JEE Main 2023 11 April Shift 1 Question Paper with Solution PDF- Download Here

A rectangle is drawn by lines x=0, x=2, y=0 and y=5. Points A and B lie on coordinate axes. If line AB divides the area of rectangle in 4:1, then the locus of mid-point of AB is?

• (1) Circle
• (2) Hyperbola
• (3) Ellipse
• (4) Straight line

Let \( S = \{ M = [a_{ij}], a_{ij} \in \{0, 1, 2\}, 1 \leq i, j \leq 2 \} \) be a sample space and \( A = \{ M \in S : M \text{ is invertible} \} \) be an event. Then \( P(A) \) is equal to:

• (1) \(\frac{16}{27}\)
• (2) \(\frac{50}{81}\)
• (3) \(\frac{47}{81}\)
• (4) \(\frac{46}{81}\)

Let \(x_1, x_2, \dots, x_{100}\) be in an arithmetic progression, with \(x_1 = 2\) and their mean equal to 200. If \(y_i = (i \cdot x_i)\), then the mean of \(y_1, y_2, \dots, y_{100}\) is:

• (1) 10051.50
• (2) 10100
• (3) 10101.50
• (4) 13433

Let \( w_1 \) be the point obtained by the rotation of \( z_1 = 5 + 4i \) about the origin through a right angle in the anticlockwise direction, and \( w_2 \) be the point obtained by the rotation of \( z_2 = 3 + 5i \) about the origin through a right angle in the clockwise direction. Then the principal argument of \( w_1 - w_2 \) is equal to:

• (1) \( \pi - \tan^{-1}\left( \frac{8}{9} \right) \)
• (2) \( \pi - \tan^{-1}\left( \frac{48}{9} \right) \)
• (3) \( \pi - \tan^{-1}\left( \frac{33}{5} \right) \)
• (4) \( \pi - \tan^{-1}\left( \frac{33}{5} \right) \)

Let \(y = y(x)\) be a solution curve of the differential equation \[(1 - x^2 y)\,dx = y\,dx + x\,dy.\] If the line \(x = 1\) intersects the curve \(y = y(x)\) at \(y = 2\) and the line \(x = 2\) intersects the curve \(y = y(x)\) at \(y = \alpha\), then a value of \(\alpha\) is:

• (1) \( \frac{1 - 3e^2}{3(e^{2} - 1)} \)
• (2) \( \frac{1 - 3e^2}{2(e^{2} - 1)} \)
• (3) \( \frac{3e^2}{2(e^{2} - 1)} \)
• (4) \( \frac{3e^2}{3(e^{2} - 1)} \)

The value of the integral \[ \int_{\log_2}^{-\log_2} e^x \left( \log \left( e^x + \sqrt{1 + e^{2x}} \right) \right) dx \] is equal to:

• (1) \(\log \left( \frac{2 + \sqrt{5}}{\sqrt{5}} \right)\)
• (2) \(\log \left( \frac{2 + \sqrt{5}}{\sqrt{5}} \right) / 2\)
• (3) \(\log \left( \frac{2\sqrt{5}}{\sqrt{5}} \right)\)
• (4) \(\log \left( \frac{2 + \sqrt{5}}{\sqrt{5}} \right) / 2\)

Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is:

• (1) 36
• (2) 40
• (3) 32
• (4) 38

For any vector \( \mathbf{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} \), with \( 10 | \mathbf{a} |<1 \), \( i = 1, 2, 3 \), consider the following statements:

• (1) Only statement (A) is true
• (2) Only statement (B) is true
• (3) Both (A) and (B) are true
• (4) Neither (A) nor (B) is true

Let A be a \( 2 \times 2 \) matrix with real entries such that \( A^T = \alpha A + I \), where \( \alpha \in \mathbb{R} \setminus \{-1, 1\} \). If \( \text{det}(A^2 - A) = 4 \), then the sum of all possible values of \( \alpha \) is equal to:

• (1) 0
• (2) \( \frac{5}{2} \)
• (3) 2
• (4) \( \frac{3}{2} \)

Let f(x) = [x² - x] + [x], where x ∈ R and [t] denotes the greatest integer less than or equal to t. Then, f is:

• (1) Not continuous at \(x = 0\) and at \(x = 1\)
• (2) Continuous at \(x = 0\) and at \(x = 1\)
• (3) Continuous at \(x = 1\), but not continuous at \(x = 0\)
• (4) Continuous at \(x = 0\), but not continuous at \(x = 1\)

Consider ellipse \( E_k : \frac{x^2}{k} + \frac{y^2}{k} = 1 \), for \( k = 1, 2, \dots, 20 \). Let \( C_k \) be the circle which touches the four chords joining the end points (one on the minor axis and another on the major axis) of the ellipse \( E_k \). If \( r_k \) is the radius of the circle \( C_k \), then the value of \( \sum_{k=1}^{20} r_k^2 \) is:

• (1) 3320
• (2) 3210
• (3) 3080
• (4) 2870

Area of the region \((x, y) : x^2 + (y - 2)^2 \leq 4, \, x^2 \geq 2y\) is:

• (1) \( \frac{8}{3} \)
• (2) \( 2\pi - \frac{16}{3} \)
• (3) \( \pi - \frac{8}{3} \)
• (4) \( \pi \)

Let \( \mathbf{a} \) be a non-zero vector parallel to the line of intersection of the two planes described by \( i + j + k \) and \( -i - j - k \). If \( \theta \) is the angle between the vector \( \mathbf{a} \) and the vector \( \mathbf{b} = -2i - 2j + 2k \), and \( \left| \mathbf{a} \right| = 6 \), then ordered pair \( (\mathbf{a} \cdot \mathbf{b}) \) is equal to:

• (1) \( \left( \frac{2}{3} \sqrt{6} \right) \)
• (2) \( \left( \frac{3}{2} \sqrt{6} \right) \)
• (3) \( \left( \frac{3}{5} \sqrt{6} \right) \)
• (4) \( \left( \frac{2}{5} \sqrt{6} \right) \)

The number of triplets \( (x, y, z) \), where \( x, y, z \) are distinct non-negative integers satisfying \( x + y + z = 15 \), is:

• (1) 136
• (2) 114
• (3) 80
• (4) 92

The number of integral solutions of \( \log_2 \left( \frac{x - 7}{2x - 3} \right) \geq 0 \) is:

• (1) 5
• (2) 7
• (3) 8
• (4) 6

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then how many received medals in exactly two of three events?

• (1) 15
• (2) 9
• (3) 21
• (4) 10

Let (α, β, γ) be the image of the point P(3, 3, 5) in the plane 2x + y - 3z = 6. Then α + β + γ is equal to:

• (1) 5
• (2) 9
• (3) 10
• (4) 12

If equation of the plane that contains the point \((-2,3,5)\) and is perpendicular to each of the planes \( 2x + 4y + 5z = 8 \) and \( 3x - 2y + 3z = 5 \), is \( \alpha x + \beta y + \gamma z = 97 \), then \( \alpha + \beta + \gamma \) is:

• (1) 15
• (2) 18
• (3) 17
• (4) 16

Let \( f: [2, 4] \to \mathbb{R} \) be a differentiable function such that \( (x \log x) f'(x) + (\log x) f(x) \geq 1 \), \( x \in [2, 4] \) with \( f(2) = \frac{1}{2} \) and \( f(4) = \frac{1}{4} \). Consider the following two statements:
\( (A) \quad f(x) \geq 1 \quad \text{for all} \quad x \in [2, 4] \)
\( (B) \quad f(x) \leq \frac{1}{8} \quad \text{for all} \quad x \in [2, 4] \) Then,

• (1) Only statement (B) is true
• (2) Only statement (A) is true
• (3) Neither statement (A) nor statement (B) is true
• (4) Both the statements (A) and (B) are true

The number of elements in the set \(S = \{ \theta \in [0, 2\pi] : 3 \cos^4 \theta - 5 \cos^2 \theta - 2 \sin^2 \theta + 2 = 0 \}\) is:

• (1) 10
• (2) 9
• (3) 8
• (4) 12

Let \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 0 & 3 \\ 1 & 0 & 0 \end{bmatrix} \), where \( a, c \in \mathbb{R} \). If \( A^n = A \) and the positive value of \( a \) belongs to the interval \( (n-1, n] \), where \( n \in \mathbb{N} \), then \( n \) is equal to:

Let \( H_n : \frac{x^2}{1 + n} + \frac{y^2}{3 + n} = 1, n \in \mathbb{N} \). Let \( k \) be the smallest even value of \( n \) such that the eccentricity of \( H_n \) is a rational number. If \( l \) is the length of the latus rectum of \( H_k \), then 21 \( l \) is equal to:

For \( m, n>0 \), let \( \alpha(m,n) = \int_{0}^{1} (1 + 3t)^{n} \, dt \). If \( \alpha(10,6) = \int_{0}^{1} (1 + 3t)^{6} \, dt \) and \( \alpha(11,5) = p(14)^{5} \), then \( p \) is equal to:

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sit on the allotted seat, is:

Let a line \( l \) pass through the origin and be perpendicular to the lines \[ l_1: \vec{r}_1 = i + j + 7k + \lambda(i + 2j + 3k), \quad \lambda \in \mathbb{R} \] \[ l_2: \vec{r}_2 = -i + j + 2k + \mu(i + 2j + k), \quad \mu \in \mathbb{R} \] If \( P \) is the point of intersection of \( l_1 \) and \( l_2 \), and \( Q (a, b, \gamma) \) is the foot of perpendicular from P on \( l \), then \( (a + b + \gamma) \) is equal to:

The mean of coefficients of x, x², ....., x⁷ in the binomial expansion of (2 + x)⁹ is?

Let a and b are roots of x² – 7x – 1 = 0. The value of \(\frac{a^{21} + b^{21} + a^{17} + b^{17}}{a^{19} + b^{19}}\) is?

• (1) 29
• (2) 49
• (3) 53
• (4) 51

The number of integral terms in the expansion of (3^1/2 + 5^1/4)⁶⁸⁰ is equal to:

The number of ordered triplets of the truth values of \( p, q, r \) and such that the truth value of the statement \[ (p \lor q) \land (p \lor r) \implies (q \lor r) \text{ is True, is equal to:} \]

Let \( S = 109 + \frac{108}{5} + \frac{107}{5^2} + \frac{106}{5^3} + \cdots \). Then the value of \( (16S - (25)^{3}) \) is equal to:

Given below are two statements:
Statements 1: Astronomical unit (AU), Parsec (pc) and Light year (ly) are units for measuring astronomical distances.
Statement 2: The light of the above distances, choose the most appropriate answer from the options given below:

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

1 kg of water at 100°C is converted into steam at 100°C by boiling at atmospheric pressure. The volume of water changes from \(1.00 \times 10^{-3}\, \text{m}^3\) as a liquid to \(1.671 \times 10^{-3}\, \text{m}^3\) as steam. The change in internal energy of the system during the process will be:

• (1) + 2476 kJ
• (2) -2426 kJ
• (3) -2090 kJ
• (4) +2090 kJ

The critical angle for a denser refractive index is 45°. The speed of light in water medium is \( 3 \times 10^8 \) m/s. The speed of light in the denser medium is:

• (1) \( 2.12 \times 10^7 \, \text{m/s} \)
  
• (2) \( 5 \times 10^7 \, \text{m/s} \)
  
• (3) \( 3.12 \times 10^7 \, \text{m/s} \)
  
• (4) \( \sqrt{5} \times 10^7 \, \text{m/s} \)

On a temperature scale X, the boiling point of water is 65° X and the freezing point is 15° X. Assume that the X scale is linear. The equivalent temperature corresponding to 95° X on the Fahrenheit scale would be:

• (1) 63° F
  
• (2) 148° F
  
• (3) 48° F
  
• (4) 112° F

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are \( \rho \) and \( \frac{\rho}{3} \) respectively. The ratio of acceleration due to gravity at their surfaces (i.e. \( g_A : g_B \)) will be:

• (1) 1:16
  
• (2) 3:16
  
• (3) 3:4
  
• (4) 4:3

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed (\( V_{\text{rms}} \)) and choose the correct answer from the options given below:

• (1) \( V_{\text{rms}} \text{(mono)}>V_{\text{rms}} \text{(dia)}>V_{\text{rms}} \text{(poly)} \)
  
• (2) \( V_{\text{rms}} \text{(dia)}<V_{\text{rms}} \text{(poly)}<V_{\text{rms}} \text{(mono)} \)
  
• (3) \( V_{\text{rms}} \text{(mono)}<V_{\text{rms}} \text{(dia)}<V_{\text{rms}} \text{(poly)} \)
  
• (4) \( V_{\text{rms}} \text{(mono)} = V_{\text{rms}} \text{(dia)} = V_{\text{rms}} \text{(poly)} \)

The logic performed by the circuit shown in the figure is equivalent to:

• (1) AND gate
• (2) OR gate
• (3) NOR gate
• (4) NAND gate

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of ----- from the centre:

• (1) 6 cm
  
• (2) 4 cm
  
• (3) 2 cm
  
• (4) 1 cm

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean position to extreme position (A) is given by:

• (1) Parabola
  
• (2) Straight line
  
• (3) Kinetic energy and displacement are inversely proportional
  
• (4) Sine curve

A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is E. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is E₅. The ratio \( E_5 / E_1 \) is:

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

The electric field in an electromagnetic wave is given as \[ \vec{E} = 20 \sin \left( \omega t - \frac{x}{c} \right) \, \hat{j} \, \text{N/C} \] where \( \omega \) and \( c \) are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of \( 5 \times 10^4 \, \text{m}^3 \) will be (Given \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 / \text{Nm}^2 \)):

• (1) \( 8.85 \times 10^{-13} \, \text{J} \)
  
• (2) \( 17.7 \times 10^{-13} \, \text{J} \)
  
• (3) \( 8.85 \times 10^{-10} \, \text{J} \)
  
• (4) \( 28.5 \times 10^{-13} \, \text{J} \)

An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m/s to keep it in position. The number of bullets fired per second by the machine gun is:

• (1) 25
  
• (2) 5
  
• (3) 100
  
• (4) 50

A metallic surface is illuminated with radiation of wavelength \(\lambda\), the stopping potential is \(V_0\). If the same surface is illuminated with radiation of wavelength \(2\lambda\), the stopping potential becomes \(\frac{V_0}{4}\). The threshold wavelength for this metallic surface will be

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

The free space inside a current carrying toroid is filled with a material of susceptibility \( 2 \times 10^3 \). The percentage increase in the value of magnetic field inside the toroid will be:

• (1) 0.2%
  
• (2) 1%
  
• (3) 2%
  
• (4) 0.1%

From the v - t graph shown, the ratio of distance to displacement in 25 s of motion is:

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

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

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

As per the given graph, choose the correct representation for curve A and curve B.

• (1) \( A = X_L, B = R \)
  
• (2) \( A = X_L, B = X_C \)
  
• (3) \( A = X_C, B = R \)
  
• (4) \( A = X_C, B = X_L \)

The current sensitivity of moving coil galvanometer is increased by 25%.This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be :

• (1) +25%
• (2) -25%
• (3) -50%
• (4) Zero

Two radioactive elements A and B initially have the same number of atoms. The half-life of A is the same as the average life of B. If \( \lambda_A \) and \( \lambda_B \) are the decay constants of A and B respectively, then choose the correct relation from the given options:

• (1) \( \lambda_A = 2\lambda_B \)
  
• (2) \( \lambda_A = \lambda_B \)
  
• (3) \( \lambda_A \ln 2 = \lambda_B \)
  
• (4) \( \lambda_A = \lambda_B \ln 2 \)

A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at 4 km distance from it is \( x \times 10^{-2} \) m. The value of \( x \) is:

• (1) 125
  
• (2) 12.5
  
• (3) 1250
  
• (4) 1.25

The equation of wave is given by \( Y = 10^2 \sin 2 \pi \left( (60t - 0.5x + \frac{\pi}{4}) \right) \) where \( x \) and \( Y \) are in m and t in s. The speed of the wave is _____ km h\(^{-1}\).

As shown in the figure, a configuration of two equal point charges (q₀ = + 2 \(\mu\)C) is placed on an inclined plane. Mass of each point charge is 20g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height \( h = x \times 10^{-3} \, \text{m} \). The value of \( x \) is _____

A projectile fired at \(30^{\circ}\) to the ground is observed to be at the same height at time 3s and 5s after projection, during its flight. The speed of projection of the projectile is_____ ms\(^{-1}\).

The magnetic field B crossing normally a square metallic plate of area \( 4 \, \text{m}^2 \) is changing with time as shown in the figure. The magnitude of induced emf in the plate during \( t = 2 \, \text{s} \) to \( t = 4 \, \text{s} \) is _______ mV.

A force \( \mathbf{F} = (2 + 3x) \hat{i})\) acts on a particle in the \( x \)-direction where \( F \) is in newton and \( x \) is in meter. The work done by this force during a displacement from \( x = 0 \) to \( x = 4 \, \text{m} \) is _____ J.

A solid sphere of mass 500 g and radius 5 cm is rotated about one of its diameter with angular speed of 10 rad/s. If the moment of inertia of the sphere about its tangent is \( x \times 10^2 \) times its angular momentum about the diameter. Then the value of \( x \) will be_____

The length of a wire becomes \( l_1 \) and \( l_2 \) when 100 N and 120 N tensions are applied respectively. If \( l_1 = 11 \, \text{l}_0 \), the natural length of the wire will be \( \frac{1}{x} \, l_1 \). Here the value of \( x \) is _____

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be:

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is \( x \times 10^{15} \, \text{Hz} \). The value of \( x \) is_______

Find the current flowing in 3Ω resistor in the given circuit

• (1) 0.4A
• (2) 0.2A
• (3) 0.8A
• (4) 0.6A

Find out the correct statement from the options given below for the above 2 reactions.

• (1) Reaction (I) is of 1^st order and reaction (II) is of 2^nd order 
   
• (2) Reaction (I) and (II) both are 2^nd order 
   
• (3) Reaction (I) is of 1^st order and reaction (II) is of 1^st order 
   
• (4) Reaction (I) is of 2^nd order and reaction (II) is of 1^st order

In the above reaction 'A' and 'B' are:

• (1)

• (2)

• (3)

• (4)

The complex that dissolves in water is:

• (1) Fe₄[Fe(CN)₆]₃, Prussian Blue insoluble
  
• (2) Fe₆[Fe(CN)₆]₃
  
• (3) K₄[Co(CO)₆]
  
• (4) (NH₄)₆[As(MoO₄)₆]

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: In the photoelectric effect electrons are ejected from the metal surface as soon as the beam of light of frequency greater than threshold frequency strikes the surface.
Reason R: When the photon of any energy strikes an electron in the atom transfer of energy from the photon to the electron takes place.

• (1) Assertion A is correct but Reason R is not correct
  
• (2) Assertion A is not correct and Reason R is correct
  
• (3) Both A and R are correct and R is the correct explanation of A
  
• (4) Both A and R are correct but R is NOT the correct explanation of A

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

For elements B, C, N, Li, Be, O and F, the correct order of first ionization enthalpy is:

• (1) \(\text{B<Li<Be<C<O<N<F} \)
   
• (2) \(\text{Li<C<B<O<N<F} \)
   
• (3) \(\text{Li<C<B<O<N<F} \)
   
• (4) \(\text{Li<B<C<O<N<F}\)

25 mL of silver nitrate solution (1M) is added dropwise to 25 mL of potassium iodide (1.05 M) solution. The ions(s) present in very small quantity in the solution is/are:

• (1) NO₃⁻ only
  
• (2) Ag⁺ and I⁻ both
  
• (3) Ag⁺ only
  
• (4) I⁻ only

When a solution of mixture having two inorganic salts was treated with freshly prepared ferrous sulphate in acidic medium, a dark brown ferric ion was formed when treated with ferric chloride. It gave deep red colour which disappeared on boiling and a brown red ppt was formed. The mixture contains:

• (1) CO\(_3^{2-}\) & NO\(_3^{-}\)
  
• (2) SO\(_4^{2-}\) & CH\(_3\)COO\(^-\)
  
• (3) CH\(_3\)COO\(^-\) & FeCl\(_3\)
  
• (4) SO\(_4^{2-}\) & CH\(_3\)COO\(^-\)

Thin layer chromatography of a mixture shows the following observation:

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

\(\text{o-Phenylenediamine}\) \(\xrightarrow{HNO_3} X\text{ Major Product X is}\): 

• (1)

• (2)

• (3)

• (4)

For compound having the formula GaCl\(_3\), the correct option from the following is:

• (1) Ga forms bond with Cl in GaCl\(_3\).
  
• (2) Ga is coordinated with Cl in GaCl\(_3\).
  
• (3) Ga is more electronegative than Cl and is present as a cationic part of the salt.
  
• (4) Oxidation state of Ga in GaCl\(_3\) is +3.

The set which does not have ambidentate ligands (labeled as (i)) is:

• (1) CO\(_3^{2-}\), NO\(_3^{-}\), NCS\(^-\)
  
• (2) EDTA\(^-\), NCS\(^-\), CO\(_2^{2-}\)
  
• (3) NO\(^-\), CO\(_3^{2-}\), EDTA\(^-\)
  
• (4) CO\(_2^{2-}\), ethylene diamine, H\(_2\)O

L-isomer of tetrose X (\(C_4H_8O_4\)) gives positive Schiff’s test and has two chiral carbons. On acetylation, ‘X’ yields triacetate. ‘X’ undergoes following reactions

• (1)

• (2)

• (3)

• (4)

Which of the following complex has a possibility to exist as meridional isomer?

• (1) [Co(en)\(_3\)]Cl\(_3\)
  
• (2) [Pt(NH\(_3\))\(_2\)]Cl\(_2\)
  
• (3) [Co(en)\(_3\)]
  
• (4) [Co(NH\(_3\))\(_3\)(NO\(_3\))\(_3\)]

Arrange the following compounds in increasing order of rate of aromatic electrophilic substitution reaction:

• (1) (a)<(b)<(c)
  
• (2) (b)<(c)<(a)
  
• (3) (c)<(a)<(b)
  
• (4) (c)<(b)<(a)

The polymer X consists of linear molecules and is closely packed. It is prepared in the presence of triethylaluminium and titanium tetrachloride under low pressure. The polymer X is:

• (1) Polyacrylonitrile
  
• (2) Polyterephthalate
  
• (3) Low density polyethylene
  
• (4) High density polyethylene

Given below are two statements:
Statement I: Methane and steam passed over a heated Ni catalyst produces hydrogen gas.
Statement II: Sodium nitrate reacts with NH\(_4\)Cl to give H\(_2\)O and NaCl.

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

In the extraction process of copper, the product obtained after carrying out the reactions \[ \text{CuO} + \text{H}_2 \rightarrow \text{Cu} + \text{H}_2 \text{O} \] is called:

• (1) Reduced copper
• (2) Blister copper
   
• (3) Copper scrap
   
• (4) Copper slag

Given below are two statements:
Statement I: If BOD value is 4 ppm and dissolved oxygen is 8 ppm, it is a good quality water.
Statement II: If the concentration of zinc and nitrate is 5 ppm, then it can be used as good quality water.

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

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

A solution of sugar is obtained by mixing 200g of its 25% solution and 500g of its 40% solution (both by mass). The mass percentage of the resulting sugar solution is ______ (Nearest integer)

0.004 M K₂SO₄ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of K₂SO₄ is______ (Nearest integer)

The ratio of spin-only magnetic moment values \( \mu_{\text{eff}}[Cr(CN)_6]^{3-}/\mu_{\text{eff}}[Cr(H_2O)_6]^{3+} \) is_____

The above reaction was studied at 300 K by monitoring the concentration of FeSO₄, in which initial concentration was 10 M and after half an hour became 8.8 M. The rate of production of Fe₂(SO₄)₃ is _____ × 10⁻⁶ mol L⁻¹ s⁻¹

The number of hyperconjugation structures involved to stabilize carbocation formed in the below reaction is _______

The ratio x/y on completion of the above reaction is _____

A mixture of 1 mole of H₂O and 1 mole of CO is taken in a 10 liter container and heated to 725 K. At equilibrium, 10 M of water by mass reacts with carbon monoxide according to the equation: \[ CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g) \] The equilibrium constant \( K_c \times 10^7 \) for the reaction is ______

Solid fuel used in rocket is a mixture of Fe₂O₃ and Al (in ratio 1 : 2) the heat evolved (KJ) per gram of the mixture is ______ (Nearest integer)
Given \(\Delta H_f^{\circ}(Al_2O_3) = -1700 \, \text{KJ mol}^{-1}\)
\(\Delta H_f^{\circ}(Fe_2O_3) = -840 \, \text{KJ mol}^{-1}\)

In an electrochemical reaction of lead, at standard temperature, if \( E^{\circ}(\text{Pb}^{2+}/\text{Pb}) = m \) volt and \( E^{\circ}(\text{Pb}^{4+}/\text{Pb}^{2+}) = n \) volt, then the value of \( E^{\circ}(\text{Pb}^{4+}/\text{Pb}) \) is given by \( m - xn \). The value of \( x \) is ____

An atomic substance A of molar mass 12 g mol\(^{-1}\) has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is _____ (Nearest integer)