The area of the region enclosed by the curves $y=x^2-4 x+4$ and $y^2=16-8 x$ is :
- ✓$\frac{8}{3}$
- B$\frac{4}{3}$
- C5
- D8
Answer: A.
View full solution →Question types
JEE Main 22-Jan-2025 Paper - Shift 2 question types
75 questions across 6 question groups — pick any mix to generate a JEE paper with step-by-step answer keys.
75
Questions
6
Question groups
5
Question types
01
SECTION - A [MATHS - MCQ]
20 Q→02SECTION - B [MATHS - NUMERIC]
5 Q→03SECTION - A [PHYSICS MCQ]
20 Q→04SECTION - B [PHYSICS - NUMERIC]
5 Q→05SECTION - A [CHEMISTY - MCQ]
20 Q→06SECTION - B [CHEMISTY - NUMERIC]
5 Q→Sample Questions
JEE Main 22-Jan-2025 Paper - Shift 2 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Let the curve $z(1+i)+\bar{z}(1-i)=4, z \in C$, divide the region $|z-3| \leq 1$ into two parts of areas $\alpha$ and $\beta$. Then $|\alpha-\beta|$ equals :
- A$1+\frac{\pi}{2}$
- B$1+\frac{\pi}{3}$
- C$1+\frac{\pi}{4}$
- D$1+\frac{\pi}{6}$
The sum of all values of $\theta \in[0,2 \pi]$ satisfying $2 \sin ^2 \theta=\cos 2 \theta$ and $2 \cos ^2 \theta=3 \sin \theta$ is
- A$\frac{\pi}{2}$
- B$4 \pi$
- C$\frac{5 \pi}{6}$
- ✓$\pi$
Answer: D.
View full solution →If $A$ and $B$ are two events such that $P(A \cap B)=0.1$, and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12 x^2-7 x+1=0$, then the value of $\frac{ P (\overline{ A } \cup \overline{ B })}{ P (\overline{ A } \cap \overline{ B })}$ is:
- A$\frac{5}{3}$
- B$\frac{4}{3}$
- ✓$\frac{9}{4}$
- D$\frac{7}{4}$
Answer: C.
View full solution →Let $E : \frac{ x ^2}{ a ^2}+\frac{ y ^2}{b^2}=1, a > b$ and $H : \frac{ x ^2}{A^2}-\frac{ y ^2}{B^2}=1$. Let the distance between the foci of E and the foci of H be $2 \sqrt{3}$. If $a - A =2$, and the ratio of the eccentricities of E and H is $\frac{1}{3}$, then the sum of the lengths of their latus rectums is equal to:
- A10
- B7
- ✓8
- D9
Answer: C.
View full solution →Let $A =\{1,2,3\}$. The number of relations on A, containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is _________.
View full solution →If $\sum_{ r =1}^{30} \frac{ r ^2\left({ }^{30} C _{ r }\right)^2}{{ }^{30} C _{r-1}}=\alpha \times 2^{29}$, then $\alpha$ is equal to _________ .
View full solution →Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then $(Q R)^2$ is equal to _________.
View full solution →Let $A (6,8), B (10 \cos \alpha,-10 \quad \sin \alpha)$ and C $(-10 \sin \alpha, 10 \cos \alpha)$, be the vertices of a triangle.If $L(a, 9)$ and $G(h, k)$ be its orthocenter and centroid respectively, then $(5 a-3 h+6 k+100 \sin 2 \alpha)$ is equal to _________.
View full solution →Let $y=f(x)$ be the solution of the differential equation $\frac{d y}{d x}+\frac{x y}{x^2-1}=\frac{x^6+4 x}{\sqrt{1-x^2}}$, -1 < x < 1 such that $f(0)=0$. If $6 \int_{-1 / 2}^{1 / 2} f(x) d x=2 \pi-\alpha$ then $\alpha^2$ is equal to _____________.
View full solution →A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is $10 m / s$. The ratio of its kinetic energies at point B and C is :
(Take acceleration due to gravity as $10 m / s ^2$ )
(Take acceleration due to gravity as $10 m / s ^2$ )
- A$\frac{2+\sqrt{3}}{3}$
- B$\frac{2+\sqrt{2}}{3}$
- ✓$\frac{3+\sqrt{3}}{2}$
- D$\frac{3-\sqrt{2}}{2}$
Answer: C.
View full solution →Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure ( P ), temperature ( T ) and density ( $\rho$ ) are intensive variables.
(C) Volume (V), temperature (T) and density ( $\rho$ ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.
Choose the correct answer from the points given below :
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure ( P ), temperature ( T ) and density ( $\rho$ ) are intensive variables.
(C) Volume (V), temperature (T) and density ( $\rho$ ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.
Choose the correct answer from the points given below :
- A(C) and (D) only
- B(D) and (A) only
- ✓(A) and (B) only
- D(B) and (C) only
Answer: C.
View full solution →
The tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is $2 m / s$, then velocity of water leaving the point (2) will be :
- A$2 m / s$
- B$4 m / s$
- C$6 m / s$
- ✓$8 m / s$
Answer: D.
View full solution →A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]
- A94.8 nm
- B68.7 nm
- C137.5 nm
- D275 nm
A ball of mass 100 g is projected with velocity $20 m / s$ at $60^{\circ}$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is :
- A20 J
- ✓15 J
- Czero
- D5 J
Answer: B.
View full solution →
A tube of length 1m is filled completely with an ideal liquid of mass 2M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is $\sqrt{\frac{F}{\alpha M}}$ in SI unit. The value of $\alpha$ is _________.
View full solution →A parallel plate capacitor of area $A =16 cm^2$ and separation between the plates 10 cm, is charged by a DC current. Consider a hypothetical plane surface of area $A_0=3.2 cm^2$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6 A . At the same instant the displacement current through $A _0$ is _________ mA .
View full solution →Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5 A and 4 A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point $P$ at a distance of 4 cm from wire Y is $x \times 10^{-5} T$. The value of $x$ is _________. Take permeability of free space as $\mu_0=4 \pi \times 10^{-7}$ SI units.
View full solution →A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 \times 10^5 ms^{-1}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x \times 10^4 N / C$. the value of x is _____________.
Take the mass of the proton $=1.6 \times 10^{-27} kg$.
View full solution →Take the mass of the proton $=1.6 \times 10^{-27} kg$.
The alkane from below having two secondary hydrogens is :
- A4-Ethyl-3,4-dimethyloctane
- B2,2,4,4-Tetramethylhexane
- ✓2,2,3,3-Tetramethylpentane
- D2,2,4,5-Tetramethylheptane
Answer: C.
View full solution →Given below are two statements :
Statement (I) : Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode.
Statement (II) : The rate of corrosion is more in alkaline medium than in acidic medium.
In the light of the above statements, choose the correct answer from the options given below :
Statement (I) : Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode.
Statement (II) : The rate of corrosion is more in alkaline medium than in acidic medium.
In the light of the above statements, choose the correct answer from the options given below :
- ABoth Statement I and Statement II are false
- BStatement I is false but Statement II is true
- CBoth Statement I and Statement II are true
- ✓Statement I is true but Statement II is false
Answer: D.
View full solution →
Residue (A) + HCl (dil.) $\rightarrow$ Compound (B)
Structure of residue (A) and compound (B)
Formed respectively is :
- A
[A] [B] (1) 
- B
[A] [B] (2) 
- C
[A] [B] (3) 
- ✓
[A] [B] (4) 
Answer: D.
View full solution →Identify the homoleptic complex(es) that is/are low spin.
(A) $\left[ Fe ( CN )_5 NO \right]^{2-}$
(B) $\left[ CoF _6\right]^{3-}$
(C) $\left[ Fe ( CN )_6\right]^{+}$
(D) $\left[ Co \left( NH _3\right)_6\right]^{3+}$
(E) $\left[ Cr \left( H _2 O \right)_6\right]^{2+}$
Choose the correct answer from the options given below :
(A) $\left[ Fe ( CN )_5 NO \right]^{2-}$
(B) $\left[ CoF _6\right]^{3-}$
(C) $\left[ Fe ( CN )_6\right]^{+}$
(D) $\left[ Co \left( NH _3\right)_6\right]^{3+}$
(E) $\left[ Cr \left( H _2 O \right)_6\right]^{2+}$
Choose the correct answer from the options given below :
- A(B) and (E) only
- B(A) and (C) only
- ✓(C) and (D) only
- D(C) only
Answer: C.
View full solution →Given below are two statement :
Statement (I) : Nitrogen, sulphur, halogen and phosphorus present in an organic compound are detected by Lassaigne's Test.
Statement (II) : The elements present in the compound are converted from covalent form into ionic form by fusing the compound with Magnesium in Lassaigne's test.
In the light of the above statements, choose the correct answer from the options given below :
Statement (I) : Nitrogen, sulphur, halogen and phosphorus present in an organic compound are detected by Lassaigne's Test.
Statement (II) : The elements present in the compound are converted from covalent form into ionic form by fusing the compound with Magnesium in Lassaigne's test.
In the light of the above statements, choose the correct answer from the options given below :
- ABoth Statement I and Statement II are true
- BBoth Statement I and Statement II are false
- ✓Statement I is true but Statement II is false
- DStatement I is false but Statement II is true
Answer: C.
View full solution →20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is _________$\times 10^{-2} M$. (Nearest integer).
View full solution →Consider the following cases of standard enthalpy of reaction $\left(\Delta H _{ r }^{ o }\right.$ in $\left.kJ mol ^{-1}\right)$$
\begin{array}{l}
C_2 H_6(g)+\frac{7}{2} O_2(g) \rightarrow 2 CO_2(g)+3 H_2 O(\ell) \Delta H_1^{\circ}=-1550 \\
C \text { (graphite })+O_2(g) \rightarrow CO_2(g) \Delta H_2^{o}=-393.5 \\
H_2(g)+\frac{1}{2} O_2(g) \rightarrow H_2 O(\ell) \Delta H_3^{o}=-286
\end{array}
$
The magnitude of $\Delta H _{ fC _2 H _6(g)}^o$ is _________ $kJ mol ^{-1}$ (Nearest integer).
View full solution →\begin{array}{l}
C_2 H_6(g)+\frac{7}{2} O_2(g) \rightarrow 2 CO_2(g)+3 H_2 O(\ell) \Delta H_1^{\circ}=-1550 \\
C \text { (graphite })+O_2(g) \rightarrow CO_2(g) \Delta H_2^{o}=-393.5 \\
H_2(g)+\frac{1}{2} O_2(g) \rightarrow H_2 O(\ell) \Delta H_3^{o}=-286
\end{array}
$
The magnitude of $\Delta H _{ fC _2 H _6(g)}^o$ is _________ $kJ mol ^{-1}$ (Nearest integer).
The complex of $Ni ^{2+}$ ion and dimethyl glyoxime contains _________ number of Hydrogen $( H )$ atoms.
View full solution →Niobium $( Nb )$ and ruthenium $( Ru )$ have "x" and "y" number of electrons in their respective $4 d$ orbitals. The value of $x+y$ is _________
View full solution →The compound with molecular formula $C _6 H _6$, which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has _________$\pi$ electrons.
View full solution →Generate a JEE Main 22-Jan-2025 Paper - Shift 2 paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.