JEE Main 5 Apr 2026, Shift 1

75 questions. Answers are hidden — tap “Show answer” under each one.

Physics

Q1 · MCQ · Units and MeasurementsOpen
In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{\text{th}}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has
1. (1)0.07 cm negative zero error
2. (2)0.7 cm negative zero error
3. (3)0.07 cm positive zero error
4. (4)0.7 cm positive zero error
Q2 · MCQ · Units and MeasurementsOpen
L, C and R represent physical quantities inductance, capacitance and resistance respectively. The dimensional formula $\mathrm{M\,L^{2}T^{-4}A^{-2}}$ corresponds to .
1. (1) $\dfrac{R}{\sqrt{LC}}$
2. (2) $\dfrac{R}{LC}$
3. (3) $\dfrac{C}{\sqrt{LR}}$
4. (4) $\dfrac{1}{R}\sqrt{\dfrac{L}{C}}$
We corrected a printing error in the original paper
Source printed “represents”.
Q3 · MCQ · GravitationOpen
When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in $g$ is approximately $\alpha$ %. The value of $\alpha$ is . (Take radius of the earth $= 6400$ km.)
1. (1)0.12
2. (2)0.25
3. (3)0.50
4. (4)0.75
Q4 · MCQ · Newton's Laws of MotionOpen
Three masses $m_1 = 4$ kg, $m_2 = 4$ kg and $m_3 = 6$ kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of $T_1/T_2$ is . (take $g = 10\ \mathrm{m/s^2}$ )
1. (1) $\dfrac{5}{3}$
2. (2) $\dfrac{2}{3}$
3. (3) $\dfrac{3}{5}$
4. (4) $\dfrac{2}{5}$
We corrected a printing error in the original paper
Source printed “pully”.
Q5 · MCQ · Newton's Laws of MotionOpen
A wedge Y with mass of 10 kg has all frictionless surfaces and the inclined surface making $37^\circ$ with horizontal. A block X with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $t = 0$ wedge (Y) is pulled toward right with constant force ( $f$ ) of 24 N. Taking the block X at rest at $t = 0$ , the time taken by it to slide down 8.8 m on the slope, while Y is on the move, is approximately s. (take $\tan(37^\circ) = 3/4$ and $g = 10\ \mathrm{m/s^2}$ )
1. (1)2
2. (2)4
3. (3) $\sqrt2$
4. (4) $2\sqrt2$
We corrected a printing error in the original paper
Source printed “A wedge Y with mass of 10 kg and all frictionless surfaces” and “while Y is on the move, is s”; corrected to the intended “… has all frictionless surfaces” and “… is approximately s” (with the printed data the wedge accelerates at 1.34 m/s $^2$ , the block slides at 4.93 m/s $^2$ relative to it and $t = 1.89$ s; the key 2 s takes the wedge acceleration as $24/12 = 2$ m/s $^2$ ).
Q6 · MCQ · Mechanical Properties of SolidsOpen
The Young's modulus of steel wire of radius $r$ and length $L$ is $Y$ . If the radius $r$ and length $L$ of the wire are doubled then the value of $Y$
1. (1)increases by two times
2. (2)reduces by half
3. (3)remains unchanged
4. (4)becomes one fourth
Q7 · MCQ · ThermodynamicsOpen
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v(T_f - T_i) = \dfrac{nR}{\gamma - 1}(T_f - T_i)$ , where $\gamma = \dfrac{C_P}{C_v}$ , $T_i$ = initial temperature, $T_f$ = final temperature.
Reason R : Relation between degree of freedom $f$ and $\gamma\ (= C_p/C_v)$ is $\left(\gamma = 1 + \dfrac{2}{f}\right)$
Choose the correct answer from the options given below
1. (1)Both A and R are true and R is the correct explanation of A
2. (2)Both A and R are true but R is NOT the correct explanation of A
3. (3)A is true but R is false
4. (4)A is false but R is true
We corrected a printing error in the original paper
Source labelled the two statements “Statement I” and “Statement II” (the lead-in and options use Assertion A / Reason R); source printed “ttue” in option (4).
Q8 · MCQ · ThermodynamicsOpen
Consider the following statements:
- (A)Zeroth law of thermodynamics gives concept of temperature
- (B)First law of thermodynamics gives concept of internal energy
- (C)In isothermal expansion of ideal gas, $\Delta Q \neq \Delta W$
- (D)Product of intensive and extensive variables is extensive
- (E)The ratio of any extensive variable to mass will be an extensive variable
Choose the correct combination of statements from the options given below:
1. (1)C, D and E Only
2. (2)A, B and C Only
3. (3)A, B and D Only
4. (4)B, C and D Only
Q9 · MCQ · Current ElectricityOpen
Refer to the figure given below. The values of $I_1$ , $I_2$ and $I_3$ are .
1. (1) $I_1 = 2.5$ A, $I_2 = 1.875$ A, $I_3 = 1.875$ A
2. (2) $I_1 = 1.875$ A, $I_2 = 2.5$ A, $I_3 = 1.875$ A
3. (3) $I_1 = 1.875$ A, $I_2 = 1.875$ A, $I_3 = 2.5$ A
4. (4) $I_1 = 2.5$ A, $I_2 = 2.5$ A, $I_3 = 1.875$ A
Q10 · MCQ · Dual Nature of Radiation and MatterOpen
An electron of mass $m$ is moving in an electric field $\vec E = -2E_0\hat i$ ( $E_0$ = constant $> 0$ ), with an initial velocity $\vec V = v_0\hat i$ ( $v_0$ = constant $> 0$ ). If $\lambda_0 = \dfrac{h}{4mv_0}$ , its de Broglie wavelength at time $t$ is . ( $e$ = charge of electron)
1. (1) $\dfrac{4\lambda_0}{\left[1 - \dfrac{E_0e}{2m}\dfrac{t}{v_0}\right]}$
2. (2) $\dfrac{4\lambda_0}{\left[1 + \dfrac{E_0e}{2m}\dfrac{t}{v_0}\right]}$
3. (3) $\dfrac{4\lambda_0}{\left[1 + \dfrac{2E_0e}{m}\dfrac{t}{v_0}\right]}$
4. (4) $\dfrac{4\lambda_0}{\left[1 - \dfrac{2E_0e}{m}\dfrac{t}{v_0}\right]}$
Q11 · MCQ · AtomsOpen
In the hydrogen atom, the electron makes a transition from the higher orbit ( $i$ ) to a lower orbit ( $f$ ). The ratio of the radius of the orbits is given by $r_i : r_f = 16 : 4$ . The wavelength of photon emitted due to this transition is nm. (Given Rydberg constant $= 1.0973\times10^{7}$ /m)
1. (1)121
2. (2)242
3. (3)486
4. (4)974
We corrected a printing error in the original paper
Source printed “in given by”.
Q12 · MCQ · Electromagnetic WavesOpen
A displacement current of 4.0 A can be set up in the space between two parallel plates of $6\ \mu\mathrm{F}$ capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha\times10^{6}$ V/s. The value of $\alpha$ is .
1. (1)0.58
2. (2)0.67
3. (3)0.82
4. (4)0.75
Q13 · MCQ · Current ElectricityOpen
Refer to the figure given below, current between terminals A and B is A.
1. (1)12.5
2. (2)1.25
3. (3)7.5
4. (4)5
Q14 · MCQ · Wave OpticsOpen
In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4\ \mu\mathrm{m}$ . If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be $\mu\mathrm{m}$ .
1. (1)1.2
2. (2)2
3. (3)2.4
4. (4)2.88
We corrected a printing error in the original paper
Source printed “the frings width of the interferences pattern”.
Q15 · MCQ · Ray OpticsOpen
A ray of light passing through an equilateral prism is having velocity $2.12\times10^{8}$ m/s in the prism material, then the minimum angle of deviation is degrees.
1. (1)45
2. (2)30
3. (3)28
4. (4)58
Q16 · MCQ · Dual Nature of Radiation and MatterOpen
Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is $\alpha\times10^{-19}$ J. The value of $\alpha$ is . ( $h = 6.62\times10^{-34}$ J s, $e = 1.6\times10^{-19}$ C and $c = 3\times10^{8}$ m/s)
1. (1)3.68
2. (2)4.68
3. (3)5.68
4. (4)2.68
Q17 · MCQ · Ray OpticsOpen
A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be :-
1. (1)increased two times
2. (2)increased $\dfrac{3}{2}$ times
3. (3)decreased two times
4. (4)decreased $\dfrac{3}{2}$ times
Q18 · MCQ · Mechanical Properties of SolidsOpen
Two wires as shown in the figure below, made of steel and have breaking stress of $12\times10^{8}\ \mathrm{N/m^2}$ . Area of cross-section of upper wire is $0.008\ \mathrm{cm^2}$ and of lower wire is $0.004\ \mathrm{cm^2}$ . The maximum mass that can be added to pan without breaking any wire is kg. (take $g = 10\ \mathrm{m/s^2}$ )
1. (1)56
2. (2)38
3. (3)96
4. (4)5.6
Q19 · MCQ · Alternating CurrentOpen
An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$ . Now the frequency of the source is changed to $\omega/4$ , (keeping the voltage unchanged) the current is found to be $I/3$ . The ratio of resistance to reactance at frequency $\omega$ is
1. (1) $\sqrt{\dfrac{6}{7}}$
2. (2) $\sqrt{\dfrac{3}{5}}$
3. (3) $\sqrt{\dfrac{7}{8}}$
4. (4) $\sqrt{\dfrac{3}{4}}$
Q20 · MCQ · Semiconductor ElectronicsOpen
For the given logic circuit, which of the following inputs combination will make both LED-1 and LED-2 to glow ?
1. (1) $A = 0,\ B = 1,\ C = 1$
2. (2) $A = 1,\ B = 0,\ C = 0$
3. (3) $A = 1,\ B = 0,\ C = 1$
4. (4) $A = 1,\ B = 1,\ C = 0$
Q21 · Numerical · Mechanical Properties of SolidsOpen
A cube has side length 5 cm and modulus of rigidity $10^{5}\ \mathrm{N/m^2}$ . The displacement produced by a force of 10 N in the upper face of cube is mm.
Q22 · Numerical · Motion in a Straight LineOpen
From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity is equal to the magnitude of acceleration (in the same set of units) due to gravity is m. (Take $g = 10\ \mathrm{m/s^2}$ and neglect the air resistance)
We corrected a printing error in the original paper
Source printed “the magnitude of velocity equal to” (“is” missing).
Q23 · Numerical · WavesOpen
A transverse wave on a string is described by $y = 3\sin(36t + 0.018x + \pi/4)$ . Where $x$ , $y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is cm. (Nearest integer) ( $\pi = 3.14$ )
Q24 · Numerical · Moving Charges and MagnetismOpen
The charged particle moving in a uniform magnetic field of $\left(3\hat i + 2\hat j\right)$ T has an acceleration $\left(4\hat i - \dfrac{x}{2}\hat j\right)\ \mathrm{m/s^2}$ . The value of $x$ is
Q25 · Numerical · Electromagnetic InductionOpen
In the given circuit below inductance values of $L_1$ , $L_2$ and $L_3$ are same. The magnetic energy stored in the entire circuit is ( $U_t$ ) and that stored in the $L_2$ inductor is ( $U_l$ ). ( $U_t/U_l$ ) is . (Ignore the mutual inductance if any)

Chemistry

Q1 · MCQ · Some Basic ConceptsOpen
How many grams of residue is obtained by heating 2.76 g of silver carbonate ?
(Given : Molar mass of C, O and Ag are 12, 16 and 108 g mol $^{-1}$ respectively)
1. (1)1.08 g
2. (2)2.16 g
3. (3)3.24 g
4. (4)4.32 g
Q2 · MCQ · Structure of AtomOpen
Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.
- (A) $n = 3$ , $\ell = 2$ , $m = +1$
- (B) $n = 4$ , $\ell = 0$ , $m = 0$
- (C) $n = 6$ , $\ell = 1$ , $m = 0$
- (D) $n = 5$ , $\ell = 1$ , $m = +1$
- (E) $n = 2$ , $\ell = 1$ , $m = +1$
Choose the correct answer from the options given below :
1. (1)C $<$ D $<$ B $<$ A $<$ E
2. (2)B $<$ A $<$ E $<$ C $<$ D
3. (3)E $<$ C $<$ D $<$ B $<$ A
4. (4)E $<$ B $<$ A $<$ D $<$ C
Q3 · MCQ · Structure of AtomOpen
Identify the correct statements from the following :
- (A)Heisenberg uncertainty principle is applicable to electron.
- (B)The size of 2p $_x$ orbital is less than the size of 3p $_x$ orbital.
- (C)The energy of 2s orbital of H atom is equal to the energy of 2s orbital of Li.
- (D)The electronic configuration of Cr is [Ar] 3d $^5$ 4s $^1$
Choose the correct answer from the options given below :
1. (1)A, B and C only
2. (2)A, B and D only
3. (3)B, C, and D only
4. (4)A, C and D only
Q4 · MCQ · SolutionsOpen
What is the mole fraction of water in 10% by weight (w/w) of aqueous urea solution ?
[Given : Molar mass of H, O, C and N are 1, 16, 12 and 14 g mol $^{-1}$ respectively]
1. (1)0.825
2. (2)0.032
3. (3)0.867
4. (4)0.967
Q5 · MCQ · EquilibriumOpen
$\ce{M3A2}$ is a sparingly soluble salt of molar mass $y$ g mol $^{-1}$ and solubility $x$ g L $^{-1}$ . The ratio of the molar concentration of the anion ( $\ce{A^{3-}}$ ) to the solubility product of the salt is
1. (1) $\dfrac{1}{54}\cdot\dfrac{y^4}{x^4}$
2. (2) $\dfrac{y^5}{108x^4}$
3. (3) $108\cdot\dfrac{x^5}{y^5}$
4. (4) $\dfrac{1}{108}\,\dfrac{y^4}{x^4}$
Q6 · MCQ · EquilibriumOpen
Arrange the following resultant mixtures in increasing order of their pH values
- (A)10 mL 0.2 M $\ce{Ca(OH)2}$ + 25 mL 0.1 M HCl
- (B)10 mL 0.01 M $\ce{H2SO4}$ + 10 mL 0.01 M $\ce{Ca(OH)2}$
- (C)10 mL 0.1 M $\ce{H2SO4}$ + 10 mL 0.1 M KOH
Choose the correct answer from the options given below :
1. (1)B $<$ C $<$ A
2. (2)C $<$ A $<$ B
3. (3)C $<$ B $<$ A
4. (4)A $<$ C $<$ B
Q7 · MCQ · Chemical KineticsOpen
First order gas phase reaction
$\ce{A -> B + C}$
$p_\mathrm{i}$ = initial pressure of gas A, $p_\mathrm{t}$ = total pressure of the reaction mixture at time $t$
Expression of rate constant ( $k$ ) is
1. (1) $\dfrac{1}{t}\ln\dfrac{p_\mathrm{i}}{2p_\mathrm{i}-p_\mathrm{t}}$
2. (2) $\dfrac{1}{t}\ln\dfrac{2p_\mathrm{i}}{p_\mathrm{i}-p_\mathrm{t}}$
3. (3) $\dfrac{1}{t}\ln\dfrac{p_\mathrm{i}}{3p_\mathrm{i}-2p_\mathrm{t}}$
4. (4) $\dfrac{1}{t}\ln\dfrac{3p_\mathrm{i}}{4p_\mathrm{i}-p_\mathrm{t}}$
Q8 · MCQ · Classification & PeriodicityOpen
Statement I : The correct order of electronegativity of fluorine, oxygen and nitrogen is F $>$ O $>$ N.
Statement II : The oxidation state of oxygen in $\ce{OF2}$ is $+2$ and in $\ce{Na2O}$ is $-2$ .
In the light of the above statements, choose the correct answer from the options given below
1. (1)Both Statement I and Statement II are true
2. (2)Both Statement I and Statement II are false
3. (3)Statement I is true but Statement II is false
4. (4)Statement I is false but Statement II is true
We corrected a printing error in the original paper
Source printed “of fluorine, oxygen nitrogen”.
Q9 · MCQ · p-Block (15–18)Open
Correct statements from the following are :
- (A)Nitrogen in oxidation states from $+1$ to $+4$ disproportionates in acid medium.
- (B)Nitrogen has the ability to form d $\pi$ -p $\pi$ multiple bonds with itself and other elements with small size and high electronegativity.
- (C)N-N single bond is stronger than P-P single bond.
- (D)Nitrogen has highest density in its group due to small size.
- (E)The maximum covalency of nitrogen is four since it has only four valence orbitals for bonding.
Choose the correct answer from the options given below :
1. (1)B, C, and D only
2. (2)C, D, and E only
3. (3)A, C and E only
4. (4)A and E only
We corrected a printing error in the original paper
Source printed “the ability of form”.
Q10 · MCQ · d- and f-BlockOpen
Which of the following is NOT a physical or chemical characteristic of interstitial compounds ?
1. (1)They have high melting points, higher than those of pure metals
2. (2)They are very soft ionic in nature
3. (3)They retain metallic conductivity
4. (4)They are chemically inert and usually non-stoichiometric
We corrected a printing error in the original paper
Source printed “a physical or chemical characteristics”.
Q11 · MCQ · Coordination CompoundsOpen
The correct statements about metal carbonyls are
- (A)The metal-carbon bonds in metal carbonyls possess both $\sigma$ and $\pi$ -character.
- (B)Due to synergic bonding interactions between metals and CO ligand the metal-carbon bond becomes weak.
- (C)The metal-carbon $\sigma$ bond is formed by the donation of lone pair of electrons on the carbonyl carbon into a vacant orbital of metal.
- (D)The metal-carbon $\pi$ bond is formed by the donation of electrons from filled d-orbital of metal into vacant $\pi^*$ orbital of CO.
Choose the correct answer from the options given below :
1. (1)A and B only
2. (2)A, C and D only
3. (3)B and C only
4. (4)A and D only
We corrected a printing error in the original paper
Source printed “bonds in metals carbonyls”.
Q12 · MCQ · Coordination CompoundsOpen
Given below are two statements :
Statement I : Each electron in e $_\mathrm{g}$ orbitals destabilizes the orbitals by $+0.6\,\Delta_0$ and each electron in the t $_\mathrm{2g}$ orbitals stabilizes the orbitals by $-0.4\,\Delta_0$ in an octahedral field on the basis of crystal field theory.
Statement II : All the d-orbitals of the transition metals have the same energy in their free atomic state but when a complex is formed the ligands destroy the degeneracy of these orbitals on the basis of crystal field theory.
In the light of the above statements, choose the correct answer from the options given below.
1. (1)Both Statement I and Statement II are correct
2. (2)Both Statement I and Statement II are incorrect
3. (3)Statement I is correct but Statement II is incorrect
4. (4)Statement I is incorrect but Statement II is correct
Q13 · MCQ · Organic Basics (GOC)Open
Given below are two statements :
Statement I : On the basis of inductive effect, the order of stability of alkyl carbanions is $\ce{CH3^-}$ $>$ $\ce{CH3-CH2^-}$ $>$ $\ce{(CH3)2CH^-}$ $>$ $\ce{(CH3)3C^-}$ .
Statement II : Allyl and benzyl carbanions are more stabilised by inductive effect and not by resonance effect.
In the light of the above statements choose the correct answer from the options given below
1. (1)Both Statement I and Statement II are correct
2. (2)Both Statement I and Statement II are incorrect
3. (3)Statement I is correct and Statement II is incorrect
4. (4)Statement I is incorrect and Statement II is correct
Q14 · MCQ · Aldehydes, Ketones & AcidsOpen
“P” is hydrocarbon of molecular formula : $\ce{C8H14}$ . On ozonolysis, “P” forms “Q”. “Q” on treatment with alkali under reflux condition produces. “R”, which on treatment with $\ce{I2}$ /NaOH gives a yellow precipitate. Acidification of the solution gives “S”. The structure of “S” is given below :
The correct structure of “P” is
1. (1)
2. (2)
3. (3)
4. (4)
We corrected a printing error in the original paper
Source printed “The structure of “S” given below”.
Q15 · MCQ · HydrocarbonsOpen
For the following Friedel Craft's alkylation reaction, which of the statements are correct ?
- (A)Major product is n-propyl benzene.
- (B)iso-propyl carbocation intermediate is also generated
- (C)Multiple substitution is inevitable.
- (D)Introducing electron-donating substituent on benzene will not produce any alkylbenzene.
Choose the correct answer from the options given below :
1. (1)A and D only
2. (2)B and C only
3. (3)A and C only
4. (4)B and D only
Q16 · MCQ · AminesOpen
Benzyl isocyanide can be obtained from
- (A)
- (B)
- (C)
- (D)
- (E)
Choose the correct answer from the options given below :
1. (1)A and B only
2. (2)A and C only
3. (3)B and D only
4. (4)D and E only
Q17 · MCQ · Alcohols, Phenols & EthersOpen
Consider compounds A, B and C with following structural formulae
A = $\ce{CH3-CH2-CH2-CH2-CH2-OH}$
B = $\ce{CH2=CH-CH2-CH2-CH3}$
C = $\ce{HO-CH2-CH2-CH(OH)-CH3}$
For the conversion of B from A, reagent (D) required is and structural formula of product (E) obtained when C undergoes same reaction using excess reagent (D) is
1. (1)
  D E
  Conc. $\ce{H2SO4}$ $\ce{CH2=CH-CH(OH)-CH3}$
2. (2)
  D E
  PCC $\ce{HO-CH2-CH2-CH=CH2}$
3. (3)
  D E
  PCC $\ce{CH2=CH-CH=CH2}$
4. (4)
  D E
  Conc. $\ce{H2SO4}$ or $\ce{H3PO4}$ $\ce{CH2=CH-CH=CH2}$
We corrected a printing error in the original paper
Option (1): source printed E as “CH $_2$ = CH – CH(OH)/CH $_3$ ”.
Q18 · MCQ · AminesOpen
Identify the incorrect statements :
- (A) is a stronger base than
- (B) can be synthesized by Gabriel phthalimide synthesis.
- (C)
- (D)
  will dissolve in NaOH
Choose the correct answer from the options given below :
1. (1)A and D only
2. (2)A and C only
3. (3)B and C only
4. (4)A and B only
Q19 · MCQ · BiomoleculesOpen
Identify the correct statements
- (A)Glucose exists in two anomeric forms.
- (B)Anomers of glucose differ in configuration at C-1 in cyclic hemiacetal structure.
- (C)Melting point of $\alpha$ -anomer of glucose is greater than $\beta$ -anomer.
- (D)Specific rotation of $\alpha$ -anomer is $+19^\circ$ while for $\beta$ -anomer is $+112^\circ$
- (E) $\alpha$ and $\beta$ -anomers of glucose are prepared by crystallization of saturated glucose solution at 303 K and 371 K respectively.
Choose the correct answer from the options given below :
1. (1)A and B only
2. (2)B and C only
3. (3)A, B and D only
4. (4)A, B and E only
We corrected a printing error in the original paper
Source printed “Glucose exist in two anomeric forms”.
Q20 · MCQ · Practical / Qualitative AnalysisOpen
Statement I : Sodium dichromate and potassium dichromate are classified as primary standard in titrimetric analysis.
Statement II : Phenolphthalein is a weak base, therefore it dissociates in acidic medium.
In the light of the above statements, choose the correct answer from the options given below
1. (1)Both Statement I and Statement II are true
2. (2)Both Statement I and Statement II are false
3. (3)Statement I is true but Statement II is false
4. (4)Statement I is false but Statement II is true
Q21 · Numerical · Chemical BondingOpen
Consider the following species
$\ce{BrF5}$ , $\ce{XeF5^-}$ , $\ce{BF4^-}$ , $\ce{ICl4^-}$ , $\ce{XeF4}$ , $\ce{SF4}$ , $\ce{NH4^+}$ , $\ce{ClF3}$ , $\ce{XeF2}$ , $\ce{ICl2^-}$
Number of species having sp $^3$ d hybridized central atom is
Q22 · Numerical · Purification & CharacterisationOpen
In an estimation of sulphur by Carius method 0.2g of the substance gave 0.6 g of $\ce{BaSO4}$ . The percentage of sulphur in the substance is %.
(Given molar mass in g mol $^{-1}$ S : 32, $\ce{BaSO4}$ : 233)
We corrected a printing error in the original paper
Source printed “BaSO $_4$ : 231” (the molar mass of BaSO $_4$ is 137 + 32 + 64 = 233); corrected to 233. Answer corrected; the source key is 42 (computed with 231) — with 233, $(32/233)\times(0.6/0.2)\times100 = 41.2$ , i.e. 41.
Q23 · Numerical · Alcohols, Phenols & EthersOpen
One mole of phenol is treated with dilute $\ce{HNO3}$ at 298K to give a mixture of products. The mixture is separated by steam distillation. The steam volatile compound (X) is separated. The increase in percentage of oxygen in (X) with respect to phenol is $\times\,10^{-1}$ %
(Given molar mass in g mol $^{-1}$ H:1, C:12, N:14, O:16)
We corrected a printing error in the original paper
Source printed “The seam volatile compound”; the source prints no “ $\times$ ” between the blank and “ $10^{-1}$ %”.
Q24 · Numerical · EquilibriumOpen
The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below:
$\ce{A(g) <=> B(g) + C(g)}$
$\dfrac{1}{T}\left(\mathrm{K^{-1}}\right)$ $\mathrm{Log}_{10}K_\mathrm{p}$
0.05 3.5
0.06 2.5
0.07 1.5
The magnitude of $\dfrac{\Delta H^\circ}{R}$ calculated from the above data is . (Nearest integer)
Q25 · Numerical · Chemical KineticsOpen
If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be minutes.
(Given : $\log 2 = 0.3010$ )

Maths

Q1 · MCQ · Quadratic EquationsOpen
Let $a, b \in \mathbb{C}$ . Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$ . If $\beta - \alpha = \sqrt{11}$ and $\beta^2 - \alpha^2 = 3i\sqrt{11}$ , then $(\beta^3 - \alpha^3)^2$ is equal to:
1. (1)160
2. (2)176
3. (3)194
4. (4)187
Q2 · MCQ · Sequences & SeriesOpen
Let the sum of the first $n$ terms of an A.P. be $3n^2 + 5n$ . Then the sum of squares of the first 10 terms of the A.P. is:
1. (1)10220
2. (2)12860
3. (3)15220
4. (4)19780
Q3 · MCQ · Matrices & DeterminantsOpen
Let $A$ be a $3 \times 3$ matrix such that $A^{T}\begin{bmatrix} 1\\ 0\\ 1\end{bmatrix} = \begin{bmatrix} 5\\ 2\\ 2\end{bmatrix},\quad A^{T}\begin{bmatrix} 0\\ 0\\ 1\end{bmatrix} = \begin{bmatrix} 3\\ 1\\ 1\end{bmatrix},\quad A\begin{bmatrix} 1\\ 0\\ 1\end{bmatrix} = \begin{bmatrix} 3\\ 4\\ 4\end{bmatrix}\quad\text{and}\quad A\begin{bmatrix} 0\\ 0\\ 1\end{bmatrix} = \begin{bmatrix} 1\\ 3\\ 1\end{bmatrix}$ If $\det(A) = 1$ , then $\det(\operatorname{adj}(A^2 + A))$ is equal to:
1. (1)16
2. (2)25
3. (3)49
4. (4)64
Q4 · MCQ · Matrices & DeterminantsOpen
Consider the system of linear equations in $x, y, z$ : $\begin{aligned} &x + 2y + tz = 0,\\ &6x + y + 5tz = 0,\\ &3x + t^2y + f(t)z = 0, \end{aligned}$ Where $f : \mathbb{R} \to \mathbb{R}$ is a differentiable function. If this system has infinitely many solutions for all $t \in \mathbb{R}$ , then $f$
1. (1)is a constant function
2. (2)is strictly increasing on $\mathbb{R}$
3. (3)is strictly decreasing on $\mathbb{R}$
4. (4)has two critical points
Q5 · MCQ · Sequences & SeriesOpen
$\displaystyle\sum_{n=1}^{10}\left(\frac{528}{n(n+1)(n+2)}\right)$ is equal to:
1. (1)65
2. (2)130
3. (3)220
4. (4)440
Q6 · MCQ · TrigonometryOpen
Let $\tan A$ , $\tan B$ , where $A, B \in \left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$ , be the roots of the quadratic equation $x^2 - 2x - 5 = 0$ . Then $20\sin^2\left(\dfrac{A + B}{2}\right)$ is equal to:
1. (1) $10 + \sqrt{10}$
2. (2) $10 - 2\sqrt{10}$
3. (3) $10 - 3\sqrt{10}$
4. (4) $10 - \sqrt{10}$
Q7 · MCQ · ProbabilityOpen
A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:
1. (1) $\dfrac{7}{10}$
2. (2) $\dfrac{10}{17}$
3. (3) $\dfrac{12}{19}$
4. (4) $\dfrac{7}{19}$
We corrected a printing error in the original paper
Source printed “On the the envelope” (doubled word).
Q8 · MCQ · StatisticsOpen
The mean deviation about the mean for the data
$x_i$ 5 7 9 10 12 15
$f_i$ 8 6 2 2 2 6
is equal to:
1. (1) $\dfrac{40}{13}$
2. (2) $\dfrac{42}{13}$
3. (3) $\dfrac{44}{13}$
4. (4) $\dfrac{46}{13}$
Q9 · MCQ · Conic SectionsOpen
Let a focus of the ellipse $E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ be $S(4, 0)$ and its eccentricity be $\dfrac45$ . If the point $P(3, \alpha)$ lies on $E$ and $O$ is the origin, then the area of $\Delta POS$ is equal to:
1. (1) $12/5$
2. (2) $14/5$
3. (3) $24/5$
4. (4) $48/5$
Q10 · MCQ · CirclesOpen
Let $P$ be a moving point on the circle $x^2 + y^2 - 6x - 8y + 21 = 0$ Then, the maximum distance of $P$ from the vertex of the parabola $x^2 + 6x + y + 13 = 0$ is equal to:
1. (1)8
2. (2)10
3. (3)12
4. (4)9
Q11 · MCQ · Straight LinesOpen
In an equilateral triangle $PQR$ , let the vertex $P$ be at $(3, 5)$ and the side $QR$ be along the line $x + y = 4$ . If the orthocentre of the triangle $PQR$ is $(\alpha, \beta)$ , then $9(\alpha + \beta)$ is equal to:
1. (1)16
2. (2)27
3. (3)36
4. (4)48
Q12 · MCQ · TrigonometryOpen
The sum of all the integral values of $p$ such that the equation $3\sin^2x + 12\cos x - 3 = p$ , $x \in \mathbb{R}$ , has at least one solution, is:
1. (1) $-54$
2. (2) $-60$
3. (3) $-75$
4. (4) $-84$
Q13 · MCQ · 3D GeometryOpen
The square of the distance of the point $P(5, 6, 7)$ from the line $\dfrac{x-2}{2} = \dfrac{y-5}{3} = \dfrac{z-2}{4}$ is equal to:
1. (1)3
2. (2)5
3. (3)6
4. (4)8
Q14 · MCQ · VectorsOpen
Let $\vec a = \sqrt7\,\hat i + \hat j - \hat k$ and $\vec b = \hat j + 2\hat k$ . If $\vec r$ is a vector such that $\vec r\times\vec a + \vec a\times\vec b = \vec 0$ and $\vec r\cdot\vec a = 0$ , then $\lvert 3\vec r\rvert^2$ is equal to:
1. (1)44
2. (2)54
3. (3)86
4. (4)132
Q15 · MCQ · 3D GeometryOpen
The square of the distance of the point of intersection of the lines $\vec r = \left(\hat i + \hat j - \hat k\right) + \lambda(a\hat i - \hat j)$ , $a \neq 0$ and $\vec r = \left(4\hat i - \hat k\right) + \mu(2\hat i + a\hat k)$ from the origin is:
1. (1)5
2. (2)10
3. (3)17
4. (4)26
Q16 · MCQ · Area under CurvesOpen
The area of the region $R = \{(x, y) : xy \le 27,\ 1 \le y \le x^2,\ x \ge 0\}$ is equal to:
1. (1) $78\log_e 3 - \dfrac{52}{3}$
2. (2) $54\log_e 3 - \dfrac{52}{3}$
3. (3) $54\log_e 3 - \dfrac{26}{3}$
4. (4) $54\log_e 3 + \dfrac{26}{3}$
We corrected a printing error in the original paper
Assumption “ $x \ge 0$ ” added to the region; the source leaves it unstated (for $x \le -1$ every point with $1 \le y \le x^2$ satisfies $xy \le 27$ , so the region as printed has infinite area).
Q17 · MCQ · Limits, Continuity & DifferentiabilityOpen
The product of all possible values of $\alpha$ , for which $\lim_{x\to0}\left(\frac{1 - \cos(\alpha x)\cos\big((\alpha+1)x\big)\cos\big((\alpha+2)x\big)}{\sin^2\big((\alpha+1)x\big)}\right) = 2,$ is:
1. (1) $-2$
2. (2)1
3. (3) $-1$
4. (4) $\dfrac54$
Q18 · MCQ · Definite IntegrationOpen
The value of the integral $\displaystyle\int_0^{\infty}\frac{\log_e(x)}{x^2 + 4}\,dx$ is:
1. (1) $\dfrac{\pi\log_e(2)}{2}$
2. (2) $\dfrac{\pi\log_e(2)}{4}$
3. (3) $1 + \pi\log_e(2)$
4. (4) $2 + \pi\log_e(2)$
Q19 · MCQ · Limits, Continuity & DifferentiabilityOpen
Let $f : \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $f\left(\frac{x + y}{3}\right) = \frac{f(x) + f(y)}{3}\quad\text{for all } x, y \in \mathbb{R}$ and $f'(0) = 3$ . Then the minimum value of the function $g(x) = 3 + e^x f(x)$ , is
1. (1) $3\left(\dfrac{e + 1}{e}\right)$
2. (2) $3\left(\dfrac{e - 1}{e}\right)$
3. (3) $\dfrac{3 - e}{e}$
4. (4) $3e$
Q20 · MCQ · Definite IntegrationOpen
The value of the integral $\displaystyle\int_{\pi/6}^{\pi/3}\left(\frac{4 - \operatorname{cosec}^2x}{\cos^4x}\right)dx$ is:
1. (1) $\dfrac{11}{\sqrt3}$
2. (2) $\dfrac{16}{\sqrt3}$
3. (3) $\dfrac{32}{3\sqrt3}$
4. (4) $\dfrac{64}{3\sqrt3}$
Q21 · Numerical · Permutations & CombinationsOpen
Let $A = \{1, 2, 3, 4, 5, 6\}$ . The number of one-one functions $f : A \to A$ such that $f(1) \ge 3$ , $f(3) \le 4$ and $f(2) + f(3) = 5$ , is .
Q22 · Numerical · Permutations & CombinationsOpen
Two players $A$ and $B$ play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player $A$ wins the series is .
Q23 · Numerical · Binomial TheoremOpen
If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\dfrac{1}{x^3} - x^4\right)^n$ , $x \neq 0$ , is zero, then the value of $n$ is .
Q24 · Numerical · Inverse TrigonometryOpen
If $\dfrac{\pi}{4} + \displaystyle\sum_{p=1}^{11}\tan^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha$ , then $\tan\alpha$ is equal to .
Q25 · Numerical · Differential EquationsOpen
Let $y = y(x)$ be the solution of the differential equation $x\sin\left(\frac{y}{x}\right)dy = \left(y\sin\left(\frac{y}{x}\right) - x\right)dx,\quad y(1) = \frac{\pi}{2}$ and let $\alpha = \cos\left(\dfrac{y\left(e^{12}\right)}{e^{12}}\right)$ . Then the number of integral value of $p$ , for which the equation $x^2 + y^2 - 2px + 2py + \alpha + 2 = 0$ represents a circle of radius $r \le 6$ , is .
Flawed question. Ill-posed: the solution is $\cos(y/x) = \log_e x$ , which exists only for $e^{-1} \le x \le e$ , so $y(e^{12})$ does not exist and $\alpha = \cos(\cdot) = 12$ is impossible; even with the formal $\alpha = 12$ ( $r^2 = 2p^2 - 14$ ) only $p = \pm3, \pm4, \pm5$ give a circle (6 values), while the key 11 also counts $p$ with $r^2 < 0$ ; no minimal, evident change repairs both. It is shown for completeness and is left out of practice tests.

$\dfrac{1}{T}\left(\mathrm{K^{-1}}\right)$	$\mathrm{Log}_{10}K_\mathrm{p}$
0.05	3.5
0.06	2.5
0.07	1.5

D	E
Conc. $\ce{H2SO4}$	$\ce{CH2=CH-CH(OH)-CH3}$

D	E
PCC	$\ce{HO-CH2-CH2-CH=CH2}$

D	E
PCC	$\ce{CH2=CH-CH=CH2}$

D	E
Conc. $\ce{H2SO4}$ or $\ce{H3PO4}$	$\ce{CH2=CH-CH=CH2}$