. The polymer $X$ is-
↻ Repeated question — also appeared in
2023 (1 set)
- A. Polytetrafluoroethane
- B. Polyacrylonitrile
- C. High density polythene
- D. Low density polythene
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Q79
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
L-isomer of tetrose $X$ ($\mathrm{C_4H_8O_4}$) gives positive Schiff's test and has two chiral carbons. On acetylation, $X$ yields triacetate. $X$ also undergoes following reactions:
$X' \xrightarrow[\mathrm{NaBH_4}]{} B'$ (chiral compound)
$X'$ \xrightarrow{\mathrm{HNO_3}} A'
$X$ is
-
A.
L-erythrose
-
B.
L-threose
-
C.
D-erythrose
-
D.
D-threose
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Q80
CHEMISTRY
Unit 6: Equilibrium
When a solution of mixture having two inorganic salts was treated with freshly prepared ferrous sulphate in acidic medium, a dark brown ring was formed whereas on treatment with neutral $\mathrm{FeCl_3}$ it gave deep red colour which disappeared on boiling and a brown red ppt was formed. The mixture contains
- A. $\mathrm{C_2O_4^{2-}}$ and $\mathrm{NO_3^-}$
- B. $\mathrm{CH_3COO^-}$ and $\mathrm{NO_3^-}$
- C. $\mathrm{SO_3^{2-}}$ and $\mathrm{CH_3COO^-}$
- D. $\mathrm{SO_3^{2-}}$ and $\mathrm{C_2O_4^{2-}}$
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