JEE Main 2023 13 April Shift 1 Question Paper with Solution PDF- Download Here

Find area bounded by the curves \(y\) = \(max\{sin x, cos x\}\) and \(x-axis\) between \(x = -  \pi  \)and \(x =   \pi\)

• (1) \(2 + \sqrt{2}\)
• (2) \(\sqrt{2}\)
• (3) \(1 + \sqrt{2}\)
• (4) \(2\sqrt{2}\)

Let PQ be a focal chord of the parabola y² = 36x of length 100, making an acute angle with the positive x-axis. Let the ordinate of P be positive and M be the point on the line segment PQ such that PM:MQ = 3:1. Then which of the following points does \(\underline{NOT}\) lie on the line passing through M and perpendicular to the line PQ? 

• (1) (3,33)
• (2) (-6, 45)
• (3) (-3, 43)
• (4) (6,29)

Let a =\(\^i+4\^j​+2\^k,b=3\^i−2\^j​+7\^k \,\,\,\,and\,\,\.\ c=2\^i−\^j​+4\^k\). Find a vector d satisfies \(\overrightarrow{d}\times{\overrightarrow{b}}=\overrightarrow{c}\times{\overrightarrow{b}}\) and \(\overrightarrow{d}.\overrightarrow{a}=24\), then \(|\overrightarrow{d}|^2\) is equal to

• (1) 323
• (2) 313
• (3) 423
• (4) 413

For the system of linear equations  
2x+4y+2az=b
x+2y+3z=4 
2x-5y+2z=8 
which of the following is NOT correct ?  

• (1) It has unique solution if a = b = 6
• (2) It has unique solution if a = b = 8
• (3) It has infinitely many solution if a = 3, b = 8
• (4) It has infinitely many solutions if a = 3, b = 6

Let \(y=y_1(x)\) and \(y=y_2(x)\) be the solution curves of the differential equation \(\dfrac{dy}{dx}=y+7\) with initial conditions \(y_1(0)=0\) and \(y_2(0)=1\) respectively. Then the curves \(y=y_1(x)\) and \(y=y_2(x)\) intersect at

• (1) no point
• (2) two points
• (3) infinite number of points
• (4) one point

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then the mean of X is

• (1) \(\frac{21}{16}\)<
• (2) \(\frac{15}{16}\)
• (3) \(\frac{81}{64}\)
• (4) \(\frac{37}{16}\)

The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is

• (1) (-∞,-3)
• (2) (-6,∞)
• (3) (-∞,∞)
• (4) (-6,-3)

The integral \(∫^∞_0  \frac{6}{(e^{3x} + 6e^{2x} + 11e{x} + 6)}dx\)

• (1) ln \(32\)
• (2) ln \(27\)
• (3) ln \(\frac{32}{27}\)
• (4) ln \(\frac{27}{32}\)

Let s₁, s₂, s₃,…..,s₁₀ respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then  \(10∑^{10}_{i=1} s_i\) is

• (1) 7260
• (2) 7220
• (3) 7360
• (4) 7380

Let B =\(\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}\) , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B\(\begin{bmatrix} α \\ -2α  \\ α \end{bmatrix}\)is equal to

• (1) 0
• (2) -16
• (3) 16
• (4) 32

The fractional part of the number \(\tfrac{4^{2022}}{15}\) is equal to:

 For \(x \in \mathbb{R}\), two real‐valued functions \(f(x)\) and \(g(x)\) are such that

For differentiable function f: R-{0}⟶ R, let 3f(x)+2f(\(\frac{1}{x}\))-\(\frac{1}{x}\)-10, then |f(3)+f(\(\frac{1}{4}\))| is equal to

• (1) 7
• (2) \(\frac{29}{5}\)
• (3) \(\frac{33}{5}\)
• (4) 13

\(max\)
\({0≤x≤π}\) \(\{x−2\,\, sin. x \,\,cos+\frac{1}{3} sin\,\, 3x \}=\)

• (1) \(\frac{\pi+2-3\sqrt3}{6}\)
• (2) \(\frac{5\pi+2-3\sqrt3}{6}\)
• (3) \(\pi\)
• (4) 0

The number of symmetric matrices of order 3, with all the entries from the set \(\{0,1,2,3,4,5,6,7,8,9\}\) is :

• (1) \(10^{9}\)
• (2) \(9^{10}\)
• (3) \(10^{6}\)
• (4) \(6^{10}\)

Let the equation of plane passing through the line of intersection of the planes \(x+2y+az=2\) and \(x-y+z=3\) be \(5x-11y+bz=6a-1\). For \(c\in\mathbb{Z}\), if the distance of this plane from the point \((a,-c,c)\) is \(\dfrac{2}{\sqrt{a}}\), then \(\dfrac{a+b}{c}\) is equal to :

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

The negation of the statement \(((A\land(B\lor C)) ⇒ (A\lor B)) ⇒ A\) is

• (1) a fallacy
• (2) equivalent to \(B\lor \sim C\)
• (3) equivalent to \(\sim A\)
• (4) equivalent to \(\sim C\)

\((S1) : lim_{n→∞}\frac{1}{ n ^2} ( 2 + 4 + 6 + . . . . + 2n) = 1\)
\((S2):  lim_n→∞\frac{1}{n^{16}}( 1^15 +2^15 +3^15 + . . . . + n^15 ) = \frac{1}{16} \)

• (1) Only (S1) is true
• (2) Only (S2) is true
• (3) Both (S1) and (S2) are true
• (4) Both (S1) and (S2) are false

Let the tangent and normal at the point \((3\sqrt{3},1)\) on the ellipse \(\frac{ x^2}{36}+\frac{y^2}{4} =1\) meet the y-axis at the points A and B respectively. Let the circle C be drawn taking AB as a diameter and the line x = \(2\sqrt{5}\) intersect C at the points P and Q. If the tangents at the points P and Q on the circle intersect at the point (α,β) , then α² - β² is equal to 

• (1) 60
• (2) 61
• (3) \(\frac{304}{5}\)
• (4) \(\frac{314}{5}\)

The distance of the point ( -1,2,3) from the plane \(\overrightarrow{r}( \^i−2 \^j+3 \^k )=10\) parallel to the line of the shortest distance between the lines \(\overrightarrow{r}=(\^i=\^j)+λ(2\^i+\^k)\) and  \(\overrightarrow{r}=(2\^i=\^j)+μ(\^i+\^j+\^k)\)  is 

• (1) \(3\sqrt5\)
• (2) \(2\sqrt6\)
• (3) \(3\sqrt6\)
• (4) \(2\sqrt5\)

Let ω = z\(\bar{z}\) + k₁z + k₂iz + λ(1+i), k₁ , k₂ ∈ \(\mathbb{R}\). Let Re(ω) = 0 be the circle C of radius 1 in the first quadrant touching the line y =1 and the y-axis. If the curve Im (ω) = 0 intersects C at A and B, then 30 (AB)² is equal to _____

The number of seven-digit positive integers formed using the digits 1, 2, 3, and 4 only, and whose sum of the digits is 12, is         

• (1)

  413

If S={ x ∈ R : sin⁻¹\(( \frac{x + 1}{ √ x^ 2 + 2 x + 2} ) \)−-sin⁻¹\((\frac{x}{√x ^2+1 }) = \frac{π}{ 4} \)}
then \(∑_{x∈R }(sin( (x^2+x+5)\frac{π}{2})−cos( ( x^2+x+5)π ) ) \)is equal to ____.

Let for x∈R, S₀(x)=x,Sk(x)=Ckx+k\(∫^x_0S_{k−1}\)(t)dt, where C₀=1,C_k≡1−\(∫^1_0S_{k−1}\)(x)dx,k==1,2,3,..... Then s₂(3)+6c₃ is equal to___.

Let \(\overrightarrow{a}=3\^i+\^j −\^k\)  and \(\overrightarrow{c}=2\^i+3\^j −3\^k\)  if \(\overrightarrow{b}\) is a vector such that  \(\overrightarrow{a}=\overrightarrow{b}\times\overrightarrow{c}\) and \(|\overrightarrow{b}|=50\) , then \(|72|\overrightarrow{b}+\overrightarrow{c}|^2|\)| |  is equal to _______. 

Let α be the constant term in the binomial expansion of \( (√x−\frac{6}{x^{\frac{3}{2}}} )^n ,n≤15.\)  If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of x^-n is λα, then λ is equal to _______.

Let m1 and m2 be the slopes of the tangents drawn from the point P(4,1) to the hyperbola H : \(\frac{y^2}{25} − \frac{x^2}{16 }\)= 1. If Q is the point from which the tangents drawn to H have slopes |m₁| and |m₂| and they make positive intercepts α and β on the x-axis, then  \(\frac{( P Q ) ^2}{ α β}\) α β is equal to _____.

The sum to 20 terms of the series \(2\cdot2^{2}-3^{2}+2\cdot4^{2}-5^{2}+2\cdot6^{2}-\ldots\ldots\) is equal to __________.

Let the image of the point \(\left(\frac{5}{3},\frac{5}{3},\frac{8}{3}\right)\) in the plane x - 2y + z - 2 = 0 be P. If the distance of the point Q(6,-2,α), α > 0, from P is 13, then α is equal to___.

Select the correct graph showing the difference (d) between total energy and potential energy of a particle in linear SHM with position x of the particle (x = 0 is the mean position)

• (1)
• (2)
• (3)
• (4)

A bullet of 10 g leaves the barrel of gun with a velocity of 600 m/s. If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be :

• (1) 12 Ns
• (2) 3 Ns
• (3) 6 Ns
• (4) 36 Ns

A planet having mass \(9M_e\) and radius \(4R_e\), where \(M_e\) and \(R_e\) are mass and radius of earth respectively, has escape velocity in km/s given by: (Given escape velocity on earth \(V_e= 11.2 × 10^3 m/s\))

• (1) 67.2
• (2) 33.6
• (3) 16.8
• (4) 11.2

• (1) 27 Pa
• (2) 175 Pa
• (3) 135 Pa
• (4) 36 Pa

A vessel of depth 'd' is half filled with oil of refractive index n₁ and the other half is filled with water of refractive index n₂. The apparent depth of this vessel when viewed from above will be-

• (1) \(\frac{d\,n_1n_2}{2 (n_1+n_2)}\)
• (2) \(\frac{d\,n_1n_2}{ (n_1+n_2)}\)
• (3) \(\frac{2d(n_1+n_2)}{n_1n_2}\)
• (4) \(\frac{d(n_1+n_2)}{2n_1n_2}\)

The difference between threshold wavelengths for two metal surfaces A and B having work function \(Φ_A\)= 9 eV and \(Φ_B\) = 4.5 eV in nm is:
{Given, hc = 1242 eV nm}

• (1) 264
• (2) 540
• (3) 276
• (4) 138

The rms speed of oxygen molecule in a vessel at particular temperature is \((1+\frac{5}{x})^{\frac{1}{2}} v\), where \(v\) is the average speed of the molecule. The value of x will be : (Take \(π = \frac{22}{7}\))

• (1) 4
• (2) 8
• (3) 27
• (4) 28

The source of time varying magnetic field may be
(A) a permanent magnet
(B) an electric field changing linearly with time
(C) direct current
(D) a decelerating charge particle
(E) an antenna fed with a digital signal
Choose the correct answer from the options given below:

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

Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. If the dipole is placed in an uniform electric field of 10 dyne/C making 30º angle with \(\overrightarrow E\), the magnitude of torque acting on dipole is:

• (1) \(1.0 × 10^{-8} Nm\)
• (2) \(2.0 × 10^{-10} Nm\)
• (3) \(4.0 × 10^{-10} Nm\)
• (4) \(1.5 × 10^{-9} Nm\)

A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0, the top most point on the disc is A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

• (1) \(2R\sqrt{1+4π^2}\)
• (2) 2R
• (3) \(R\sqrt{π^2+1}\)
• (4) \(R\sqrt{π^2+4}\)

\(_{92}^{238}A\to\,_{90}^{234}B+\,_{2}^{4}D+Q\)
In the given nuclear reaction, the approximate amount of energy released will be:
[Given, mass of \(_{92}^{238}A=238.05079\times931.5\ \mathrm{MeV/c^2}\), mass of \(_{90}^{234}B=234.04363\times931.5\ \mathrm{MeV/c^2}\), mass of \(_{2}^{4}D=4.00260\times931.5\ \mathrm{MeV/c^2}\)]

• (1) \(2.12\ \mathrm{MeV}\)
• (2) \(4.25\ \mathrm{MeV}\)
• (3) \(3.82\ \mathrm{MeV}\)
• (4) \(5.9\ \mathrm{MeV}\)

Pressure for polytropic process P varies with volume V as P=av-3, find out the bulk modulus.

• (1) 3V
• (2) 3P
• (3) P
• (4) V

Two trains 'A' and 'B' of length \('l'\) and \('4l'\) are travelling into a tunnel of length 'L' in parallel tracks from opposite directions with velocities 108 km/h and 72 km/h, respectively. If train 'A' takes 35s less time than train 'B' to cross the tunnel then. length 'L' of tunnel is:
(Given L = 60 \(l\))

• (1) 1800 m
• (2) 900 m
• (3) 1200 m
• (4) 2700 m

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions:

• (1) \(∮\vec{B}.\vec{dl}=μ _0I\)
• (2) \(∮\vec{E}.\vec{dl}=-\frac{\partialϕ_B}{\partial t}\)
• (3) \(∮\vec{D}.\vec{dA}=Q\)
• (4) \(∮\vec{E}.\vec{dl}=0\)

Different combination of 3 resistors of equal resistance \(R\) are shown in the figures. The increasing order for power dissipation is:

• (1) \(P_B\lt P_C\lt P_D\lt P_A\)
• (2) \(P_C\lt P_B\lt P_A\lt P_D\)
• (3) \(P_C\lt P_D\lt P_A\lt P_B\)
• (4) \(P_A\lt P_B\lt P_C\lt P_D\)

For the following circuit and given inputs A and B, choose the correct option for output 'Y'

• (1)
• (2)
• (3)
• (4)

A body of mass \( (5 \pm 0.5) \, \text{kg} \) is moving with a velocity of \( (20 \pm 0.4) \, \text{m/s} \). Its kinetic energy will be:

• (1) (1000 ± 0.14) J
• (2) (1000 ± 140) J
• (3) (500 ± 0.14) J
• (4) (500 ± 140) J

The ratio of powers of two motors is \(\frac{3\sqrt x}{\sqrt x+1}\), that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be

• (1) 2
• (2) 4
• (3) 16
• (4) 2.4

Two bodies having the same linear momentum have a ratio of kinetic energy as 16:9. Find the ratio of masses of these bodies.

• (1) \(\frac{9}{16}\)
• (2) \(\frac{4}{3}\)
• (3) \(\frac{3}{4}\)
• (4) \(\frac{16}{9}\)

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

When a resistance of 5Ω is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of 250 mA, however when 1050Ω resistance is connected with it in series, it gives full scale deflection for 25 volt. The resistance of galvanometer is _____Ω .

A fish rising vertically upward with a uniform velocity of 8 ms^-1, observes that a bird is diving vertically downward towards the fish with the velocity of 12 ms^-1. If the refractive index of water is \(\frac{4}{3}\) , then the actual velocity of the diving bird to pick the fish, will be _______ ms^-1

radius of 2^nd orbit of He⁺ of Bohr's model is r₁ and that of fourth orbit of Be³⁺ is represented as r₂. Now the ratio\(\frac{ r_2}{r_1} \)is x: 1. The value of x is___.

If a wire of resistance R is connected across Vo, then power is Po. The wire is cut into two equal parts and connected with Vo individually, then the sum of power dissipated is P1, then \(\frac{Po}{Pi}\) is \(\frac{1}{x}\). Find the value of x.

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. \(\frac{E^a}{2b}\) j/s represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of \(\frac{b}{a}\) will be ______.
 

A particle is performing \(SHM\) having position \(x\) = \(A\; cos\; 30°\), and \(A\; = 40 \;cm\). If its kinetic energy at this position is \(200 \;J\), the value of force constant in \((kN/m)\) is?

A thin infinite sheet charge and an infinite line charge of respective charge densities +σ and +λ are placed parallel at 5 m distance from each other. Points ‘P’ and ‘Q’ are at \(\frac{3}{π} \)m and \(\frac{4}{π}\) m perpendicular distance from line charge towards sheet charge, respectively. ‘E_P’ and ‘E_Q’ are the magnitudes of resultant electric field intensities at point ‘P’ and ‘Q’, respectively. If \(\frac{E_p}{E_Q} =\frac{ 4}{a}\) for 2|σ| = |λ|. Then the value of a is _______.

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π : 22 then, the value of its angular speed will be ______ rad/s.

The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is______ mm² . (Given, y = 2.0 x 10¹¹ Nm^-2)

From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is 10^x, for R_B = 10 kΩ, and R_c = 1 kΩ. The value of x is_____.

In which of the following options the species changes from paramagnetic to diamagnetic and bond order increases.

• (1) \(N_2→N_{2}^{+}\)
• (2) \(O_2→O_{2}^{+}\)
• (3) \(NO→NO^+\)
• (4) \(O_2→O^+\)

Which of the following statements are not correct?
A. The electron gain enthalpy of F is more negative than that of Cl.
B. Ionization enthalpy decreases in a group of periodic table.
C. The electronegativity of an atom depends upon the atoms bonded to it.
D. Al₂O₃ and NO are examples of amphoteric oxides.
Choose the most appropriate answer from the options given below:

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

In the following reaction 'X' is
CH₃ (CH₂)₄ CH₃ \(\frac{A n h y . A l C l _3 }{HCL\triangle}X\) major product

• (1) CH₃ (CH₂)₄ CH₂Cl
• (2) Cl-CH₂-(CH2)₄-CH₂-Cl
• (3)
• (4)

In the reaction given below ‘A’ is

• (1)
• (2)
• (3)
• (4)

The mismatched combinations are
A. Chlorophyll - Co 
B. Water hardness - EDTA 
C. Photography - [Ag(CN)₂]- 
D. Wilkinson catalyst - [(Ph₃P)₃ RhCl]  
E. Chelating ligand-D- Penicillamine

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

ClF5 at room temperature is:

• (1) Colourless liquid with trigonal bipyramidal geometry.
• (2) Colourless liquid with square pyramidal geometry
• (3) Colourless gas with square pyramidal geometry
• (4) Colourless gas with trigonal bipyramidal geometry.

Among the following compounds, the one which shows highest dipole moment is

• (1)
• (2)
• (3)
• (4)

2-Methyl propyl bromide reacts with C₂H₅O^- and gives 'A' whereas on reaction with C₂H₅OH it gives 'B'. The mechanism followed in these reactions and the products 'A' and 'B' respectively are

• (1) S_N2. A iso-butyl ethyl ether; S_N1, B = tert- butyl ethyl ether
• (2) S_N1, A tert-butyl ethyl ether; S_N2, B = iso- butyl ethyl ether
• (3) S_N1, A = tert-butyl ethyl ether; S_N1, B = 2- butyl ethyl ether
• (4) S_N2, A = 2-butyl ethyl ether; S_N2, B = iso- butyl ethyl ether

The pair of lanthanides will exceptionally high 3^rd ionisation enthalpy than neighbouring elements:

• (1) Lu and Yb
• (2) Eu and Gb
• (3) Eu and Yb
• (4) Dy and Yb

In the reaction given below ‘B’ is:

• (1)
• (2)
• (3)
• (4)

In the above reaction. Left hand side and right hand side rings are named as 'A' and 'B' respectively. They undergo ring expansion. The correct statement for this process is:

• (1) Finally both rings will become six membered each.
• (2) Finally both rings will become five membered each.
• (3) Ring expansion can go upto seven membered rings
• (4) Only 'A' will become 6 membered.

D-(+)- Glyceraldehyde  
The two products formed in above reaction are

• (1) Two optically active products
• (2) One optically active and one meso product
• (3) wo optically inactive products
• (4) One optically inactive and one meso product.

The energy of an electron in the first Bohr orbit of hydrogen atom is \(-2.18×10^{-18}J\). Its energy in the third Bohr orbit is ____.

• (1) One third of this value
• (2) \(\frac{1}{9}\) th of this value
• (3) Three times of this value
• (4) \(\frac{1}{27}\) of this value

Which of the following free radicals helps in depletion of the ozone layer?

• (1) NO
• (2) Cl
• (3) OH
• (4) CH₃

What happens when lyophilic sol is added to lyophobic sol. prevention from coagulation precipitation emulsion electrophoresis

• (1) Prevention from coagulation
• (2) Precipitation
• (3) Emulsion
• (4) Electrophoresis

Which of the following shows an incorrect method of refining?

• (1) Zinc : Liquation
• (2) Copper : Electrolysis
• (3) Titanium : Van Arkel Method
• (4) Nickel : Mond’s Process

Incorrect statement about Borazine is:

• (1) It has banana shape bonds
• (2) It has electron delocalisation
• (3) It reacts with water
• (4) Cyclic in nature

• (1) a→ II, b→ III, c→ IV, d→I
• (2) a→ III, b→II, c→I, d→ IV
• (3) a→ III, b→ IV, c→I, d→ II
• (4) a→ IV, b-III, c→ II, d→I

Be(OH)₂ reacts with Sr(OH)₂ to yield an ionic salt. Choose the incorrect option related to this reaction from the following:

• (1) Both Sr and Be elements are present in the ionic salt.
• (2) The reaction is an example of acid - base neutralization reaction.
• (3) The element Be is present in the cationic part of the ionic salt.
• (4) Be is tetrahedrally coordinated in the ionic salt.

Given below are two statements:
Statement I: Permutit process is more efficient compared to the synthetic resin method for the softening of water.
Statement II: Synthetic resin method results in the formation of soluble sodium salts.
In the light of the above statements, choose the most appropriate answer from the options given below:

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

KMnO₄ is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute H₂SO₄. Number of water molecules produced for 2 molecules of KMnO₄ is______.

An organic compound on combustion gives 0.22 g of CO₂ and 0.126 g of H₂O. If the percentage of C in given organic compound is 40%, the percentage of H will be?

For a first-order reaction, if the value of \(t_{\frac{1}{2}}\) is T, then the value of \(t_{\frac{7}{8}}\) will be_____ T.

For the given reaction

The total number of possible products formed by tertiary carbocation of A is____.

20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown solution of H₂SO4. Also 20 mL standard solution of 0.5 M HCI containing 2 drops of phenolphthalein was titrated with calcium hydroxide the mixture showed pink colour when burette displayed the value of 35.5 mL whereas the burette showed 25.5 mL initially. The concentration of H₂SO₄ is_____M (Nearest integer)

Solution of 12 g of non-electrolyte (A) prepared by dissolving it in 1000 mL of water exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The empirical formula of A is CH₂O. The molecular mass of A is ____ g. (Nearest integer)

A metal surface of 100 cm2 area has to be coated with nickel layer of thickness 0.001mm. A current of 2A was passed through a solution of Ni (NO₃)₂ for 'x' seconds to coat the desired layer. The value of x is_____ (Nearest integer)
 (P_Ni (density of Nickel) is 10 gmL^-1, Molar mass of Nickel is 60 gmol^-1 F = 96500 C mol^-1)

A₂+B₂→2AB. \(ΔH^0_f\)= -200 kJ mol^-1 AB, A2 and B2 are diatomic molecule. If the bond enthalpies of A₂, B₂ and AB are in the ratio 1:0.5:1, then the bond enthalpy of A₂ is ___ kJmol^-1 (Nearest integer)

25.0 mL of 0.050 M Ba(NO₃)₂ is mixed with 25.0 mL of 0.020 M NaF. K_sp of BaF₂ is 0.5 x 10^-6 at 298 K. The ratio of [Ba2+] [F^-]² and K_sp is__ (Nearest integer)

A certain quantity of real gas occupies a volume of 30.15 dm3 at 100 atm and 500 K when its compressibility factor is 1.07. Its volume at 300 atm and 300K (When its compressibility factor is 1.4) is _____ x 10-4 dm3 (Nearest integer)