Mathematics
Q1Sets
If a set $A$ has 5 elements, the number of proper subsets of $A$ is
- a30
- b32
- c25
- d31
Answer (d): A set with $n$ elements has $2^n$ subsets; excluding $A$ itself gives $2^5-1=31$.
Revise: Algebra (Class 11 notes)
Q2Logic
The negation of the statement $p \wedge q$ is
- a$\neg p \wedge \neg q$
- b$p \vee \neg q$
- c$\neg p \rightarrow \neg q$
- d$\neg p \vee \neg q$
Answer (d): By De Morgan's law, $\neg(p\wedge q)\equiv \neg p\vee\neg q$.
Revise: Algebra (Class 11 notes)
Q3Functions
If $f(x)=2x+3$, then $f^{-1}(7)$ equals
- a5
- b2
- c11
- d1
Answer (b): Solve $2x+3=7$, so $x=2$, hence $f^{-1}(7)=2$.
Revise: Algebra (Class 11 notes)
Q4Determinants
The value of the determinant $\begin{vmatrix}2&3\4&5\end{vmatrix}$ is
- a−2
- b2
- c22
- d−7
Answer (a): $2\cdot5-3\cdot4=10-12=-2$.
Revise: Algebra (Class 11 notes)
Q5Matrices
If $A$ is a $3\times3$ matrix with $|A|=4$, then $|2A|$ equals
- a8
- b32
- c16
- d64
Answer (b): $|kA|=k^n|A|$ for an $n\times n$ matrix, so $|2A|=2^3\cdot4=32$.
Revise: Algebra (Class 11 notes)
Q6Complex numbers
The value of $i^{47}$ is
- ai
- b1
- c−1
- d−i
Answer (d): $i^{47}=i^{44}\cdot i^{3}=1\cdot(-i)=-i$.
Revise: Algebra (Class 11 notes)
Q7Straight lines
The distance from the point $(3,4)$ to the line $3x+4y-5=0$ is
- a5
- b4
- c20
- d2
Answer (b): $d=\dfrac{|9+16-5|}{\sqrt{9+16}}=\dfrac{20}{5}=4$.
Revise: Analytic geometry (Class 11 notes)
Q8Sequences and series
The sum of the first 10 terms of the AP with first term 2 and common difference 3 is
- a150
- b145
- c160
- d155
Answer (d): $S_{10}=\dfrac{10}{2}[2\cdot2+9\cdot3]=5\cdot31=155$.
Revise: Algebra (Class 11 notes)
Q9Combinations
If ${}^{n}C_2=45$, then $n$ equals
- a10
- b9
- c11
- d12
Answer (a): $\dfrac{n(n-1)}{2}=45$ gives $n(n-1)=90$, so $n=10$.
Revise: Algebra (Class 11 notes)
Q10Binomial theorem
The coefficient of $x^2$ in the expansion of $(1+x)^6$ is
- a15
- b6
- c20
- d30
Answer (a): The coefficient is ${}^{6}C_2=15$.
Revise: Algebra (Class 11 notes)
Q11Trigonometry
The value of $\sin^2 30^\circ+\cos^2 60^\circ$ is
- a1
- b$\dfrac14$
- c$\dfrac34$
- d$\dfrac12$
Answer (d): $\left(\tfrac12\right)^2+\left(\tfrac12\right)^2=\tfrac14+\tfrac14=\tfrac12$.
Revise: Trigonometry (Class 11 notes)
Q12Inverse trigonometry
The value of $\sin^{-1}\tfrac12+\cos^{-1}\tfrac12$ is
- a$\dfrac{\pi}{3}$
- b$\dfrac{\pi}{6}$
- cπ
- d$\dfrac{\pi}{2}$
Answer (d): For $x\in[-1,1]$, $\sin^{-1}x+\cos^{-1}x=\pi/2$.
Revise: Trigonometry (Class 12 notes)
Q133D planes
The distance of the plane $2x-2y+z=9$ from the origin is
- a3
- b9
- c1
- d2
Answer (a): $d=\dfrac{|{-9}|}{\sqrt{4+4+1}}=\dfrac{9}{3}=3$.
Revise: Analytic geometry (Class 12 notes)
Q14Circle
The centre of the circle $x^2+y^2-6x+4y-12=0$ is
- a$(-3,2)$
- b$(6,-4)$
- c$(3,2)$
- d$(3,-2)$
Answer (d): Centre is $(-g,-f)$ with $2g=-6$, $2f=4$, so $(3,-2)$.
Revise: Analytic geometry (Class 11 notes)
Q15Conics
The eccentricity of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$ is
- a$\dfrac35$
- b$\dfrac45$
- c$\dfrac34$
- d$\dfrac53$
Answer (a): $e=\sqrt{1-\tfrac{b^2}{a^2}}=\sqrt{1-\tfrac{16}{25}}=\tfrac35$.
Revise: Analytic geometry (Class 12 notes)
Q16Limits
$\displaystyle\lim_{x\to0}\frac{\sin 3x}{x}$ equals
- a3
- b1
- c$\dfrac13$
- d0
Answer (a): $\dfrac{\sin3x}{x}=3\cdot\dfrac{\sin3x}{3x}\to3\cdot1=3$.
Revise: Calculus (Class 11 notes)
Q17Derivatives
The derivative of $xe^{x}$ with respect to $x$ is
- a$xe^{x}$
- b$e^{x}$
- c$e^{x}(x-1)$
- d$e^{x}(1+x)$
Answer (d): Product rule: $e^x+xe^x=e^x(1+x)$.
Revise: Calculus (Class 11 notes)
Q18Integration
The value of $\displaystyle\int_0^1(3x^2+2x),dx$ is
- a3
- b2
- c1
- d$\dfrac52$
Answer (b): $[x^3+x^2]_0^1=1+1=2$.
Revise: Calculus (Class 12 notes)
Q19Vectors
The angle between the vectors $\vec a=(1,2,3)$ and $\vec b=(2,-1,0)$ is
- a$0^\circ$
- b$60^\circ$
- c$90^\circ$
- d$180^\circ$
Answer (c): $\vec a\cdot\vec b=2-2+0=0$, so the vectors are perpendicular.
Revise: Vectors (Class 11 notes)
Q20Statistics
The variance of the data 2, 4, 6, 8 is
- a5
- b20
- c4
- d6
Answer (a): Mean $=5$; squared deviations $9,1,1,9$ sum to 20; variance $=20/4=5$.
Revise: Statistics and Probability (Class 11 notes)
Q21 (2 marks)Sets
In a group, $n(A)=30$, $n(B)=25$ and $n(A\cup B)=45$. The number of elements belonging to exactly one of $A$ and $B$ is
- a20
- b35
- c15
- d55
Answer (b): $n(A\cap B)=30+25-45=10$. Exactly one set: $45-10=35$.
Revise: Algebra (Class 11 notes)
Q22 (2 marks)Matrices
If $A=\begin{pmatrix}1&2\3&4\end{pmatrix}$, then $A^2-5A$ equals
- aI
- b2I
- c$-2I$
- d5I
Answer (b): $A^2=\begin{pmatrix}7&10\15&22\end{pmatrix}$ and $5A=\begin{pmatrix}5&10\15&20\end{pmatrix}$, so $A^2-5A=\begin{pmatrix}2&0\0&2\end{pmatrix}=2I$.
Revise: Algebra (Class 11 notes)
Q23 (2 marks)Complex numbers
If $z_1,z_2$ are the roots of $z^2-2z+5=0$, then $z_1^2+z_2^2$ equals
- a6
- b−1
- c−6
- d14
Answer (c): Sum $=2$, product $=5$, so $z_1^2+z_2^2=(z_1+z_2)^2-2z_1z_2=4-10=-6$.
Revise: Algebra (Class 11 notes)
Q24 (2 marks)Sequences and series
The sum of the infinite series $1+\dfrac23+\dfrac39+\dfrac4{27}+\cdots$ is
- a$\dfrac94$
- b$\dfrac32$
- c$\dfrac92$
- d$\dfrac49$
Answer (a): The series is $\sum nx^{n-1}$ with $x=\tfrac13$, whose sum is $\dfrac1{(1-x)^2}=\dfrac1{(2/3)^2}=\dfrac94$.
Revise: Algebra (Class 11 notes)
Q25 (2 marks)Permutations
The number of distinct arrangements of the letters of the word LEVEL is
- a60
- b120
- c30
- d20
Answer (c): Five letters with L repeated twice and E repeated twice: $\dfrac{5!}{2!,2!}=30$.
Revise: Algebra (Class 11 notes)
Q26 (2 marks)Binomial theorem
The term independent of $x$ in the expansion of $\left(x^2+\dfrac1x\right)^9$ is
- a126
- b36
- c84
- d168
Answer (c): $T_{r+1}={}^9C_r,x^{18-3r}$; the power is zero when $r=6$, giving ${}^9C_6=84$.
Revise: Algebra (Class 11 notes)
Q27 (2 marks)Properties of triangles
In a triangle $ABC$ with $a=7$, $b=8$, $c=9$, the value of $\cos A$ is
- a$\dfrac23$
- b$\dfrac13$
- c$\dfrac34$
- d$\dfrac56$
Answer (a): $\cos A=\dfrac{b^2+c^2-a^2}{2bc}=\dfrac{64+81-49}{144}=\dfrac{96}{144}=\dfrac23$.
Revise: Trigonometry (Class 11 notes)
Q28 (2 marks)Circle
The length of the tangent drawn from the point $(5,4)$ to the circle $x^2+y^2-2x-4y-4=0$ is
- a11
- b$\sqrt{15}$
- c$\sqrt{11}$
- d3
Answer (c): $S_1=25+16-10-16-4=11$, so the tangent length is $\sqrt{S_1}=\sqrt{11}$.
Revise: Analytic geometry (Class 11 notes)
Q29 (2 marks)Pair of lines
The pair of lines $x^2-5xy+6y^2=0$ makes an angle $\theta$ with each other. Then $\tan\theta$ equals
- a$\dfrac15$
- b$\dfrac17$
- c$\dfrac12$
- d$\dfrac67$
Answer (b): The lines are $x=2y$ and $x=3y$, with slopes $\tfrac12$ and $\tfrac13$. $\tan\theta=\dfrac{1/2-1/3}{1+1/6}=\dfrac{1/6}{7/6}=\dfrac17$.
Revise: Analytic geometry (Class 11 notes)
Q30 (2 marks)Limits
$\displaystyle\lim_{x\to\infty}\left(\sqrt{x^2+3x}-x\right)$ equals
- a3
- b$\dfrac32$
- c0
- d$\dfrac12$
Answer (b): Multiply by the conjugate: $\dfrac{3x}{\sqrt{x^2+3x}+x}=\dfrac{3}{\sqrt{1+3/x}+1}\to\dfrac32$.
Revise: Calculus (Class 11 notes)
Q31 (2 marks)Applications of derivatives
The local minimum value of $f(x)=x^3-12x+5$ is
- a−11
- b21
- c5
- d−27
Answer (a): $f'(x)=3x^2-12=0$ gives $x=\pm2$; $f''(x)=6x>0$ at $x=2$, so the minimum is $f(2)=8-24+5=-11$.
Revise: Calculus (Class 12 notes)
Q32 (2 marks)Area by integration
The area enclosed between the curves $y=x^2$ and $y=x$ is
- a$\dfrac13$
- b$\dfrac16$
- c$\dfrac12$
- d$\dfrac1{12}$
Answer (b): They meet at $x=0,1$. Area $=\int_0^1(x-x^2),dx=\tfrac12-\tfrac13=\tfrac16$.
Revise: Calculus (Class 12 notes)
Q33 (2 marks)Differential equations
The solution of $\dfrac{dy}{dx}=2xy$ with $y(0)=3$ gives $y(1)$ equal to
- a$e^3$
- b3e
- c$3e^2$
- d3
Answer (b): $\dfrac{dy}{y}=2x,dx$ gives $y=Ae^{x^2}$; $y(0)=3$ gives $A=3$, so $y(1)=3e$.
Revise: Calculus (Class 12 notes)
Q34 (2 marks)Vectors
If $|\vec a|=3$, $|\vec b|=4$ and $\vec a\cdot\vec b=6$, then $|\vec a\times\vec b|$ equals
- a12
- b$6\sqrt3$
- c6
- d$2\sqrt3$
Answer (b): $|\vec a\times\vec b|^2=|\vec a|^2|\vec b|^2-(\vec a\cdot\vec b)^2=144-36=108$, so the value is $6\sqrt3$.
Revise: Vectors (Class 11 notes)
Q35 (2 marks)Probability
A bag has 5 red and 3 blue balls. Two balls are drawn at random without replacement. The probability that both are of the same colour is
- a$\dfrac{15}{28}$
- b$\dfrac{13}{28}$
- c$\dfrac12$
- d$\dfrac{9}{28}$
Answer (b): Favourable: ${}^5C_2+{}^3C_2=10+3=13$ out of ${}^8C_2=28$.
Revise: Statistics and Probability (Class 11 notes)
Physics
Q36Kinematics
A car starting from rest accelerates uniformly at $2\ \text{m/s}^2$. The distance covered in 5 s is
- a10 m
- b25 m
- c50 m
- d5 m
Answer (b): $s=\tfrac12at^2=\tfrac12(2)(25)=25$ m.
Revise: Kinematics (Class 11 notes)
Q37Laws of motion
A ball of mass 0.5 kg hits a wall at 4 m/s and rebounds at 4 m/s along the same line. The magnitude of the change in its momentum is
- a2 kg m/s
- b8 kg m/s
- c4 kg m/s
- d0
Answer (c): $\Delta p=m(v-(-v))=0.5\times8=4$ kg m/s.
Revise: Dynamics (Class 11 notes)
Q38Work and energy
The kinetic energy of a 2 kg body moving at 3 m/s is
- a6 J
- b9 J
- c18 J
- d4.5 J
Answer (b): $\tfrac12mv^2=\tfrac12(2)(9)=9$ J.
Revise: Work, Energy and Power (Class 11 notes)
Q39Circular motion
A particle moves in a circle of radius 5 m with a uniform speed of 10 m/s. Its centripetal acceleration is
- a$2\ \text{m/s}^2$
- b$50\ \text{m/s}^2$
- c$20\ \text{m/s}^2$
- d$10\ \text{m/s}^2$
Answer (c): $a=v^2/r=100/5=20\ \text{m/s}^2$.
Revise: Circular Motion (Class 11 notes)
Q40Gravitation
At a height equal to the radius of the Earth above its surface, the acceleration due to gravity is
- a$g/2$
- b$g/9$
- c$g/4$
- d$2g$
Answer (c): The distance from the centre is $2R$, and $g\propto1/r^2$, so $g'=g/4$.
Revise: Gravitation (Class 11 notes)
Q41Rotational dynamics
The moment of inertia of a uniform solid disc of mass $M$ and radius $R$ about its central axis perpendicular to its plane is
- a$MR^2$
- b$\dfrac25MR^2$
- c$\dfrac14MR^2$
- d$\dfrac12MR^2$
Answer (d): For a solid disc $I=\tfrac12MR^2$.
Revise: Rotational Dynamic (Class 12 notes)
Q42Elasticity
A wire stretches by $x$ under a load. A wire of the same material and cross-section but double the length, under the same load, stretches by
- ax
- b$x/2$
- c2x
- d4x
Answer (c): $\Delta L=\dfrac{FL}{AY}\propto L$, so doubling the length doubles the extension.
Revise: Elasticity (Class 11 notes)
Q43Fluid statics
The gauge pressure at a depth of 10 m in water is about ($\rho=1000\ \text{kg/m}^3$, $g=10\ \text{m/s}^2$)
- a$10^4$ Pa
- b$10^5$ Pa
- c$10^6$ Pa
- d$10^3$ Pa
Answer (b): $P=\rho gh=1000\times10\times10=10^5$ Pa.
Revise: Fluid Statics (Class 12 notes)
Q44Heat
The heat needed to raise the temperature of 2 kg of water by $10^\circ$C is ($c=4200\ \text{J kg}^{-1}\text{K}^{-1}$)
- a8400 J
- b84000 J
- c42000 J
- d840000 J
Answer (b): $Q=mc\Delta\theta=2\times4200\times10=84000$ J.
Revise: Quantity of Heat (Class 11 notes)
Q45First law of thermodynamics
A gas absorbs 200 J of heat and does 50 J of work. The change in its internal energy is
- a150 J
- b250 J
- c200 J
- d50 J
Answer (a): $\Delta U=Q-W=200-50=150$ J.
Revise: First Law of Thermodynamics (Class 12 notes)
Q46Optics
An object is placed 20 cm in front of a concave mirror of focal length 10 cm. The image is
- avirtual, at 10 cm behind the mirror
- bformed at infinity
- creal, at 30 cm in front of the mirror
- dreal, at 20 cm in front of the mirror
Answer (d): The object is at the centre of curvature ($2f$), so the image forms at $2f=20$ cm, real and inverted.
Revise: Reflection at Curved Mirrors (Class 11 notes)
Q47Waves
A wave of frequency 50 Hz has a wavelength of 4 m. Its speed is
- a12.5 m/s
- b54 m/s
- c100 m/s
- d200 m/s
Answer (d): $v=f\lambda=50\times4=200$ m/s.
Revise: Wave Motion (Class 12 notes)
Q48Electrostatics
Two capacitors of 6 $\mu$F and 3 $\mu$F are connected in series. The equivalent capacitance is
- a9 μF
- b3 μF
- c2 μF
- d1.5 μF
Answer (c): $C=\dfrac{6\times3}{6+3}=2\ \mu$F.
Revise: Capacitor (Class 11 notes)
Q49Electromagnetic induction
A straight rod of length 0.5 m moves at 4 m/s perpendicular to a uniform magnetic field of 0.2 T. The induced emf across its ends is
- a0.04 V
- b4 V
- c0.8 V
- d0.4 V
Answer (d): $\varepsilon=Blv=0.2\times0.5\times4=0.4$ V.
Revise: Electromagnetic Induction (Class 12 notes)
Q50Semiconductors
In an n-type semiconductor the majority charge carriers are
- aholes
- belectrons
- cprotons
- dneutrons
Answer (b): Donor impurities supply extra free electrons, so electrons are the majority carriers.
Revise: Semiconductor Devices (Class 12 notes)
Q51Photoelectric effect
The energy of a photon of wavelength 620 nm is about (use $E=1240/\lambda$ eV with $\lambda$ in nm)
- a1 eV
- b4 eV
- c2 eV
- d0.5 eV
Answer (c): $E=1240/620=2$ eV.
Revise: Photons (Class 12 notes)
Q52 (2 marks)Kinematics
A ball is thrown vertically upward at 20 m/s ($g=10\ \text{m/s}^2$). The total distance it travels in the first 3 s is
- a15 m
- b45 m
- c20 m
- d25 m
Answer (d): It rises for 2 s to a height $20$ m, then falls for 1 s through $\tfrac12(10)(1)^2=5$ m. Distance $=20+5=25$ m.
Revise: Kinematics (Class 11 notes)
Q53 (2 marks)Laws of motion
Masses of 3 kg and 2 kg hang from the two ends of a light string over a smooth pulley ($g=10\ \text{m/s}^2$). The tension in the string is
- a20 N
- b30 N
- c24 N
- d25 N
Answer (c): $a=\dfrac{(3-2)g}{5}=2\ \text{m/s}^2$. For the 2 kg mass, $T-20=2\times2$, so $T=24$ N.
Revise: Dynamics (Class 11 notes)
Q54 (2 marks)Work-energy theorem
A 2 kg block slides from rest down a rough incline from a height of 5 m and reaches the bottom at 8 m/s ($g=10\ \text{m/s}^2$). The work done against friction is
- a64 J
- b100 J
- c164 J
- d36 J
Answer (d): Loss of PE $=mgh=100$ J; KE gained $=\tfrac12(2)(64)=64$ J. Work against friction $=100-64=36$ J.
Revise: Work, Energy and Power (Class 11 notes)
Q55 (2 marks)Gravitation
A planet has 8 times the mass and 2 times the radius of the Earth. If the Earth's escape speed is 11.2 km/s, the escape speed from this planet is
- a22.4 km/s
- b44.8 km/s
- c11.2 km/s
- d15.8 km/s
Answer (a): $v_e=\sqrt{2GM/R}\propto\sqrt{M/R}$, so the ratio is $\sqrt{8/2}=2$ and $v=22.4$ km/s.
Revise: Gravitation (Class 11 notes)
Q56 (2 marks)Rotation
A uniform disc of mass 2 kg and radius 0.5 m rotates about its axis at 10 rad/s. Its rotational kinetic energy is
- a25 J
- b6.25 J
- c12.5 J
- d50 J
Answer (c): $I=\tfrac12MR^2=\tfrac12(2)(0.25)=0.25\ \text{kg m}^2$; $K=\tfrac12I\omega^2=\tfrac12(0.25)(100)=12.5$ J.
Revise: Rotational Dynamic (Class 12 notes)
Q57 (2 marks)Second law of thermodynamics
A Carnot engine works between 400 K and 300 K and absorbs 1000 J from the source per cycle. The work done per cycle is
- a250 J
- b750 J
- c300 J
- d400 J
Answer (a): $\eta=1-\tfrac{300}{400}=0.25$, so $W=0.25\times1000=250$ J.
Revise: Second Law of Thermodynamics (Class 12 notes)
Q58 (2 marks)Lenses
An object is placed 30 cm from a convex lens of focal length 20 cm. The image distance is
- a12 cm
- b50 cm
- c20 cm
- d60 cm
Answer (d): $\dfrac1v=\dfrac1f-\dfrac1u=\dfrac1{20}-\dfrac1{30}=\dfrac1{60}$, so $v=60$ cm (real image).
Revise: Lenses (Class 11 notes)
Q59 (2 marks)Waves in pipes
A pipe closed at one end is 0.5 m long. If the speed of sound is 340 m/s, its fundamental frequency is
- a340 Hz
- b170 Hz
- c680 Hz
- d85 Hz
Answer (b): $f=\dfrac{v}{4L}=\dfrac{340}{4\times0.5}=170$ Hz.
Revise: Wave in Pipes and Strings (Class 12 notes)
Q60 (2 marks)Interference
In Young's double slit experiment, $\lambda=600$ nm, slit separation $d=1$ mm and screen distance $D=1$ m. The fringe width is
- a0.6 mm
- b0.06 mm
- c6 mm
- d1.2 mm
Answer (a): $\beta=\dfrac{\lambda D}{d}=\dfrac{600\times10^{-9}\times1}{10^{-3}}=6\times10^{-4}$ m $=0.6$ mm.
Revise: Interference (Class 12 notes)
Q61 (2 marks)Current electricity
A cell of emf 10 V and internal resistance 1 $\Omega$ is connected to an external resistor of 4 $\Omega$. The terminal potential difference is
- a10 V
- b2 V
- c8 V
- d9 V
Answer (c): $I=\dfrac{10}{1+4}=2$ A; $V=IR=2\times4=8$ V.
Revise: Electrical Circuit One (Class 12 notes)
Q62 (2 marks)Alternating current
In a series RLC circuit, $R=30\ \Omega$, $X_L=60\ \Omega$ and $X_C=20\ \Omega$. The impedance is
- a70 Ω
- b110 Ω
- c10 Ω
- d50 Ω
Answer (d): $Z=\sqrt{R^2+(X_L-X_C)^2}=\sqrt{900+1600}=50\ \Omega$.
Revise: Alternating Currents (Class 12 notes)
Q63 (2 marks)Radioactivity
A radioactive sample of 80 g has a half-life of 10 days. The mass remaining after 30 days is
- a20 g
- b40 g
- c26.7 g
- d10 g
Answer (d): 30 days is 3 half-lives, so the mass is $80/2^3=10$ g.
Revise: Radioactivity and Nuclear Reaction (Class 12 notes)
Chemistry
Q64Mole concept
The number of moles in 11 g of $\ce{CO2}$ (molar mass 44 g/mol) is
- a0.25
- b0.5
- c4
- d2
Answer (a): $n=11/44=0.25$ mol.
Revise: Stoichiometry (Class 11 notes)
Q65Gas laws
A gas occupying 2 L at 1 atm is compressed isothermally to 1 L. The new pressure is
- a0.5 atm
- b1 atm
- c4 atm
- d2 atm
Answer (d): Boyle's law: $P_1V_1=P_2V_2$, so $P_2=1\times2/1=2$ atm.
Revise: States of Matter (Class 11 notes)
Q66Atomic structure
The number of neutrons in the nuclide $^{23}_{11}\text{Na}$ is
- a12
- b11
- c23
- d10
Answer (a): Neutrons $=A-Z=23-11=12$.
Revise: Atomic Structure (Class 11 notes)
Q67Bonding
The shape of the $\ce{NH3}$ molecule is
- atrigonal planar
- btetrahedral
- ctrigonal pyramidal
- dbent
Answer (c): Nitrogen has three bond pairs and one lone pair, giving a pyramidal shape.
Revise: Chemical Bonding (Class 11 notes)
Q68Chemical equilibrium
For $\ce{N2 + 3H2 <=> 2NH3}$ (exothermic), increasing the pressure at constant temperature shifts the equilibrium
- ato the left
- bneither way
- cfirst right then left
- dto the right
Answer (d): Pressure favours the side with fewer gas moles (2 versus 4), which is the product side.
Revise: Chemical Equilibrium (Class 11 notes)
Q69Ionic equilibrium
The pH of 0.01 M HCl solution is
- a1
- b12
- c0.01
- d2
Answer (d): $[\ce{H+}]=10^{-2}$, so $\text{pH}=2$.
Revise: Ionic Equilibrium (Class 12 notes)
Q70Electrochemistry
In a galvanic cell, oxidation takes place at the
- acathode
- bsalt bridge
- canode
- delectrolyte only
Answer (c): The anode of a galvanic cell is where the species loses electrons (oxidation).
Revise: Electrochemistry (Class 12 notes)
Q71Chemical kinetics
The unit of the rate constant of a first-order reaction is
- a$\text{mol L}^{-1}\text{s}^{-1}$
- b$\text{L mol}^{-1}\text{s}^{-1}$
- c$\text{s}^{-1}$
- dmol s
Answer (c): Rate $=k[A]$, so $k=\text{rate}/[A]$ has units of $\text{s}^{-1}$.
Revise: Chemical Kinetics (Class 12 notes)
Q72Thermochemistry
For $A\to B$, $\Delta H=-50$ kJ and for $B\to C$, $\Delta H=+20$ kJ. For $A\to C$, $\Delta H$ is
- a−70 kJ
- b−30 kJ
- c+30 kJ
- d+70 kJ
Answer (b): By Hess's law, $\Delta H=-50+20=-30$ kJ.
Revise: Chemical Thermodynamic (Class 12 notes)
Q73Non-metals
The catalyst used in the Contact process for manufacturing sulphuric acid is
- aFe
- bPt gauze
- cNi
- d$\ce{V2O5}$
Answer (d): $\ce{SO2}$ is oxidised to $\ce{SO3}$ over vanadium(V) oxide.
Revise: Chemistry of Non-Metals (Class 11 notes)
Q74Metallurgy
Heating a sulphide ore strongly in excess air to convert it into its oxide is called
- aroasting
- bcalcination
- csmelting
- dleaching
Answer (a): Roasting is done in excess air for sulphide ores; calcination is done in limited or no air for carbonates and hydrated ores.
Revise: Chemistry of Metals (Class 11 notes)
Q75IUPAC nomenclature
The IUPAC name of $\ce{CH3CH(CH3)CH2CH3}$ is
- a3-methylbutane
- b2-ethylpropane
- c2-methylbutane
- d2,2-dimethylpropane
Answer (c): The longest chain has 4 carbons (butane) with a methyl on carbon 2.
Revise: Fundamental Principles (Class 11 notes)
Q76Hydrocarbons
Propene reacts with HBr (no peroxide) to give mainly
- a1-bromopropane
- b1,2-dibromopropane
- cpropane
- d2-bromopropane
Answer (d): Markovnikov's rule: H adds to the carbon with more hydrogens, so Br ends on the middle carbon.
Revise: Hydrocarbons (Class 11 notes)
Q77Carbonyl compounds
Which of the following gives a silver mirror with Tollens' reagent?
- aacetone
- bacetaldehyde
- cethanol
- ddiethyl ether
Answer (b): Aldehydes are oxidised by Tollens' reagent, depositing silver; ketones do not react.
Revise: Aldehydes and Ketones (Class 12 notes)
Q78 (2 marks)Stoichiometry
When 6 g of carbon burns completely in excess oxygen, the mass of $\ce{CO2}$ formed is (C = 12, O = 16)
- a44 g
- b11 g
- c22 g
- d16.5 g
Answer (c): $6/12=0.5$ mol C gives 0.5 mol $\ce{CO2}$, i.e. $0.5\times44=22$ g.
Revise: Stoichiometry (Class 11 notes)
Q79 (2 marks)States of matter
Under the same conditions, the ratio of the rate of diffusion of $\ce{H2}$ to that of $\ce{O2}$ is
- a16
- b2
- c4
- d1/4
Answer (c): Graham's law: $\sqrt{M_{O_2}/M_{H_2}}=\sqrt{32/2}=4$.
Revise: States of Matter (Class 11 notes)
Q80 (2 marks)Ionic equilibrium
The pH of 0.1 M weak acid HA with $K_a=1\times10^{-5}$ is (assume dissociation is small)
- a3
- b1
- c5
- d4
Answer (a): $[\ce{H+}]=\sqrt{K_aC}=\sqrt{10^{-6}}=10^{-3}$, so $\text{pH}=3$.
Revise: Ionic Equilibrium (Class 12 notes)
Q81 (2 marks)Electrochemistry
Given $E^\circ(\ce{Zn^2+/Zn})=-0.76$ V and $E^\circ(\ce{Cu^2+/Cu})=+0.34$ V, the standard emf of the Zn-Cu cell is
- a0.42 V
- b1.10 V
- c−1.10 V
- d0.76 V
Answer (b): $E^\circ_{cell}=E^\circ_{cathode}-E^\circ_{anode}=0.34-(-0.76)=1.10$ V.
Revise: Electrochemistry (Class 12 notes)
Q82 (2 marks)Chemical kinetics
A first-order reaction has a half-life of 20 minutes. The fraction of the reactant left after 60 minutes is
- a1/8
- b1/6
- c1/4
- d1/3
Answer (a): 60 min is 3 half-lives, so the fraction left is $(1/2)^3=1/8$.
Revise: Chemical Kinetics (Class 12 notes)
Q83 (2 marks)Chemical equilibrium
For $\ce{H2 + I2 <=> 2HI}$, equilibrium concentrations are $[\ce{H2}]=0.1$, $[\ce{I2}]=0.1$ and $[\ce{HI}]=0.4$ mol/L. The value of $K_c$ is
- a4
- b16
- c40
- d0.4
Answer (b): $K_c=\dfrac{[\ce{HI}]^2}{[\ce{H2}][\ce{I2}]}=\dfrac{0.16}{0.01}=16$.
Revise: Chemical Equilibrium (Class 11 notes)
Q84 (2 marks)Amines
Acetamide is treated with $\ce{Br2}$ and aqueous NaOH (Hofmann bromamide reaction). The main product is
- aethylamine
- bmethylamine
- cacetic acid
- dmethanol
Answer (b): The amide loses its carbonyl carbon as carbonate, giving an amine with one carbon less: $\ce{CH3NH2}$.
Revise: Amines (Class 12 notes)
Q85 (2 marks)Carbonyl compounds
A compound $\ce{C3H6O}$ gives a positive iodoform test but does not reduce Tollens' reagent. It is
- apropanal
- ballyl alcohol
- cacetone
- dpropylene oxide
Answer (c): It has the $\ce{CH3CO-}$ group (iodoform positive) and is a ketone (no Tollens' reaction): propanone.
Revise: Aldehydes and Ketones (Class 12 notes)
English
Q86Tenses
Choose the correct form: She ___ in Pokhara since 2015.
- alives
- bhas lived
- cis living
- dlived
Answer (b): 'Since 2015' marks a period up to now, so the present perfect is used.
Revise: Grammar and Usage (Class 11 notes)
Q87Subject-verb agreement
Choose the correct form: Neither of the two answers ___ correct.
- aare
- bwere
- cis
- dbe
Answer (c): 'Neither' takes a singular verb.
Revise: Grammar and Usage (Class 11 notes)
Q88Articles
Fill in the blank: He is ___ honest man.
- aa
- bthe
- cno article
- dan
Answer (d): 'Honest' begins with a vowel sound (silent h), so 'an' is used.
Revise: Grammar and Usage (Class 11 notes)
Q89Prepositions
Fill in the blank: She is very good ___ mathematics.
- ain
- bon
- cat
- dwith
Answer (c): The adjective 'good' takes the preposition 'at' for skill in a subject.
Revise: Grammar and Usage (Class 11 notes)
Q90Voice
The passive form of 'They are building a bridge.' is
- aA bridge is being built by them.
- bA bridge is built by them.
- cA bridge has been built by them.
- dA bridge was being built by them.
Answer (a): Present continuous passive: is/are + being + past participle.
Revise: Grammar and Usage (Class 11 notes)
Q91Narration
The indirect form of: He said, "I am tired." is
- aHe said that I was tired.
- bHe said that he had been tired.
- cHe said that he was tired.
- dHe said that she were tired.
Answer (c): In reported speech the present tense backshifts to the past and the pronoun changes: 'I am tired' becomes 'he was tired'.
Revise: Grammar and Usage (Class 11 notes)
Q92Conditionals
Fill in the blank: If I ___ you, I would apologise.
- aam
- bbe
- cwill be
- dwere
Answer (d): A hypothetical second conditional takes 'were' in the if-clause for all subjects.
Revise: Grammar and Usage (Class 11 notes)
Q93Question tags
Complete the tag question: She can swim, ___?
- adoesn't she
- bisn't she
- cwon't she
- dcan't she
Answer (d): A positive statement takes a negative tag with the same auxiliary: can... can't she.
Revise: Grammar and Usage (Class 11 notes)
Q94Vocabulary
The word closest in meaning to 'benevolent' is
- akind
- bhostile
- clazy
- dcareless
Answer (a): 'Benevolent' means well-meaning and generous, i.e. kind.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q95Phonetics
Which of these words is stressed on the second syllable?
- agarden
- bhappy
- cbegin
- dwindow
Answer (c): 'Begin' is stressed as be-GIN, while the others carry stress on the first syllable.
Q96 (2 marks)Comprehension
Read: "Rivers are not merely sources of water; they carry silt that renews farmland, power turbines that light cities, and stories that bind communities. When a river is dammed without care, all three are put at risk." The main idea of the passage is that
- arivers serve several roles that careless damming can harm
- brivers should never be dammed
- csilt is harmful to farmland
- dturbines are the most important use of rivers
Answer (a): The passage lists farmland, power and community roles and ends by warning that careless damming endangers all three.
Revise: Reading Comprehension (Class 11 notes)
Q97 (2 marks)Comprehension
Read: "Dipa slept early the night before the exam and walked in calm. 'I have revised a little every day since June,' she said, 'so that night I only polished.'" What can be inferred?
- aDipa had not studied at all
- bDipa had prepared steadily over several months
- cDipa crammed everything the night before
- dDipa was nervous about the exam
Answer (b): Her words 'a little every day since June' show steady preparation, which explains her calm.
Revise: Reading Comprehension (Class 11 notes)
Q98 (2 marks)Error spotting
Choose the grammatically correct sentence.
- aThe furniture in the rooms is new.
- bEach of the players have their own kit.
- cThe news are good today.
- dHe suggested me to go there.
Answer (a): 'Furniture' is uncountable and takes a singular verb; the others misuse agreement or the verb pattern ('suggested that I go').
Revise: Grammar and Usage (Class 11 notes)
Q99 (2 marks)Conditionals
Fill in the blank: Had she studied harder, she ___ the examination.
- awould have passed
- bwould pass
- cwill pass
- dhad passed
Answer (a): 'Had + past participle' signals the third conditional, which needs 'would have + past participle' in the main clause.
Revise: Grammar and Usage (Class 11 notes)
Q100 (2 marks)Vocabulary
The idiom 'to bite the bullet' means
- ato face a painful situation bravely
- bto eat very quickly
- cto start an argument
- dto waste money
Answer (a): The idiom describes enduring something unpleasant with courage.
Revise: Vocabulary and Word Formation (Class 11 notes)