JEE Main 2021 February 25 Shift 1 Question Paper is available here with solutions PDF and detailed solutions for every question. NTA conducted the first shift on February 25, 2021, from 9:00 AM to 12:00 PM. The JEE Main 2021 Paper 1 (B.E./B.Tech) question paper includes the following:
- 90 questions in a 3-hour CBT Mode: 30 each from Mathematics, Physics and Chemistry (75 to be attempted)
- Section A: 20 multiple choice questions (MCQs) per subject, all compulsory, 4 marks each
- Section B: 10 numerical value questions per subject, any 5 to be attempted, 4 marks each
- Marking: +4 for a correct answer, -1 for an incorrect MCQ, 0 for an unattempted question; no negative marking for numerical value questions
- Maximum marks: 300 (100 per subject)
JEE Main 2021 February 25 Shift 1 Question Paper with Solution PDF
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JEE Main 2021 February 25 Shift 1 Questions with Solutions
Mathematics - Section A (Q1 - Q20)
When a missile is fired from a ship, the probability that it is intercepted is 1/3 and the probability that the missile hits the target, given that it is not intercepted, is 3/4. If three missiles are fired independently from the ship, then the probability that all three hit the target, is :
The equation of the line through the point (0, 1, 2) and perpendicular to the line (x-1)/2 = (y+1)/3 = (z-1)/(-2) is:
The value of \( \displaystyle \int_{-1}^{1} x^2 e^{x^3} \, dx \), where \( [t] \) denotes the greatest integer \( \leq t \), is :
The integer k, for which the inequality x² - 2(3k-1)x + 8k² - 7>0 is valid for every x in ℝ, is :
The total number of positive integral solutions (x, y, z) such that xyz=24 is :
If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is (x² - 4x + y + 8)/(x - 2), then this curve also passes through the point :
Let f,g : ℕ → ℕ such that f(n+1) = f(n) + f(1) ∀ n ∈ ℕ and g be any arbitrary function. Which of the following statements is NOT true?
Let the lines \( (2 - i)z = (2 + i)\bar{z} \) and \( (2 + i)z + (i - 2)\bar{z} - 4i = 0 \), (here \( i^2 = -1 \)) be normal to a circle \( C \). If the line \( iz + \bar{z} + 1 + i = 0 \) is tangent to this circle \( C \), then its radius is :
\( \displaystyle \lim_{n \to \infty} \frac{1 + \frac{1}{2} + \cdots + \frac{1}{n}}{n} \) is equal to :
Let α be the angle between the lines whose direction cosines satisfy the equations l + m - n = 0 and l² + m² - n² = 0. Then the value of sin⁴α + cos⁴α is :
The value of the integral ∫ sinθ sin2θ (sin⁶θ + sin⁴θ + sin²θ) / √(2sin⁴θ + 3sin²θ + 6) dθ is: (where c is a constant of integration)
The coefficients a, b and c of the quadratic equation, ax² + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :
The image of the point (3, 5) in the line x - y + 1 = 0, lies on :
All possible values of θ ∈ [0, 2π] for which sin 2θ + tan 2θ>0 lie in :
Angle of depression from tower top to A is 30°. After 20 seconds at B, it is 45°. Time taken from B to reach the base is :
The statement A → (B → A) is equivalent to :
A tangent is drawn to the parabola y² = 6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT lie on it ?
If Rolle's theorem holds for the function f(x) = x³ - ax² + bx - 4, x ∈ [1, 2] with f'(4/3) = 0, then ordered pair (a, b) is equal to :
If the curves, x²/a + y²/b = 1 and x²/c + y²/d = 1 intersect each other at an angle of 90°, then which of the following relations is TRUE?
If \( 0 < \theta, \phi < \frac{\pi}{2} \), \( x = \sum_{n=0}^{\infty} \cos^{2n} \theta \), \( y = \sum_{n=0}^{\infty} \sin^{2n} \phi \) and \( z = \sum_{n=0}^{\infty} \cos^{2n} \theta \cdot \sin^{2n} \phi \) then :
Mathematics - Section B (Q21 - Q30)
The locus of the point of intersection of the lines (√3)kx + ky - 4√3 = 0 and √3 x - y - 4(√3)k = 0 is a conic, whose eccentricity is _________
The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A⁴ is equal to __________
The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is _________
If \( A = \begin{bmatrix} 0 & -\tan\left(\frac{\theta}{2}\right) \\ \tan\left(\frac{\theta}{2}\right) & 0 \end{bmatrix} \) and \( (I_2 + A)(I_2 - A)^{-1} = \begin{bmatrix} a & -b \\ b & a \end{bmatrix} \), then \( 13(a^2 + b^2) \) is equal to __________.
Let A₁, A₂, A₃, … be squares such that for each n ≥ 1, the length of the side of \(A_n\) equals the length of diagonal of \(A_{n+1}\). If the length of \(A_1\) is 12 cm, then the smallest value of n for which area of \(A_n\) is less than one, is __________.
If the system of equations \(kx + y + 2z = 1\), \(3x - y - 2z = 2\), \(-2x - 2y - 4z = 3\) has infinitely many solutions, then k is equal to ________
The number of points, at which the function f(x) = |2x + 1| - 3|x + 2| + |x² + x - 2|, x ∈ ℝ is not differentiable, is ________
Let \(\vec{a} = \hat{i} + 2\hat{j} - \hat{k}\), \(\vec{b} = \hat{i} - \hat{j}\) and \(\vec{c} = \hat{i} - \hat{j} - \hat{k}\). If \(\vec{r}\) is a vector such that \(\vec{r} \times \vec{a} = \vec{c} \times \vec{a}\) and \(\vec{r} \cdot \vec{b} = 0\), then \(\vec{r} \cdot \vec{a}\) is equal to __________.
Let \( f(x) \) be a polynomial of degree 6 in \( x \), in which the coefficient of \( x^6 \) is unity and it has extrema at \( x = -1 \) and \( x = 1 \). If \( \displaystyle \lim_{x \to 0} \frac{f(x)}{x^3} = 1 \), then \( 5 \cdot f(2) \) is equal to __________.
Let \( A = \begin{bmatrix} x & y & z \\ y & z & x \\ z & x & y \end{bmatrix} \), where \( x, y \) and \( z \) are real numbers such that \( x + y + z > 0 \) and \( xyz = 2 \). If \( A^2 = I_3 \), then the value of \( x^3 + y^3 + z^3 \) is __________.
Physics - Section A (Q31 - Q50)
A proton, a deuteron and an \(\alpha\) particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is __________ and their speed is __________, in the ratio.
A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force \(F_1\). Now a spherical cavity of radius (R/2) is made in the sphere (as shown in figure) and the force becomes \(F_2\). The value of \(F_1 : F_2\) is : 
An \(\alpha\) particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are \(\lambda_\alpha\) and \(\lambda_p\) respectively. The ratio \(\lambda_p/\lambda_\alpha\) is :
The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser. (Note: Based on typical values for this specific question where \(V_L = V_C\) or resonance is implied). 
Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is _____________
Match List - I with List - II :
List - I: (a) h (Planck's constant), (b) E (kinetic energy), (c) V (electric potential), (d) P (linear momentum)
List - II: (i) [M L T\(^{-1}\)], (ii) [M L\(^2\) T\(^{-1}\)], (iii) [M L\(^2\) T\(^{-2}\)], (iv) [M L\(^2\) T\(^{-3}\) I\(^{-1}\)]
Choose the correct answer from the options given below :
Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If \(T_A\) and \(T_B\) are the time periods of A and B respectively then the value of \(T_B - T_A\) is : [\(R_e = 6400\) km, \(M_e = 6 \times 10^{24}\) kg]
Two coherent light sources having intensity in the ratio \(2x\) produce an interference pattern. The ratio \((I_{max} - I_{min}) / (I_{max} + I_{min})\) will be :
An engine of a train, moving with uniform acceleration, passes the signal-post with velocity \(u\) and the last compartment with velocity \(v\). The velocity with which middle point of the train passes the signal post is :
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : When a rod lying freely is heated, no thermal stress is developed in it.
Reason R : On heating, the length of the rod increases.
In the light of the above statements, choose the correct answer :
The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72nd division on circular scale coincides with the reference line. The radius of the wire is :
If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :
A diatomic gas, having \(C_p = \frac{7}{2}R\) and \(C_v = \frac{5}{2}R\), is heated at constant pressure. The ratio \(dU : dQ : dW\):
A 5V battery is connected across the points X and Y. Assume D1 and D2 to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X and -ve to point Y. 
A correct experiment is performed to measure the speed of sound in air using a resonance column tube of diameter 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound is given as 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column tube, when the first resonance occurs is :
In an octagon ABCDEFGH of equal side, what is the sum of \(\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF} + \vec{AG} + \vec{AH}\), if \(\vec{AO} = 2i + 3j - 4k\)?
The current (i) at time t=0 and t=∞ respectively for the given circuit is : 
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass.
Reason R : The product of their mass and radius must be same. \(M_1R_1 = M_2R_2\)
In the light of the above statements, choose the most appropriate answer from the options given below :
Two radioactive substances X and Y originally have \(N_1\) and \(N_2\) nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio \(N_1/N_2\) will be equal to :
Given below are two statements : Statement I : A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz. Statement II : The side band frequencies are 1002 kHz and 998 kHz. In the light of the above statements, choose the correct answer :
Physics - Section B (Q51 - Q60)
A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ________ m/s. (Take g=10 m/s²)
A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R= gas constant) is \(\frac{x}{3R}\). Value of x is ________.
The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is _________ cm.
A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t=0, then the energy stored in the coil after 4 s is _________ J.
The potential energy (U) of a diatomic molecule is \(U = \frac{\alpha}{r^{10}} - \frac{\beta}{r^5} - 3\). The equilibrium distance between two atoms will be \(\left( \frac{2\alpha}{\beta} \right)^{\frac{a}{b}}\) , where a = _________.
The electric field is \(\vec{E} = \left( \frac{3}{5} E_0 \hat{i} + \frac{4}{5} E_0 \hat{j} \right)\). The ratio of flux through surface of area 0.2 m² (parallel to y-z plane) to that of area 0.3 m² (parallel to x-z plane) is a : b, where a = _________.
In a thermodynamical process, \(P = kV^3\). The work done when the temperature changes from 100°C to 300°C will be ________ nR.
512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ______ V.
A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 µF is used in the resonant circuit. The self inductance of coil necessary for resonance is _________ x10\^{-8} H.
In the given potentiometer circuit, for key K₁ closed, null point is at J₁. For K₂ closed, null point is at J₂. The value of \(\frac{E_1}{E_2}\) is \(\frac{a}{b}\), where a= _________ . (Note: Using standard balancing lengths \(l_1\) and \(l_2\) typically provided in this diagram, e.g., \(l_1=4\)m, \(l_2=2\)m).
Chemistry - Section A (Q61 - Q80)
The solubility of AgCN in a buffer solution of pH=3 is x. The value of x is : [Assume : No cyano complex is formed ; \(K_{sp}(\text{AgCN}) = 2.2 \times 10^{-16}\) and \(K_a(\text{HCN}) = 6.2 \times 10^{-10}\)]
Which one of the following reactions will not form acetaldehyde ?
The plots of radial distribution functions for various orbitals of hydrogen atom against r are given below: The correct plot for 3s orbital is : 
Identify A in the given chemical reaction. CH\(_2\)=CH-CH(CH\(_3\))-CH\(_3\) \(\xrightarrow{Mo_2O_3, 773 K, 10-20 atm}\) A (major product) 
Given below are two statements : Statement I : CeO\(_2\) can be used for oxidation of aldehydes and ketones. Statement II : Aqueous solution of EuSO\(_4\) is a strong reducing agent. In the light of the above statements, choose the correct answer :
Compound(s) which will liberate carbon dioxide with sodium bicarbonate (\(NaHCO_3\)) solution is/are : A = Urea, B = Benzoic acid, C = p-Nitrophenol
Which of the glycosidic linkage between galactose and glucose is present in lactose ?
According to molecular orbital theory, the species among the following that does not exist is :
Complete combustion of 1.80 g of an oxygen containing compound (C\(_x\)H\(_y\)O\(_z\)) gave 2.64 g of CO\(_2\) and 1.08 g of H\(_2\)O. The percentage of oxygen in the organic compound is :
The hybridization and magnetic nature of [Mn(CN)\(_6\)]\(^{4-}\) and [Fe(CN)\(_6\)]\(^{3-}\), respectively are :
The major product of the following chemical reaction is :
In which of the following pairs, the outer most electronic configuration will be the same ?
Which of the following reaction/s will not give p-aminoazobenzene ? 
Given below are two statements : Statement I : An allotrope of oxygen is an important intermediate in the formation of reducing smog. Statement II : Gases such as oxides of nitrogen and sulphur present in troposphere contribute to the formation of photochemical smog. In the light of the above statements, choose the correct answer from the options given below :
In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption \((x/m)\) is directly proportional to \(P^x\). The value of x is :
Which statement is correct ?
The correct statement about B\(_2\)H\(_6\) is :
Ellingham diagram is a graphical representation of :
Which of the following equation depicts the oxidizing nature of \(H_2O_2\)?
Chemistry - Section B (Q81 - Q90)
Using the provided information in paper chromatography
The calculated \(R_f\) value of A is __________ \(\times 10^{-1}\).
The reaction of cyanamide, NH\(_2\)CN(s), with oxygen was run in a bomb calorimeter and \(\Delta U\) was found to be -742.24 kJ mol\(^{-1}\). The magnitude of \(\Delta H_{298}\) for the reaction NH\(_2\)CN(s) + 3/2 O\(_2\)(g) \(\rightarrow\) N\(_2\)(g) + CO\(_2\)(g) + H\(_2\)O(l) is _________ kJ.
The ionization enthalpy of Na\(^+\) formation is 495.8, electron gain enthalpy of Br is -325.0, and lattice enthalpy of NaBr is -728.4 kJ mol\(^{-1}\). The energy for the formation of NaBr ionic solid is (-) __________ \(\times 10^{-1}\) kJ mol\(^{-1}\).
0.4 g mixture of NaOH, Na\(_2\)CO\(_3\) and some inert impurities was first titrated with N/10 HCl using phenolphthalein as an indicator, 17.5 mL of HCl was required at the end point. After this methyl orange was added and titrated. 1.5 mL of same HCl was required for the next end point. The weight percentage of Na\(_2\)CO\(_3\) in the mixture is _________
In basic medium CrO\(_4^{2-}\) oxidises S\(_2\)O\(_3^{2-}\) to form SO\(_4^{2-}\) and itself changes into Cr(OH)\(_4^-\). The volume of 0.154 M CrO\(_4^{2-}\) required to react with 40 mL of 0.25 M S\(_2\)O\(_3^{2-}\) is _________ mL.
Consider the reaction: CH\(\equiv\)CH \(\xrightarrow{\text{Red hot Fe}}\) (1) \(\xrightarrow{CO, HCl, AlCl_3}\) (2). The number of sp\(^2\) hybridized carbon atom(s) in the product is __________.
1 molal aqueous solution of an electrolyte A\(_3\)B\(_3\) is 60% ionised. The boiling point of the solution at 1 atm is __________ K. [Given \(K_b\) (H\(_2\)O) = 0.52 K kg mol\(^{-1}\), \(T_b\) pure water = 373.15 K]
Among the following, the number of halide(s) which is/are inert to hydrolysis is ___________: (A) BF\(_3\), (B) SiCl\(_4\), (C) PCl\(_5\), (D) SF\(_6\)
For aA + bB \(\rightarrow\) cC + dD, the plot of log k vs 1/T is given below :
The temperature at which the rate constant is \(10^{-4}\) s\(^{-1}\) is __________ K. [Rate constant is \(10^{-5}\) s\(^{-1}\) at 500 K.]
A car tyre is filled with nitrogen gas at 35 psi at 27\(^\circ\)C. It will burst if pressure exceeds 40 psi. The temperature in \(^\circ\)C at which the car tyre will burst is ___________
JEE Main 2021 Exam Pattern and Marking Scheme
| Particulars | Details |
|---|---|
| Exam Mode | Online (Computer-Based Test) |
| Paper | B.E./B.Tech (Paper 1) |
| Duration | 3 hours (180 minutes) |
| Type of Questions | Multiple Choice Questions (MCQs) + Numerical Value Questions |
| Subjects | Mathematics, Physics, Chemistry |
| Total Questions | 90 questions (75 to be attempted) |
| Total Marks | 300 marks |
| Marking Scheme | +4 for correct answer & -1 for incorrect MCQ; no negative marking for Numerical Value Questions |
JEE Main 2021 February 25 Shift 1 Difficulty Level
JEE Main 2021 B.E./B.Tech Question Paper - February 25, 2021- Forenoon Session was rated to be of an above moderate level of difficulty. This was mostly due to the high difficulty level of the Mathematics section. The Physics and Chemistry sections were rated moderate and easy respectively.
JEE Main 2021 B.E./B.Tech Question Paper February 25 (FN): Difficulty Level
JEE Main 2021 B.E./B.Tech February 25 Forenoon Session was conducted between 9.00 AM to 12.00 Noon and was reported as above moderate in terms of overall difficulty level.
- Mathematics was the toughest section of the exam and contributed solely to the above-average difficulty level status of the paper.
- High weightage was given to Integral Calculus, Vectors, and Matrices & Determinants in the Mathematics Section. Questions framed from these topics were mostly lengthy and difficult to solve. Check JEE Main Mathematics Syllabus
- The Physics section was moderate in difficulty and the questions based on Electrodynamics & Mechanics were dominant in the paper. Check JEE Main Physics Syllabus
- The Chemistry section was the easiest and the majority of questions were asked from Organic Chemistry and Physical Chemistry. Check JEE Main Chemistry Syllabus
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