JEE Main 2022 July 26 Shift 1 Question Paper with Solution PDF- Download Here

Let \(f : R \rightarrow R\) be a continuous function such that \(f (3x)- f(x)= x\). If \(f(8)=7\), then \(f (14)\) is equal to :

• (1) 4
• (2) 10
• (3) 11
• (4) 16

Let O be the origin and A be the point \(z_1 = 1 + 2i\). If B is the point \(z_2, Re(z_2) < 0\), such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

• (1) \(arg\ z_2=\pi–tan^{−1}3\)
• (2) \((arg)(z_1−2z_2)=−tan^{−1⁡}\frac 43\)
• (3) \(|z_2|=\sqrt {10}\)
• (4) \(|2z_1−z_2|=5\)

If the system of linear equations \( 8 x+y+4 z=-2 \), \( x+y+z=0 \), \( \lambda x-3 y=\mu\) has infinitely many solutions, then the distance of the point \(\left(\lambda, \mu,-\frac{1}{2}\right)\) from the plane \(8 x + y +4 z +2=0\) is :

• (1) \(3 \sqrt{5}\)
• (2) 4
• (3) \(\frac{26}{9}\)
• (4) \(\frac{10}{3}\)

The odd natural number a, such that the area of the region bounded by \(y = 1, y = 3, x = 0, x = y^a\) is \(\frac {364}{3}\), is equal to

• (1) 3
• (2) 5
• (3) 7
• (4) 9

Consider two G.Ps. \(2, 2^2, 2^3, ….\) and \(4, 4^2, 4^3, …\) of \(60\) and n terms respectively. If the geometric mean of all the \(60 + n\) terms is \((2)^{\frac {225}{8}}\) then \(\sum_{k=1}^{n}k(n−k)\) is equal to

• (1) 560
• (2) 1540
• (3) 1330
• (4) 2600

If the function
\(f(x) =   \begin{cases}    \frac {log_e(1−x+x^2)+log_e(1+x+x_2)}{sec⁡\ x−cos⁡\ x},      & \quad x∈(−\frac \pi2,\frac \pi2)−{0}\\     k,  & \quad x=0   \end{cases}\)
is continuous at \(x = 0\), then k is equal to

• (1) 1
• (2) -1
• (3) e
• (4) 0

If 
\(f(x) = \begin{cases}     x + a, & x \leq 0 \\     |x - 4|, &  x > 0 \end{cases}\) and \(g(x) = \begin{cases}     x + 1, & x < 0 \\     (x - 4)^2 + b, &  x \geq 0 \end{cases}\)
 are continuous on R, then (gof) (2) + (fog) (–2) is equal to

• (1) -10
• (2) 10
• (3) 8
• (4) -8

Let 
\(f(x) = \begin{cases}     x^3 - x^2 + 10x - 7, & x \leq 1 \\     -2x + \log_2(b^2 - 4), &  x > 1 \end{cases}\)
Then the set of all values of b, for which f(x) has maximum value at x = 1, is

• (1) (-6, -2)
• (2) (2,6)
• (3) \((-6,-2) ∪ (2, 6)\)
• (4) \([-\sqrt6, -2] ∪ (2, \sqrt6]\)

If 
\(\frac{dy}{dx}+2y \tan⁡x=\sin⁡x, 0<x<\frac{π}{2} and\ y(\frac{π}{3})=0 \)
then the maximum value of y(x) is:

• (1) \(\frac{1}{8}\)
• (2) \(\frac{3}{4}\)
• (3) \(\frac{1}{4}\)
• (4) \(\frac{3}{8}\)

A point P moves so that the sum of squares of its distances from the points (1, 2) and (–2, 1) is 14. Let f(x, y) = 0 be the locus of P, which intersects the x-axis at the points A, B and the y-axis at the points C, D. Then the area of the quadrilateral ACBD is equal to

• (1) \(\frac{9}{2}\)
• (2) \(\frac{3\sqrt17}{2}\)
• (3) \(\frac{3\sqrt17}{4}\)
• (4) 9

The length of the perpendicular from the point (1, –2, 5) on the line passing through (1, 2, 4) and parallel to the line x + y – z = 0 = x – 2y + 3z – 5 is

• (1) \(\sqrt{\frac{21}{2}}\)
• (2) \(\sqrt{\frac{9}{2}}\)
• (3) \(\sqrt{\frac{73}{2}}\)
• (4) 1

Let 
\(\vec{a}=α\hat{i}+\hat{j}−\hat{k}\ and\ \vec{b}=2\hat{i}+\hat{j}−α\hat{k},α>0\). 
If the projection of \(\vec{a}×\vec{b}\) on the vector \(−\hat{i}+2\hat{j}−2\hat{k}\) 
is 30, then α is equal to

• (1) \(\frac{15}{2}\)
• (2) 8
• (3) \(\frac{13}{2}\)
• (4) 7

Let E₁, E₂, E₃ be three mutually exclusive events such that
\(P(E_1)=\frac{2+3p}{6}, P(E_2)=\frac{2−p}{8} and\ P(E_3)=\frac{1−p}{2}.\)
If the maximum and minimum values of p are p₁ and p₂, then (p₁ + p₂) is equal to :

• (1) \(\frac{2}{3}\)
• (2) \(\frac{5}{3}\)
• (3) \(\frac{5}{4}\)
• (4) 1

\(\tan⁡(2\tan^{−1}\frac{⁡1}{5}+\sec^{−1}⁡\frac{\sqrt5}{2}+2\tan^{−1}⁡\frac{1}{8})\)
is equal to :

• (1) 1
• (2) 2
• (3) \(\frac{1}{4}\)
• (4) \(\frac{5}{4}\)

Let A be a \(2×2\) matrix with \(det (A) = –1\) and \(det((A + I) (Adj (A) + I)) = 4\). Then the sum of the diagonal elements of A can be

• (1) \(-1\)
• (2) \(2\)
• (3) \(1\)
• (4) \(-\sqrt 2\)

If \(a = \lim_{{n \to \infty}} \sum_{{k=1}}^{n} \frac{2n}{{n^2 + k^2}}\)and
\(f(x) = \sqrt{\frac{1 - \cos x}{1 + \cos x}}, \quad x \in (0, 1)\) then

• (1) \(2\sqrt2f(\frac{a}{2})=f^′(\frac{a}{2})\)
• (2) \(f(\frac{a}{2})f^′(\frac{a}{2})=\sqrt2\)
• (3) \(\sqrt2f(\frac{a}{2})=f^′(\frac{a}{2})\)
• (4) \(f(\frac{a}{2})=\sqrt2f^′(\frac{a}{2})\)

Let the tangent drawn to the parabola y² = 24x at the point (α, β) is perpendicular to the line 2x + 2y = 5. Then the normal to the hyperbola
\(\frac{x^2}{α^2}−\frac{y^2}{β^2}=1\)
at the point (α + 4, β + 4) does NOT pass through the point

• (1) (25, 10)
• (2) (20, 12)
• (3) (30, 8)
• (4) (15, 13)

The mean and variance of a binomial distribution are α and α/3, respectively. 
If P(X = 1) = 4/243 then P(X = 4 or 5) is equal to :

• (1) \(\frac{5}{9}\)
• (2) \(\frac{64}{81}\)
• (3) \(\frac{16}{27}\)
• (4) \(\frac{145}{243}\)

Let \(S=\left\{θ∈[0,2π]:8^{2sin^2⁡θ}+8^{2cos^2⁡θ}=16\right\}\) .
Then\(n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)\)is equal to :

• (1) 0
• (2) -2
• (3) -4
• (4) 12

The statement 
\((∼(p ⇔∼q))∧q \)
is :

• (1) A tautology
• (2) A contradiction
• (3) \(Equivalent\ to\ (p⇒q)∧q\)
• (4) \(Equivalent\ to\ (p⇒q)∧p\)

If for some p, q, r ∈ R, not all have same sign, one of the roots of the equation (p² + q²)x² – 2q(p + r)x + q² + r² = 0 is also a root of the equation x² + 2x – 8 = 0, then (q² + r²)/p² is equal to _______ .

The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ .

The number of distinct real roots of the equation x⁵(x³ – x² – x + 1) + x (3x³ – 4x² – 2x + 4) – 1 = 0 is ______ .

If 
\(n(2n+1)\int_{0}^{1}(1−xn)^{2n}dx=1177\int_{0}^{1}(1−x^n)^{2n+1}dx\)
,then n ∈ N is equal to ______.

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x – y = 3, respectively. If its orthocentre is
\((2, a),−\frac{1}{2}<a<2 \)
then p is equal to _______.

Let the function f(x) = 2x² – log_ex, x> 0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola y² = 4ax at a point P on it passes through the point (8a, 8a –1) but does not pass through the point (-1/a, 0). If the equation of the normal at P is
\(\frac{x}{α}+\frac{y}{β}=1\)
 then α + β is equal to _______ .

Let Q and R be two points on the line 
\(\frac{x+1}{2}=\frac{y+2}{3}=\frac{z−1}{2}\) at a distance \(\sqrt{26}\) 
from the point P(4, 2, 7). Then the square of the area of the triangle PQR is _______ .

The series of positive multiples of 3 is divided into sets: {3}, {6, 9, 12}, {15, 18, 21, 24, 27},…… Then the sum of the elements in the 11^th set is equal to ________.

If the coefficients of x and x² in the expansion of (1 + x)^p (1 – x)^q, p, q≤15, are – 3 and – 5 respectively, then coefficient of x³ is equal to ______.

Let a curve y = y(x) pass through the point (3, 3) and the area of the region under this curve, above the x-axis and between the abscissae 3 and 
\(x(>3)\ be\ (\frac{y}{x})^3\)
. If this curve also passes through the point (α,6√10) in the first quadrant, then α is equal to _______.

Three masses M = 100 kg, m₁ = 10 kg and m₂ = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m₂ moves upward with an acceleration of 2 ms^–2. The value of F is
(Take g = 10 ms^–2)

• (1) 3360 N
• (2) 3380 N
• (3) 3120 N
• (4) 3240 N

A parallel beam of light of wavelength 900 nm and intensity 100 Wm^–2 is incident on a surface perpendicular to the beam. The number of photons crossing 1 cm^–2 area perpendicular to the beam in one second is

• (1) \(3 × 10^{16}\)
• (2) \(4.5 × 10^{16}\)
• (3) \(4.5 × 10^{17}\)
• (4) \(4.5 × 10^{20}\)

In young's double slit experiment, the fringe width is \(12\, mm\) If the entire arrangement is placed in water of refractive index \(\frac{4}{3}\), then the fringe width becomes (in \(mm\) )

• (1) 16
• (2) 9
• (3) 48
• (4) 12

The magnetic field of a plane electromagnetic wave is given by:
\(\vec B=2×10^{−8}sin⁡(0.5×10^3x+1.5×10^{11}t)\hat jT\).
The amplitude of the electric field would be

• (1) 6 Vm^–1 along x-axis
• (2) 3 Vm^–1 along z-axis
• (3) 6 Vm^–1 along z-axis
• (4) 2 × 10^–8 Vm^–1 along z-axis

In a series LR circuit \(X_L=R\) and power factor of the circuit is \(P _1\) When capacitor with capacitance \(C\) such that \(X _{ L }= X _{ C }\) is put in series, the power factor becomes \(P _2\) The ratio \(\frac{ P _1}{ P _2}\) is

• (1) \(\frac{1}{2}\)
• (2) \(\frac{1}{\sqrt{2}}\)
• (3) \(\frac{\sqrt{3}}{\sqrt{2}}\)
• (4) \(2: 1\)

A charge particle is moving in a uniform magnetic field \((2 \hat{ i }+3 \hat{ j }) T\) If it has an acceleration of \((\alpha \hat{i}-4 \hat{j}) m / s ^2\), then the value of \(\alpha\) will be

• (1) 3
• (2) 6
• (3) 12
• (4) 2

B_X and B_Y are the magnetic field at the centre of two coils X and Y, respectively each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of B_X and B_Y is

• (1) 1:1
• (2) 1:2
• (3) 2:1
• (4) 4:1

The current I in the given circuit will be

• (1) 10 A
• (2) 20 A
• (3) 4 A
• (4) 40 A

The total charge on the system of capacitors C₁ = 1 μF, C₂ = 2 μF, C₃ = 4 μF and C₄ = 3 μF, connected in parallel is :
(Assume a battery of 20 V is connected to the combination)

• (1) \(200\ μC\)
• (2) \(200\ C\)
• (3) \(10\ μC\)
• (4) \(10\ C\)

When a particle executes Simple Harmonic Motion, the nature of graph of velocity as a function of displacement will be :

• (1) Circular
• (2) Elliptical
• (3) Sinusoidal
• (4) Straight line

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40 K at constant pressure. The increase in the internal energy of the gas in this process is:
(Given R = 8.3 JK^–1 mol^–1)

• (1) 5810 J
• (2) 3486 J
• (3) 11620 J
• (4) 6972 J

A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

• (1) P
• (2) 8P
• (3) 32P
• (4) 64P

A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given \(\pi\) = 3.14)

• (1) \(8.5 × 10^{–4} J\)
• (2) \(8.2 × 10^{–4} J\)
• (3) \(7.5 × 10^{–4} J\)
• (4) \(5.3 × 10^{–4} J\)

The percentage decrease in the weight of a rocket, when taken to a height of \(32 \,km\) above the surface of earth will, be : (Radius of earth \(=6400 \,km\) )

• (1) \(1 \%\)
• (2) \(3 \%\)
• (3) \(4 \%\)
• (4) \(0.5 \%\)

• (1) \(\frac{ V }{2 \sqrt{2}}\)
• (2) \(\frac{v}{2}\)
• (3) \(\frac{v}{4}\)
• (4) \(\frac{ v }{\sqrt{2}}\)

A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s² and then climbs up with an acceleration of 5 m/s². Choose the correct option (g = 10 m/s²).

• (1) T = 700 N while climbing upward
• (2) T = 350 N while going downward
• (3) Rope will break while climbing upward
• (4) Rope will break while going downward

Two projectiles thrown at 30° and 45° with the horizontal, respectively, reach the maximum height in same time. The ratio of their initial velocities is :

• (1) \(1:\sqrt 2\)
• (2) \(2:1\)
• (3) \(\sqrt 2:1\)
• (4) \(1:2\)

A screw gauge of pitch 0.5 mm is used to measure the diameter of uniform wire of length 6.8 cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale.]

• (1) \(6.8\ cm^2\)
• (2) \(3.4\ cm^2\)
• (3) \(3.9\ cm^2\)
• (4) \(2.4\ cm^2\)

A radio can tune to any station in 6 MHz to 10 MHz band. The value of corresponding wavelength bandwidth will be

• (1) 4 m
• (2) 20 m
• (3) 30 m
• (4) 50 m

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is
(Take log₁₀1.88 = 0.274)

• (1) 0.02 min^–1
• (2) 2.7 min^–1
• (3) 0.063 min^–1
• (4) 6.3 min^–1

If the initial velocity in horizontal direction of a projectile is unit vector \(\hat i\) and the equation of trajectory is \(y = 5x(1 – x)\). The y component vector of the initial velocity is ______ \(\hat j\).
(Take \(g=10\ m/s^2\))

A disc of mass 1 kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc of fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, it angular speed will be \(4\sqrt {\frac {x}{3R}}\) rad s⁻¹ where x = ______ .(g = 10 ms^–2)

In an experiment of determine the Young’s modulus of wire of a length exactly 1 m, the extension in the length of the wire is measured as 0.4 mm with an uncertainty of ±0.02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0.4 mm with an uncertainty of ±0.02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0.4 mm with an uncertainty of ± 0.01 mm. The error in the measurement of Young’s modulus (ΔY) is found to be x × 10¹⁰ Nm^–2. The value of x is ___.
(Take g=10 m/s²)

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness (t₁ and t₂) as shown in figure. The two different dielectric materials are separated by a conducting foil F. The voltage of the conducting foil is _____V.

Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length l₁ is 40 cm. Now an unknown resistance x is connected in series with P and new balancing length is found to be 80 cm measured from the same end. Then the value of x will be ________ Ω.

The effective current I in the given circuit at very high frequencies will be ______ A.

The graph between \(\frac 1u\) and \(\frac 1v\) for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5, and its both the surfaces have the same radius of curvature R. The value of R will be______cm.
(where u = object distance, v = image distance)

In the hydrogen spectrum, λ be the wavelength of first transition line of Lyman series. The wavelength difference will be “aλ” between the wavelength of 3^rd transition line of the Paschen series and that of 2^nd transition line of Balmer series where a = ______.

In the circuit shown below, maximum Zener diode current will be ________ mA.

When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be \(\frac x3\) Hz, where x = _____ .

Match List - I with List - II 
List-I (Compound)                                              List-II (Shape)
A \(BrF _5\)                                                                    I bent 
B \(\left[ CrF _6\right]^{3-}\)                                                             II square pyramidal
C \(O _3\)                                                                     III trigonal bipyramidal 
D \(PCl _5\)                                                                    IV octahedral 
Choose the correct answer from the optionsgiven below :

• (1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
• (2) (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
• (3) (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
• (4) (A) - (III), (B) - (IV), (C) - (II), (D) - (I)

• (1) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
• (2) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
• (3) (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
• (4) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)

Given two statements below:
Statement I : In \(Cl_2\) molecule the covalent radius is double of the atomic radius of chlorine.
Statement II : Radius of anionic species is always greater than their parent atomic radius.
Choose the most appropriate answer from options given below:

• (1) Both Statement I and Statement II are correct.
• (2) Both Statement I and Statement II are incorrect.
• (3) Statement I is correct but Statement II is incorrect.
• (4) Statement I is incorrect but Statement II is correct.

Which of the given reactions is not an example of a disproportionation reaction?

• (1) \(2H_2O_2 → 2H_2O + O_2\)
• (2) \(2NO_2 + H_2O → HNO_3 + HNO_2\)
• (3) \(MnO4^– + 4H^+ + 3e^– → MnO_2 + 2H_2O\)
• (4) \(3MnO_4^{2–} + 4H^+ → 2MnO_4^– + MnO_2 + 2H_2O\)

The dark purple colour of \(KMnO_4\) disappears in the titration with oxalic acid in acidic medium. The overall change in the oxidation number of manganese in the reaction is :

• (1) 5
• (2) 1
• (3) 7
• (4) 2

\(\dot Cl + CH_4 → A + B\)
A and B in the above atmospheric reaction step are:

• (1) \(C_2H_6\) and \(Cl_2\)
• (2) \(\dot CHCl_2 \) and \(H_2\)
• (3) \(\dot CH_3\) and \(HCl\)
• (4) \(C_2H_6\) and \(HCl\)

Which technique among the following, is most appropriate in separation of a mixture of 100 mg of p-nitrophenol and picric acid?

• (1) Steam distillation
• (2) 2-5 ft long column of silica gel
• (3) Sublimation
• (4) Preparative TLC (Thin Layer Chromatography)

The difference in the reaction of phenol with bromine in chloroform and bromine in water medium is due to :

• (1) Hyperconjugation in substrate
• (2) Polarity of solvent
• (3) Free radical formation
• (4) Electromeric effect of the substrate

Which of the following compounds is not aromatic?

• (1)
• (2)
• (3)
• (4)

The products formed in the following reaction, A and B are

• (1)
• (2)
• (3)
• (4)

Which reactant will give the following alcohol on reaction with one mole of phenyl magnesium bromide (PhMgBr) followed by acidic hydrolysis?

• (1) \(CH_3-C≡N\)
• (2) \(Ph-C≡N\)
• (3)
• (4)

The major product of the following reaction is

(Substrate: 1-methoxy-2-nitrobenzene (2-nitroanisole), \(\mathrm{OCH_3}\) and \(\mathrm{NO_2}\) on adjacent ring carbons.) Reagents: (i) Na/liq. \(\mathrm{NH_3}\); (ii) \(\mathrm{CH_3CH_2OH}\).

• (1)
• (2)
• (3)
• (4)

The correct stability order of the following diazonium salt is

• (1) (A) > (B) > (C) > (D)
• (2) (A) > (C) > (D) > (B)
• (3) (C) > (A) > (D) > (B)
• (4) (C) > (D) > (B) > (A)

Which one of the following is a reducing sugar?

• (1)
• (2)
• (3)
• (4)

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Experimental reaction of \(CH_3Cl\) with aniline and anhydrous \(AlCl_3\) does not give o and p-methylaniline.
Reason (R): The \(–NH_2\)group of aniline becomes deactivating because of salt formation with anhydrous \(AlCl_3\) and hence yields m-methyl aniline as the product.
In the light of the above statements, choose the most appropriate answer from the options given below :

• (1) Both (A) and (R) are true and (R) is the correct explanation of (A).
• (2) Both (A) and (R) are true but (R) is not the correct explanation of (A).
• (3) (A) is true, but (R) is false.
• (4) (A) is false, but (R) is true.

Refining using liquation method is the most suitable for metals with :

• (1) Low melting point
• (2) High boiling point
• (3) High electrical conductivity
• (4) Less tendency to be soluble in melts than impurities

Which of the following can be used to prevent the decomposition of \(H_2O_2\)?

• (1) Urea
• (2) Formaldehyde
• (3) Formic acid
• (4) Ethanol

1. \(AlCl_3\)
2. \(BeH_2\)
3. \(LiH\)
4. \(LiCl\)
5. \(BeAlH_4\)

• (1) (A), (D) and (E)
• (2) (A), (B) and (D)
• (3) (D) and (E)
• (4) (B), (C) and (D)

Borazine, also known as inorganic benzene, can be prepared by the reaction of 3-equivalents of “X” with 6-equivalents of “Y”. “X” and “Y”, respectively are:

• (1) \(B(OH)_3 \)and \(NH_3\)
• (2) \(B_2H_6\) and \(NH_3\)
• (3) \(B_2H_6 \)and \(HN_3\)
• (4) \(NH_3\) and \(B_2O_3\)

Stearic acid and polyethylene glycol react to form which one of the following soap/s detergents?

• (1) Cationic detergent
• (2) Soap
• (3) Anionic detergent
• (4) Non-ionic detergent

Chlorophyll extracted from the crushed green leaves was dissolved in water to make 2 L solution of Mg of concentration 48 ppm. The number of atoms of Mg in this solution is \(x × 10^{20}\) atoms. The value of \(x\) is ________. (Nearest integer)
(Given : Atomic mass of Mg is 24 g mol^–1; N_A = 6.02 × 10²³ mol^–1)

The wavelength of an electron and a neutron will become equal when the velocity of the electron is x times the velocity of neutron. The value of x is ______. (Nearest integer)
(Mass of electron is 9.1 × 10^–31 kg and mass of neutron is 1.6 × 10^–27 kg)

2.4 g coal is burnt in a bomb calorimeter in excess of oxygen at 298 K and 1 atm pressure. The temperature of the calorimeter rises from 298 K to 300 K. The enthalpy change during the combustion of coal is –x kJ mol^–1. The value of x is ______.(Nearest integer)
(Given : Heat capacity of bomb calorimeter is 20.0 kJ K^–1. Assume coal to be pure carbon)

When 800 mL of 0.5 M nitric acid is heated in a beaker, its volume is reduced to half and 11.5 g of nitric acid is evaporated. The molarity of the remaining nitric acid solution is \(x × 10^{–2} M\). (Nearest integer)
(Molar mass of nitric acid is 63 g mol^–1)

At \(298\ K\), the equilibrium constant is \(2 × 10^{15}\) for the reaction:
\(Cu(s)+2Ag+(Aq)⇌Cu^{2+}(aq)+2Ag(s)\)
The equilibrium constant for the reaction:
\(\frac 12Cu^{2+}(aq)+Ag(s)+(Aq)⇌\frac 12Cu(s)+Ag^+(aq)\) is \(x \times10^{-8}\).
The value of \(x\) is ______ . (Nearest integer)

The amount of charge in F (Faraday) required to obtain one mole of iron from \(Fe_3O_4\) is ______ . (Nearest integer)

For a reaction \(A → 2B + C\) the half lives are 100 s and 50 s when the concentration of reactant A is 0.5 and 1.0 mol L^–1, respectively. The order of the reaction is ______ .(Nearest integer)

The difference between spin only magnetic moment value of \([Co(H_2O)_6]Cl_2\) and \([Cr(H_2O)_6]Cl_3\) is ________ .

In the presence of sunlight, benzene reacts with CI₂ to give product X. The number of hydrogens in X is _________.

A mixture of hydrogen and oxygen contains 40% hydrogen by mass when the pressure is 2.2 bar. The partial pressure of hydrogen is _______ bar. (Nearest integer)