Q1
MATHS
Unit 2: Complex Numbers and Quadratic Equations
Let $D$ be the domain of the function $f(x)=\sin^{-1}\!\left(\log_{3x}\!\left(\frac{6+2\log_3 x}{-5x}\right)\right)$. If the range of the function $g:D\to\mathbb{R}$ defined by $g(x)=x-[x]$, $[x]$ is the greatest integer function, is $(\alpha,\beta)$, then $\alpha^2+\frac{5}{\beta}$ is equal to
- A. 45
- B. 46
- C. 135
- D. 136
Correct answer & explanation hidden
Log in to view solution →
Q2
MATHS
Unit 2: Complex Numbers and Quadratic Equations
Let $\alpha,\beta$ be the roots of the quadratic equation $x^2+\sqrt{6}\,x+3=0$. Then $\dfrac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}$ is equal to
- A. 9
- B. 72
- C. 81
- D. 729
Correct answer & explanation hidden
Log in to view solution →
Q3
MATHS
Unit 3: Matrices and Determinants
Let $A=\begin{bmatrix}1 & \tfrac{1}{51}\\[2pt] 0 & 1\end{bmatrix}$. If $B=\begin{bmatrix}1 & 2\\ -1 & -1\end{bmatrix}A\begin{bmatrix}-1 & -2\\ 1 & 1\end{bmatrix}$, then the sum of all the elements of the matrix $\sum_{n=1}^{50}B^n$ is equal to
- A. 50
- B. 75
- C. 100
- D. 125
Correct answer & explanation hidden
Log in to view solution →
Q4
MATHS
Unit 4: Permutations and Combinations
The number of five digit numbers, greater than 40000 and divisible by $5$, which can be formed using the digits $0,1,3,5,7$ and $9$ without repetition, is equal to
- A. 72
- B. 96
- C. 120
- D. 132
Correct answer & explanation hidden
Log in to view solution →
Q5
MATHS
Unit 5: Binomial Theorem and its Simple Applications
The sum of the coefficients of the first $50$ terms in the binomial expansion of $(1-x)^{100}$, is equal to
- A. ${}^{99}C_{49}$
- B. $-{}^{99}C_{49}$
- C. ${}^{101}C_{50}$
- D. $-{}^{101}C_{50}$
Correct answer & explanation hidden
Log in to view solution →
Q6
MATHS
Unit 4: Permutations and Combinations
If $\dfrac{1}{n+1}{^nC_n}+\dfrac{1}{n}{^nC_{n-1}}+\cdots+\dfrac{1}{2}{^nC_1}+{^nC_0}=\dfrac{1023}{10}$ then $n$ is equal to
- A. 6
- B. 7
- C. 8
- D. 9
Correct answer & explanation hidden
Log in to view solution →
Q7
MATHS
Unit 2: Complex Numbers and Quadratic Equations
Let $C$ be the circle in the complex plane with centre $z_0=\tfrac{1}{2}(1+3i)$ and radius $r=1$. Let $z_1=1+i$ and the complex number $z_2$ outside the circle $C$ such that $|z_1-z_0|\,|z_2-z_0|=1$. If $z_0$, $z_1$ and $z_2$ are collinear, then the smaller value of $|z_2|^2$ is equal to
- A. $\tfrac{3}{2}$
- B. $\tfrac{5}{2}$
- C. $\tfrac{7}{2}$
- D. $\tfrac{13}{2}$
Correct answer & explanation hidden
Log in to view solution →
Q8
MATHS
Unit 6: Sequence and Series
Let $\langle a_n\rangle$ be a sequence such that $a_1+a_2+\cdots+a_n=\dfrac{n^2+3n}{(n+1)(n+2)}$. If $28\sum_{k=1}^{10}\dfrac{1}{a_k}=p_1p_2p_3\cdots p_m$, where $p_1,p_2,\dots,p_m$ are the first $m$ prime numbers, then $m$ is equal to
- A. 5
- B. 6
- C. 7
- D. 8
Correct answer & explanation hidden
Log in to view solution →
Q9
MATHS
Unit 8: Integral Calculus
If the local maximum value of the function $f(x)=\left(\frac{\sqrt{3}e}{2\sin x}\right)^{\sin^2 x}$, $x\in\left(0,\frac{\pi}{2}\right)$, is $\frac{k}{e}$, then $\left(\frac{k}{e}\right)^8+\frac{k^8}{e^5}+k^8$ is equal to
- A. $e^5+e^6+e^{11}$
- B. $e^3+e^6+e^{10}$
- C. $e^3+e^5+e^{11}$
- D. $e^3+e^6+e^{11}$
Correct answer & explanation hidden
Log in to view solution →
Q10
MATHS
Unit 8: Integral Calculus
The area of the region enclosed by the curve $y=x^3$ and its tangent at the point $(-1,-1)$ is
- A. $\frac{19}{4}$
- B. $\frac{23}{4}$
- C. $\frac{27}{4}$
- D. $\frac{31}{4}$
Correct answer & explanation hidden
Log in to view solution →
Q11
MATHS
Unit 9: Differential Equations
Let $y=y(x)$, $y>0$, be a solution curve of the differential equation $(1+x^2)\,dy=y(x-y)\,dx$. If $y(0)=1$ and $y(2\sqrt{2})=\beta$, then
- A. $e^{\beta^{-1}}=e^{-2}(3+2\sqrt{2})$
- B. $e^{3\beta^{-1}}=e(5+\sqrt{2})$
- C. $e^{\beta^{-1}}=e^{-2}(5+\sqrt{2})$
- D. $e^{3\beta^{-1}}=e(3+2\sqrt{2})$
Correct answer & explanation hidden
Log in to view solution →
Q12
MATHS
Unit 10: Co-ordinate Geometry
Let $P\left(\frac{2\sqrt{3}}{\sqrt{7}},\frac{6}{\sqrt{7}}\right)$, $Q$, $R$ and $S$ be four points on the ellipse $9x^2+4y^2=36$. Let $PQ$ and $RS$ be mutually perpendicular and pass through the origin. If $\frac{1}{(PQ)^2}+\frac{1}{(RS)^2}=\frac{p}{q}$, where $p$ and $q$ are coprime, then $p+q$ is equal to
- A. 137
- B. 143
- C. 147
- D. 157
Correct answer & explanation hidden
Log in to view solution →
Q13
MATHS
Unit 10: Co-ordinate Geometry
If the point $(\alpha,\frac{7\sqrt{3}}{3})$ lies on the curve traced by the mid-points of the line segments of the lines $x\cos\theta+y\sin\theta=7$, $\theta\in\left(0,\frac{\pi}{2}\right)$ between the co-ordinate axes, then $\alpha$ is equal to
- A. -7
- B. -7\sqrt{3}
- C. 7
- D. 7\sqrt{3}
Correct answer & explanation hidden
Log in to view solution →
Q14
MATHS
Unit 11: Three Dimensional Geometry
Let the plane $P: 4x-y+z=10$ be rotated by an angle $\frac{\pi}{2}$ about its line of intersection with the plane $x+y-z=4$. If $a$ is the distance of the point $(2,3,-4)$ from the new position of the plane $P$, then $35a$ is equal to
- A. 85
- B. 90
- C. 105
- D. 126
Correct answer & explanation hidden
Log in to view solution →
Q15
MATHS
Unit 11: Three Dimensional Geometry
Let the lines $l_1: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}$ and $l_2: 3x+2y+z-2=0= x-3y+2z-13$ be coplanar. If the point $P(a,b,c)$ on $l_1$ is nearest to the point $Q(-4,-3,2)$, then $|a|+|b|+|c|$ is equal to
- A. 8
- B. 10
- C. 12
- D. 14
Correct answer & explanation hidden
Log in to view solution →
Q16
MATHS
Unit 12: Vector Algebra
Let $a$, $b$, $c$ be three distinct real numbers, none equal to one. If the vectors $a\hat{i}+\hat{j}+\hat{k}$, $\hat{i}+b\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}+c\hat{k}$ are coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is equal to
- A. -1
- B. 1
- C. -2
- D. 2
Correct answer & explanation hidden
Log in to view solution →
Q17
MATHS
Unit 12: Vector Algebra
Let $\lambda \in \mathbb{Z}$, $\vec{a} = \lambda \hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = 3\hat{i} - \hat{j} + 2\hat{k}$. Let $\vec{c}$ be a vector such that $(\vec{a} + \vec{b} + \vec{c}) \times \vec{c} = \vec{0}$, $\vec{a} \cdot \vec{c} = -17$ and $\vec{b} \cdot \vec{c} = -20$. Then $\left|\vec{c} \times (\lambda \hat{i} + \hat{j} + \hat{k})\right|^2$ is equal to
- A. 46
- B. 49
- C. 53
- D. 62
Correct answer & explanation hidden
Log in to view solution →
Q18
MATHS
Unit 13: Statistics and Probability
Two dice $A$ and $B$ are rolled. Let the numbers obtained on $A$ and $B$ be $\alpha$ and $\beta$ respectively. If the variance of $\alpha-\beta$ is $\dfrac{p}{q}$, where $p$ and $q$ are co-prime, then the sum of the positive divisors of $p$ is equal to
- A. 31
- B. 36
- C. 48
- D. 72
Correct answer & explanation hidden
Log in to view solution →
Q19
MATHS
Unit 14: Trigonometry
In a triangle $ABC$, if $\cos A + 2\cos B + \cos C = 2$ and the lengths of the sides opposite to the angles $A$ and $C$ are $3$ and $7$ respectively, then $\cos A - \cos C$ is equal to
- A. $\dfrac{3}{7}$
- B. $\dfrac{10}{7}$
- C. $\dfrac{5}{7}$
- D. $\dfrac{9}{7}$
Correct answer & explanation hidden
Log in to view solution →
Q20
MATHS
Unit 2: Complex Numbers and Quadratic Equations
Among the two statements
$(S1): (p \Rightarrow q) \wedge (p \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology
- A. both are true.
- B. both are false.
- C. only (S1) is true.
- D. only (S2) is true.
Correct answer & explanation hidden
Log in to view solution →
Q31
PHYSICS
Unit 6: Gravitation
Two satellites $A$ and $B$ move round the earth in the same orbit. The mass of $A$ is twice the mass of $B$. The quantity which is same for the two satellites will be
- A. Speed
- B. Kinetic energy
- C. Potential energy
- D. Total energy
Correct answer & explanation hidden
Log in to view solution →
Q32
PHYSICS
Unit 1: Units and Measurements
Match List I with List II
LIST I
A. Spring constant
B. Angular speed
C. Angular momentum
D. Moment of Inertia
LIST II
I. $[T^{-1}]$
II. $[M T^{-2}]$
III. $[M L^2]$
IV. $[M L^2 T^{-1}]$
Choose the correct answer from the options given below:
- A. A-I, B-III, C-II, D-IV
- B. A-II, B-I, C-IV, D-III
- C. A-IV, B-I, C-III, D-II
- D. A-II, B-III, C-I, D-IV
Correct answer & explanation hidden
Log in to view solution →
Q33
PHYSICS
Unit 3: Laws of Motion
Given below are two statements:
Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance.
Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.
In the light of given statements, choose the most appropriate answer given below
- A. Both Statement I and Statement II are correct.
- B. Both Statement I and Statement II are incorrect.
- C. Statement I is correct but Statement II is incorrect.
- D. Statement I is incorrect but Statement II is correct.
Correct answer & explanation hidden
Log in to view solution →
Q34
PHYSICS
Unit 15: Electromagnetic Waves
The amplitude of $15\sin(1000\pi t)$ is modulated by $10\sin(4\pi t)$ signal. The amplitude modulated signal contains frequencies of
A. 500 Hz
B. 2 Hz
C. 250 Hz
D. 498 Hz
E. 502 Hz
Choose the correct answer from the options given below:
- A. A, D and E only
- B. A and B only
- C. A and C only
- D. A and D only
Correct answer & explanation hidden
Log in to view solution →
Q35
PHYSICS
Unit 12: Current Electricity
Given below are two statements:
Statement I : When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.
Statement II : In a series LCR circuit, the value of power factor at resonance is one.
In the light of given statements, choose the most appropriate answer from the options given below.
- A. Both Statement I and Statement II are true.
- B. Both Statement I and Statement II are False.
- C. Statement I is correct but Statement II is false.
- D. Statement I is incorrect but Statement II is true.
Correct answer & explanation hidden
Log in to view solution →
Q36
PHYSICS
Unit 6: Gravitation
The ratio of escape velocity of a planet to the escape velocity of earth will be:-
Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.
- A. 2:1
- B. 1:$\sqrt{2}$
- C. 4:1
- D. 1:4
Correct answer & explanation hidden
Log in to view solution →
Q37
PHYSICS
Unit 8: Thermodynamics
A body cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 5 minutes. The temperature of the surrounding is $20^\circ\text{C}$. The time it takes to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$ is:
- A. $\frac{25}{3}$ s
- B. 500 s
- C. 450 s
- D. 420 s
Correct answer & explanation hidden
Log in to view solution →
Q38
PHYSICS
Unit 8: Thermodynamics
An engine operating between the boiling and freezing points of water will have
A. efficiency more than 27%.
B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.
C. efficiency equal to 27%
D. efficiency less than 27%
Choose the correct answer from the options given below:
- A. B and C only
- B. B and D only
- C. A and B only
- D. B, C and D only
Correct answer & explanation hidden
Log in to view solution →
Q39
PHYSICS
Unit 9: Kinetic Theory of Gases
If the r. m. s speed of chlorine molecule is 490 m/s at $27^\circ\text{C}$, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon = 39.9 u, molar mass of chlorine = 70.9 u)
- A. 451.7 m/s
- B. 551.7 m/s
- C. 651.7 m/s
- D. 751.7 m/s
Correct answer & explanation hidden
Log in to view solution →
Q40
PHYSICS
Unit 10: Oscillations and Waves
A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
- A. 1:4
- B. 1:3
- C. 2:1
- D. 1:1
Correct answer & explanation hidden
Log in to view solution →
Q41
PHYSICS
Unit 11: Electrostatics
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : If an electric dipole of dipole moment $30\times 10^{-5}$ C m is enclosed by a closed surface, the net flux coming out of the surface will be zero.
Reason R : Electric dipole consists of two equal and opposite charges.
In the light of above, statements, choose the correct answer from the options given below.
- A. Both A and R are true but R is NOT the correct explanation of A
- B. A is true but R is false
- C. A is false but R is true
- D. Both A and R are false
Correct answer & explanation hidden
Log in to view solution →
Q42
PHYSICS
Unit 12: Current Electricity
160 $\Omega$ प्रतिरोध वाले तार को पिघलाकर इसकी लंबाई की एक-चौथाई लंबाई के बराबर का एक तार बनाया जाता है तार का नया प्रतिरोध होगा:
- A. 10 $\Omega$
- B. 16 $\Omega$
- C. 40 $\Omega$
- D. 640 $\Omega$
Correct answer & explanation hidden
Log in to view solution →
Q44
PHYSICS
Unit 2: Kinematics
A ball is thrown vertically upwards from a high tower with an initial velocity of $5\,\text{m s}^{-1}$ and after $3\,\text{s}$ and $5\,\text{s}$ its velocities are $x$ and $\frac{x+1}{x}$ respectively. Find the value of $x$ if $g = 10\,\text{m s}^{-2}$.
- A. 6
- B. 10
- C. -5
- D. 5
Correct answer & explanation hidden
Log in to view solution →
Q45
PHYSICS
Unit 3: Laws of Motion
A $5\,\text{kg}$ block is placed on a smooth horizontal surface. Forces $F_1=10\,\text{N}$, $F_2=8\,\text{N}$ and $F_3=6\,\text{N}$ act on it. If $F_2$ and $F_3$ are opposite in direction and the body is in equilibrium, then if $F_1$ is removed, the acceleration of the block is:
- A. $2\,\text{m s}^{-2}$
- B. $7\,\text{m s}^{-2}$
- C. $4.8\,\text{m s}^{-2}$
- D. $0.5\,\text{m s}^{-2}$
Correct answer & explanation hidden
Log in to view solution →
Q47
PHYSICS
Unit 11: Electrostatics
A proton and an $\alpha$-particle are accelerated through potentials of $2\,\text{V}$ and $4\,\text{V}$ respectively. The ratio of their de-Broglie wavelengths is:
- A. 1
- B. 2
- C. 3
- D. 4
Correct answer & explanation hidden
Log in to view solution →
Q48
PHYSICS
Unit 18: Atoms and Nuclei
A gaseous ion produced in a discharge tube has kinetic energy $12.5\,\text{eV}$ when placed in a magnetic field. The number of excited states is:
- A. 0.9
- B. 9
- C. 110
- D. 210
Correct answer & explanation hidden
Log in to view solution →
Q49
PHYSICS
Unit 19: Electronic Devices
In an $n$-$p$-$n$ transistor (CE configuration), if the base current changes from $100\,\mu\text{A}$ to $200\,\mu\text{A}$ and the collector current changes from $5\,\text{mA}$ to $16\,\text{mA}$, the transistor current gain is:
- A. 0.9
- B. 9
- C. 110
- D. 210
Correct answer & explanation hidden
Log in to view solution →
Q61
CHEMISTRY
Unit 5: Solutions
एक धातु क्लोराइड में भार के अनुसार 55.0% क्लोरीन उपस्थित है। STP पर धातु क्लोराइड के $100\,\text{mL}$ वाष्प का भार $0.57\,\text{g}$ है। धातु क्लोराइड का अणु सूत्र है (दिया गया है: क्लोरीन परमाणु द्रव्यमान $35.5\,u$)
- A. MCl
- B. MCl$_2$
- C. MCl$_3$
- D. MCl$_4$
Correct answer & explanation hidden
Log in to view solution →
Q62
CHEMISTRY
Unit 6: Equilibrium
$\mathrm{O_2^+}$, $\mathrm{N_2^+}$, $\mathrm{NO^+}$, $\mathrm{O_2^-}$ में से एसिटिलाइड आयन की आबन्ध कोटि एवं चुंबकीय आघूर्ण किसके समान है?
- A. $\mathrm{O_2^+}$
- B. $\mathrm{N_2^+}$
- C. $\mathrm{NO^+}$
- D. $\mathrm{O_2^-}$
Correct answer & explanation hidden
Log in to view solution →
Q63
CHEMISTRY
Unit 11: d- and f-Block Elements
लेड संचायक बैटरी के संदर्भ में, सही कथनों को चुनें:
A. बैटरी के चार्जिंग के दौरान, एनोड पर PbSO$_4$ परिवर्तित होता है PbO$_2$ में।
B. बैटरी के चार्जिंग के दौरान, कैथोड पर PbSO$_4$ परिवर्तित होता है PbO$_2$ में।
C. लेड संचायक बैटरी में लेड का एक ग्रिड होता है जिसमें भरा हुआ PbO$_2$ एनोड का कार्य करता है।
D. लेड संचायक बैटरी में विद्युत अपघट्य के रूप में लगभग $38\%$ सल्फ्यूरिक अम्ल होता है।
नीचे दिए गए विकल्पों में से सही उत्तर चुनें:
- A. A, B, D only
- B. B, D only
- C. B, C only
- D. B, C, D only
Correct answer & explanation hidden
Log in to view solution →
Q64
CHEMISTRY
Unit 3: Chemical Bonding and Molecular Structure
चार गैसों A, B, C और D का क्रमिक तापमान क्रमशः $5.3$, $33.2$, $126.0$ और $154.3\,\text{K}$ है। चारकोल के समीप मात्रा पर उनके अधिशोषण का सही क्रम है:
- A. D > C > B > A
- B. D > C > A > B
- C. C > D > B > A
- D. C > B > D > A
Correct answer & explanation hidden
Log in to view solution →
Q65
CHEMISTRY
Unit 10: p-Block Elements
धार धातुओं के घनत्व का क्रम है:
- A. $K < Na < Rb < Cs$
- B. $Na < K < Cs < Rb$
- C. $K < Cs < Na < Rb$
- D. $Na < Rb < K < Cs$
Correct answer & explanation hidden
Log in to view solution →
Q66
CHEMISTRY
Unit 4: Chemical Thermodynamics
नीचे दो कथन दिए गए हैं, एक को अभिकथन A और दूसरे को कारण R के कारण R कहा गया है:
अभिकथन A : एल्युमिनियम चित्र में $\sim 1120^\circ\text{C}$ पर Mg $\to$ MgO के लिए रेखा के ढाल में तीव्र परिवर्तन देखा गया है।
कारण R : अवस्था में परिवर्तन के साथ एन्थैल्पी में बड़ा परिवर्तन जुड़ा है।
उपरोक्त कथनों के प्रकाश में, नीचे दिए गए विकल्पों में से सही उत्तर चुनें:
- A. Both A and R are true and R is the correct explanation of A
- B. Both A and R are true but R is NOT the correct explanation of A
- C. A is true but R is false
- D. A is false but R is true
Correct answer & explanation hidden
Log in to view solution →
Q67
CHEMISTRY
Unit 3: Chemical Bonding and Molecular Structure
सूची I का सूची II से मिलान करें
सची I
A. इलेक्ट्रॉन न्यून हाइड्राइड
B. इलेक्ट्रॉन समुद्र हाइड्राइड
C. इलेक्ट्रॉन परिशुद्ध हाइड्राइड
D. लवणीय हाइड्राइड
सूची II
I. MgH$_2$
II. HF
III. B$_2$H$_6$
IV. CH$_4$
नीचे दिए गए विकल्पों में से सही उत्तर चुनें:
- A. A-II, B-III, C-I, D-IV
- B. A-II, B-III, C-IV, D-I
- C. A-III, B-II, C-IV, D-I
- D. A-III, B-II, C-I, D-IV
Correct answer & explanation hidden
Log in to view solution →
Q69
CHEMISTRY
Unit 10: p-Block Elements
नीचे दो कथन दिए गए हैं:
कथन I : बोरॉन अपेक्षाकृत कठोर है जो इसके उच्च जालक ऊर्जा को इंगित करता है।
कथन II : समूह के अन्य सदस्यों की तुलना में बोरॉन का गलनांक एवं क्वथनांक सर्वाधिक है।
उपयुक्त कथनों के संदर्भ में, नीचे दिए गए विकल्पों में से सर्वाधिक उपयुक्त उत्तर चुनें:
- A. Both statement I and Statement II are correct
- B. Both statement I and Statement II are incorrect
- C. Statement I is correct but Statement II is incorrect
- D. Statement I is incorrect but Statement II is correct
Correct answer & explanation hidden
Log in to view solution →
Q70
CHEMISTRY
Unit 10: p-Block Elements
नीचे दो कथन दिए गए हैं:
कथन I : $\mathrm{SbCl_3}$ की तुलना में $\mathrm{SbCl_5}$ अधिक सहसंयोजी है।
कथन II : हैलोजनों के उच्च आवासाइड निम्न की तुलना में अधिक स्थायी होते हैं।
उपयुक्त कथनों के संदर्भ में, नीचे दिए गए विकल्पों में से सर्वाधिक उपयुक्त उत्तर चुनें:
- A. Both statement I and Statement II are correct
- B. Both statement I and Statement II are incorrect
- C. Statement I is correct but Statement II is incorrect
- D. Statement I is incorrect but Statement II is correct
Correct answer & explanation hidden
Log in to view solution →
Q71
CHEMISTRY
Unit 11: d- and f-Block Elements
नीचे दो कथन दिए हैं, एक को अभिकथन $A$ एवं दूसरे को कारण $R$ कहा गया है।
अभिकथन $A$ : $4f$ इलेक्ट्रॉनों की तुलना में $5f$ इलेक्ट्रॉन आवरण में अधिक मात्रा में भाग तो सकते हैं।
कारण $R$ : $5f$ कक्षक उतने नहीं घेरते हैं जितने कि $4f$ कक्षक।
उपयुक्त कथनों के प्रकाश में, नीचे दिए गए विकल्पों में से सही उत्तर चुनें:
- A. Both A and R are true and R is the correct explanation of A
- B. Both A and R are true but R is NOT the correct explanation of A
- C. A is true but R is false
- D. A is false but R is true
Correct answer & explanation hidden
Log in to view solution →
Q72
CHEMISTRY
Unit 12: Coordination Compounds
सूची I का मिलान सूची II से करें
सचि I संकुल
A. $[\mathrm{Cu(NH_3)_6}]^{2+}$
B. $[\mathrm{Ti(H_2O)_6}]^{3+}$
C. $[\mathrm{Fe(CN)_6}]^{3-}$
D. $[\mathrm{NiF_6}]^{4-}$
सचि II CFSE ($\Delta_o$)
I. $-0.6$
II. $-2.0$
III. $-1.2$
IV. $-0.4$
नीचे दिए गए विकल्पों में से सही उत्तर चुनें:
- A. A-III, B-IV, C-I, D-II
- B. A-I, B-IV, C-II, D-III
- C. A-II, B-III, C-I, D-IV
- D. A-I, B-II, C-IV, D-III
Correct answer & explanation hidden
Log in to view solution →
Q73
CHEMISTRY
Unit 12: Coordination Compounds
सूची I का मिलान सूची II से करें
सूची I
A. वायु में नाइट्रोजन ऑक्साइड
B. वायु में मीथेन
C. कर्बन डाइऑक्साइड
D. जल में फ्लोराइड उत्के
सूची II
I. सुपोषण (eutrophication)
II. वर्षा जल pH 5.6 हो जाता है
III. ग्लोबल वार्मिंग (भूषलीय तापवृद्धि)
IV. अम्ल वर्षा
नीचे दिए गए विकल्पों में से सही उत्तर चुनें:
- A. A-B, C and D only
- B. B, C and D only
- C. A, C and D only
- D. A, B and D only
Correct answer & explanation hidden
Log in to view solution →
Q74
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
व्यख्या के लिए
A. यौगिक $B'$ एरोमैटिक है
B. उपयुक्त अभिक्रिया की पूर्ति अवघटन धमी है
C. $A$ चालकवयता प्रदर्शित करता है
D. यौगिक $B'$ में $C$- $C$ की लंबाई समान पायी गई है
नीचे दिए गए विकल्पों में से सही उत्तर चुनें:
$A$ एक चक्रीय डाइकीटो-डाइहाइड्रॉक्सी यौगिक है जिसमें दोहरे बंधों वाला रिंग है, तथा $B'$ प्राप्त होता है जब उस पर $\mathrm{OH^-}$, $2$ eq की क्रिया होती है.
- A. A, B and C only
- B. B, C and D only
- C. A, C and D only
- D. A, B and D only
Correct answer & explanation hidden
Log in to view solution →
Q75
CHEMISTRY
Unit 15: Hydrocarbons
2-hexene पर
(i) $\mathrm{O_3}$
(ii) $\mathrm{H_2O}$
की क्रिया से बनने वाले उत्पाद हैं:
- A. Butanoic acid and acetic acid
- B. Butanal and acetaldehyde
- C. Butanoic acid and acetaldehyde
- D. Butanal and acetic acid
Correct answer & explanation hidden
Log in to view solution →
Q76
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
निम्न अभिक्रिया में $A$ है:
$\mathrm{CH_3COCH_2CH(CH_3)Br}$ $\xrightarrow[(ii)\ H_2O]{(i)\ Mg}$ $A$ (Major Product)
-
A.
Structure with a tertiary alcohol and bromine side chain
-
B.
Ketone with a $\mathrm{MgBr}$ substituent
-
C.
Gem-diol alcohol product
-
D.
Cyclopropanol derivative
Correct answer & explanation hidden
Log in to view solution →
Q77
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
The major product in the following reaction is:
↻ Repeated question — also appeared in
2023 (1 set)
-
A.
A diketone with the left and right terminal ketone groups retained and an internal alkene, with a methyl substituent on one alkene carbon and a carbonyl group on the other side of the double bond.
-
B.
A cyclic ketone: 3-methylcyclohex-2-en-1-one type structure is not shown; rather a six-membered ring with one carbonyl and one methyl substituent.
-
C.
3-methylcyclopent-2-en-1-one
-
D.
2-methylcyclohept-2-en-1-one
Correct answer & explanation hidden
Log in to view solution →
Q78
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
Which of the following is the most appropriate product 'P' in the following sequence of reactions?
-
A.
An aromatic side chain product containing an alkene and a terminal alcohol: $\mathrm{Ph{-}CH_2{-}CH{=}CH{-}CH_2{-}CH(OH){-}NH{-}R}$ type structure.
-
B.
An aromatic side chain product containing an alkene and a primary amine: $\mathrm{Ph{-}CH_2{-}CH{=}CH{-}CH_2{-}CH_2{-}NH{-}R}$ type structure.
-
C.
An aromatic side chain product containing a secondary amine, chlorine substituent, and terminal alcohol.
-
D.
No clear option image was provided; the intended correct product is the reduced amino alcohol after $\mathrm{LiAlH_4}$/$\mathrm{H_3O^+}$ workup.
Correct answer & explanation hidden
Log in to view solution →
Q79
CHEMISTRY
Unit 18: Organic Compounds Containing Nitrogen
The product 'B' formed in the above reaction is p-nitroso compound at low temperature.
- A. The reaction occurs at low temperature
- B. The electrophile involved in the reaction is $\mathrm{NO^+}$
- C. 'B' is N-nitroso ammonium compound
- D. The statement is false; the product is not a p-nitroso compound under these conditions
Correct answer & explanation hidden
Log in to view solution →
Q80
CHEMISTRY
Unit 12: Coordination Compounds
Match the compounds in List I with their type in List II and choose the correct option.
- A. A-II, B-IV, C-I, D-III
- B. A-II, B-I, C-IV, D-III
- C. A-IV, B-I, C-III, D-II
- D. A-IV, B-III, C-I, D-II
Correct answer & explanation hidden
Log in to view solution →