2024 · 4 Apr · Shift 1

90 questions · JEE Main

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2024 · 4 Apr · Shift 1

2024 · 4 Apr · Shift 1

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.Number of complexes from the following with even number of unpaired " $d$ " electrons is $[V (H_{2} O)_{6}]^{3 +}, [Cr (H_{2} O)_{6}]^{2 +}, [Fe (H_{2} O)_{6}]^{3 +}, [Ni (H_{2} O)_{6}]^{3 +}, [Cu (H_{2} O)_{6}]^{2 +}$ …
Chemistry · Coordination Compounds · MCQ
Q2.What will be the decreasing order of basic strength of the following conjugate bases? $^{-} OH, R \overline{O}, CH_{3} CO \overline{O}, Cl$
Chemistry · Basics of Organic Chemistry · MCQ
Q3.Given below are two statements : Statements I : Acidity of $α$ -hydrogens of aldehydes and ketones is responsible for Aldol reaction. Statement II : Reaction between benzaldehyde and ethanal will NOT give Cross - Aldol product. In the…
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q4.Match List I with List II : Choose the correct answer from the options given below : Includes table Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q5.Identify B and C and how are A and C related? Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q6.Identify the correct set of reagents or reaction conditions ' $X$ ' and ' $Y$ ' in the following set of transformation. Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q7.In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride is added before adding ammonium hydroxide to :
Chemistry · Salt Analysis · MCQ
Q8.The element which shows only one oxidation state other than its elemental form is :
Chemistry · D and F Block Elements · MCQ
Q9.Which of the following is the correct structure of L-Glucose?
Chemistry · Biomolecules · MCQ
Q10.Identify the product in the following reaction: Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q11.Number of molecules/ions from the following in which the central atom is involved in $sp^{3}$ hybridization is . $NO_{3}^{-}, BCl_{3}, ClO_{2}^{-}, ClO_{3}^{-}$
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q12.The correct sequence of ligands in the order of decreasing field strength is :
Chemistry · Coordination Compounds · MCQ
Q13.The Molarity (M) of an aqueous solution containing $5.85 g$ of $NaCl$ in $500 mL$ water is : (Given : Molar Mass $Na : 23$ and $Cl : 35.5 gmol^{- 1}$ )
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q14.Which among the following is incorrect statement?
Chemistry · Basics of Organic Chemistry · MCQ
Q15.One of the commonly used electrode is calomel electrode. Under which of the following categories, calomel electrode comes?
Chemistry · Electrochemistry · MCQ
Q16.The correct order of first ionization enthalpy values of the following elements is : (A) O (B) N (C) Be (D) F (E) B Choose the correct answer from the options given below :
Chemistry · Periodic Table and Periodicity · MCQ
Q17.Which of the following nitrogen containing compound does not give Lassaigne's test ?
Chemistry · Compounds Containing Nitrogen · MCQ
Q18.Which one of the following molecules has maximum dipole moment?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q19.What pressure (bar) of $H_{2}$ would be required to make emf of hydrogen electrode zero in pure water at $2 5^{\circ} C$ ?
Chemistry · Electrochemistry · MCQ
Q20.Number of elements from the following that CANNOT form compounds with valencies which match with their respective group valencies is . B, C, N, S, O, F, P, Al, Si
Chemistry · Periodic Table and Periodicity · MCQ
Q21. $2.5 g$ of a non-volatile, non-electrolyte is dissolved in $100 g$ of water at $2 5^{\circ} C$ . The solution showed a boiling point elevation by $2^{\circ} C$ . Assuming the solute concentration is…
Chemistry · Solutions · Numerical
Q22.Only $2 mL$ of $KMnO_{4}$ solution of unknown molarity is required to reach the end point of a titration of $20 mL$ of oxalic acid $(2 M)$ in acidic medium. The molarity of $KMnO_{4}$ solution…
Chemistry · Redox Reactions · Numerical
Q23.Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. Some details of the above reactions are listed below. If the overall rate constant of the above… Includes table Includes diagram
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q24.The enthalpy of formation of ethane $(C_{2} H_{6})$ from ethylene by addition of hydrogen where the bond-energies of $C - H, C - C, C = C, H - H$ are $414 kJ, 347 kJ, 615 kJ$ …
Chemistry · Thermodynamics · Numerical
Q25. $Xg$ of ethylamine is subjected to reaction with $NaNO_{2} / HCl$ followed by water; evolved dinitrogen gas which occupied $2.24 L$ volume at STP. X is $\times 1 0^{- 1} g$ …
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q26.The number of the correct reaction(s) among the following is . Includes diagram
Chemistry · Compounds Containing Nitrogen · Numerical
Q27.The de-Broglie's wavelength of an electron in the $4^{th}$ orbit is $π a_{0}$ . ( $a_{0} =$ Bohr's radius)
Chemistry · Structure of Atom · Numerical
Q28.The number of different chain isomers for C $_{7}$ H $_{16}$ is .
Chemistry · Basics of Organic Chemistry · Numerical
Q29.Number of molecules/species from the following having one unpaired electron is . $O_{2}, O_{2}^{- 1}, NO, CN^{- 1}, O_{2}^{2 -}$
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q30.Consider the following reaction $MnO_{2} + KOH + O_{2} \to A + H_{2} O .$ Product ' $A$ ' in neutral or acidic medium disproportionate to give products ' $B$ ' and…
Chemistry · D and F Block Elements · Numerical
Q31. $Let f (x) = {- 2, x - 2, - 2 \leq x \leq 0 0 < x \leq 2 and h (x) = f (∣ x ∣) + ∣ f (x) ∣ . Then \int_{- 2}^{2} h (x) d x is equal to:$ …
Mathematics · Definite Integration · MCQ
Q32.One of the points of intersection of the curves $y = 1 + 3 x - 2 x^{2}$ and $y = \frac{1}{x}$ is $(\frac{1}{2}, 2)$ . Let the area of the region enclosed by these curves be $\frac{1}{24} (l 5 + m) - n lo g_{e} (1 + 5)$ …
Mathematics · Area Under the Curves · MCQ
Q33.Let $α \in (0, \infty)$ and $A = 110201 α 12$ . If $det (adj (2 A - A^{T}) \cdot adj (A - 2 A^{T})) = 2^{8}$ …
Mathematics · Matrices and Determinants · MCQ
Q34.There are 5 points $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}$ on the side $A B$ , excluding $A$ and $B$ , of a triangle $A B C$ . Similarly there are 6 points $P_{6}, P_{7}, \dots, P_{11}$ on the side $BC$ and 7 points $P_{12}, P_{13}, \dots, P_{18}$ …
Mathematics · Permutations and Combinations · MCQ
Q35.A square is inscribed in the circle $x^{2} + y^{2} - 10 x - 6 y + 30 = 0$ . One side of this square is parallel to $y = x + 3$ . If $(x_{i}, y_{i})$ are the vertices of the square, then $Σ (x_{i}^{2} + y_{i}^{2})$ is equal to:
Mathematics · Circle · MCQ
Q36.Let $α, β \in R$ . Let the mean and the variance of 6 observations $- 3, 4, 7, - 6, α, β$ be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is :
Mathematics · Statistics · MCQ
Q37.Let $f (x) = x^{5} + 2 e^{x /4}$ for all $x \in R$ . Consider a function $g (x)$ such that $(g \circ f) (x) = x$ for all $x \in R$ . Then the value of $8 g^{'} (2)$ is :
Mathematics · Differentiation · MCQ
Q38.Let a unit vector which makes an angle of $6 0^{\circ}$ with $2 \hat{i} + 2 \hat{j} - \hat{k}$ and an angle of $4 5^{\circ}$ with $\hat{i} - \hat{k}$ be $C$ . Then $C + (- \frac{1}{2} \hat{i} + \frac{1}{3 2} \hat{j} - \frac{2}{3} \hat{k})$ …
Mathematics · Vector Algebra · MCQ
Q39.If the domain of the function $sin^{- 1} (\frac{3 x - 22}{2 x - 19}) + lo g_{e} (\frac{3 x ^{2} - 8 x + 5}{x ^{2} - 3 x - 10})$ is $(α, β]$ , then $3 α + 10 β$ is equal to:
Mathematics · Inverse Trigonometric Functions · MCQ
Q40.Let the point, on the line passing through the points $P (1, - 2, 3)$ and $Q (5, - 4, 7)$ , farther from the origin and at a distance of 9 units from the point $P$ , be $(α, β, γ)$ . Then $α^{2} + β^{2} + γ^{2}$ is equal to :
Mathematics · 3D Geometry · MCQ
Q41.The vertices of a triangle are $A (- 1, 3), B (- 2, 2)$ and $C (3, - 1)$ . A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q42.Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from…
Mathematics · Probability · MCQ
Q43.If the solution $y = y (x)$ of the differential equation $(x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 2) d y - (2 x^{2} + 2 x + 3) d x = 0$ satisfies $y (- 1) = - \frac{π}{4}$ , then $y (0)$ is equal to :
Mathematics · Differential Equations · MCQ
Q44.Let the first three terms 2, p and q, with $q e q 2$ , of a G.P. be respectively the $7^{th}, 8^{th}$ and $1 3^{th}$ terms of an A.P. If the $5^{th}$ term of the G.P. is the $n^{th}$ term of the…
Mathematics · Sequences and Series · MCQ
Q45.The sum of all rational terms in the expansion of $(2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q46.If 2 and 6 are the roots of the equation $a x^{2} + b x + 1 = 0$ , then the quadratic equation, whose roots are $\frac{1}{2 a + b}$ and $\frac{1}{6 a + b}$ , is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q47.Let the sum of the maximum and the minimum values of the function $f (x) = \frac{2 x ^{2} - 3 x + 8}{2 x ^{2} + 3 x + 8}$ be $\frac{m}{n}$ , where $gcd (m, n) = 1$ . Then $m + n$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q48.If the system of equations $x + (2 sin α) y + (2 cos α) z = 0 x + (cos α) y + (sin α) z = 0 x + (sin α) y - (cos α) z = 0$ has a non-trivial solution,…
Mathematics · Matrices and Determinants · MCQ
Q49.Let $α$ and $β$ be the sum and the product of all the non-zero solutions of the equation $(\overset{z}{ˉ})^{2} + ∣ z ∣ = 0, z \in C$ . Then $4 (α^{2} + β^{2})$ is equal to :
Mathematics · Complex Numbers · MCQ
Q50.Let $f : R \to R$ be a function given by $f (x) = {\frac{1 - c o s 2 x}{x ^{2}}, x 0$ where $α, β \in R$ . If $f$ is continuous at $x = 0$ , then $α^{2} + β^{2}$ is equal…
Mathematics · Limits Continuity and Differentiability · MCQ
Q51.Let the solution $y = y (x)$ of the differential equation $\frac{d y}{d x} - y = 1 + 4 sin x$ satisfy $y (π) = 1$ . Then $y (\frac{π}{2}) + 10$ is equal to .
Mathematics · Differential Equations · Numerical
Q52.If the shortest distance between the lines $\frac{x + 2}{2} = \frac{y + 3}{3} = \frac{z - 5}{4}$ and $\frac{x - 3}{1} = \frac{y - 2}{- 3} = \frac{z + 4}{2}$ is $\frac{38}{3 5} k$ , and $0 \int k [x^{2}] d x = α - α$ …
Mathematics · Definite Integration · Numerical
Q53.Let $A$ be a square matrix of order 2 such that $∣ A ∣ = 2$ and the sum of its diagonal elements is $-$ 3 . If the points $(x, y)$ satisfying $A^{2} + x A + y I = O$ lie on a hyperbola, whose transverse axis is…
Mathematics · Matrices and Determinants · Numerical
Q54.If $lim_{x \to 1} \frac{( 5 x + 1 ) ^{1/3} - ( x + 5 ) ^{1/3}}{( 2 x + 3 ) ^{1/2} - ( x + 4 ) ^{1/2}} = \frac{m 5}{n ( 2 n ) ^{2/3}}$ , where $gcd (m, n) = 1$ , then $8 m + 12 n$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q55.Let $A$ be a $3 \times 3$ matrix of non-negative real elements such that $A 111 = 3111$ . Then the maximum value of $det (A)$ …
Mathematics · Matrices and Determinants · Numerical
Q56.If $\int_{0}^{\frac{π}{4}} \frac{s i n ^{2} x}{1 + s i n x c o s x} d x = \frac{1}{a} lo g_{e} (\frac{a}{3}) + \frac{π}{b 3}$ , where $a, b \in N$ , then $a + b$ …
Mathematics · Definite Integration · Numerical
Q57.In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied…
Mathematics · Sets and Relations · Numerical
Q58.Let the length of the focal chord PQ of the parabola $y^{2} = 12 x$ be 15 units. If the distance of $PQ$ from the origin is $p$ , then $10 p^{2}$ is equal to .
Mathematics · Parabola · Numerical
Q59.Let $ABC$ be a triangle of area $152$ and the vectors $AB = \hat{i} + 2 \hat{j} - 7 \hat{k}, BC = a \hat{i} + b \hat{j} + c \hat{k}$ and $AC = 6 \hat{i} + d \hat{j} - 2 \hat{k}, d > 0$ …
Mathematics · Vector Algebra · Numerical
Q60.Let $a = 1 + \frac{^{2} C _{2}}{3 !} + \frac{^{3} C _{2}}{4 !} + \frac{^{4} C _{2}}{5 !} + ...., b = 1 + \frac{^{1} C _{0} + ^{1} C _{1}}{1 !} + \frac{^{2} C _{0} + ^{2} C _{1} + ^{2} C _{2}}{2 !} + \frac{^{3} C _{0} + ^{3} C _{1} + ^{3} C _{2} + ^{3} C _{3}}{3 !} + ....$ …
Mathematics · Binomial Theorem · Numerical
Q61.An infinitely long positively charged straight thread has a linear charge density $λ Cm^{- 1}$ . An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the…
Physics · Electrostatics · MCQ
Q62.An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :
Physics · Magnetics · MCQ
Q63.A metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :
Physics · Gravitation · MCQ
Q64.An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $25 D$ . Focal length of each of the convex lens is:
Physics · Geometrical Optics · MCQ
Q65.Given below are two statements : Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P_{1} - P_{2} = ρ g (h_{2} - h_{1})$ . Statement II :… Includes diagram
Physics · Properties of Matter · MCQ
Q66.If a rubber ball falls from a height $h$ and rebounds upto the height of $h /2$ . The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :
Physics · Work Power and Energy · MCQ
Q67.In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to : A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and…
Physics · Alternating Current · MCQ
Q68.Which of the following nuclear fragments corresponding to nuclear fission between neutron $(_{0}^{1} n)$ and uranium isotope $(_{92}^{235} U)$ is correct :
Physics · Atoms and Nuclei · MCQ
Q69.A body travels $102.5 m$ in $n^{th}$ second and $115.0 m$ in $(n + 2)^{th}$ second. The acceleration is :
Physics · Motion in A Straight Line · MCQ
Q70.In an experiment to measure focal length ( $f$ ) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are $Δ u$ and $Δ v$ , respectively. The error in the…
Physics · Geometrical Optics · MCQ
Q71.The co-ordinates of a particle moving in $x$ - $y$ plane are given by : $x = 2 + 4 t, y = 3 t + 8 t^{2}$ . The motion of the particle is :
Physics · Motion in A Plane · MCQ
Q72.The equation of stationary wave is : $y = 2 a sin (\frac{2 π nt}{λ}) cos (\frac{2 π x}{λ}) .$ Which of the following is NOT correct :
Physics · Units and Measurements · MCQ
Q73.Which figure shows the correct variation of applied potential difference (V) with photoelectric current (I) at two different intensities of light $(I_{1} < I_{2})$ of same wavelengths :
Physics · Dual Nature of Radiation · MCQ
Q74.P-T diagram of an ideal gas having three different densities $ρ_{1}, ρ_{2}, ρ_{3}$ (in three different cases) is shown in the figure. Which of the following is correct : Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q75.The electric field in an electromagnetic wave is given by $E = \hat{i} 40 cos ω (t - z / c) NC^{- 1}$ . The magnetic field induction of this wave is (in SI unit) :
Physics · Electromagnetic Waves · MCQ
Q76.The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8Ω$ and $10Ω$ respectively. After inserting in a hot bath of temperature $40 0^{\circ} C$ , the resistance…
Physics · Heat and Thermodynamics · MCQ
Q77.The value of net resistance of the network as shown in the given figure is : Includes diagram
Physics · Electronic Devices · MCQ
Q78.A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $t$ . Which of the following curve best describes acceleration of the block with time :
Physics · Laws of Motion · MCQ
Q79.To measure the internal resistance of a battery, potentiometer is used. For $R = 10Ω$ , the balance point is observed at $l = 500 cm$ and for $R = 1Ω$ the balance point is observed at $l = 400 cm$ . The…
Physics · Current Electricity · MCQ
Q80.On celcius scale the temperature of body increases by $4 0^{\circ} C$ . The increase in temperature on Fahrenheit scale is :
Physics · Heat and Thermodynamics · MCQ
Q81.A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$ . The sphere and the cylinder reaches upto maximum heights $h_{1}$ and $h_{2}$ respectively, above the initial level. The ratio $h_{1} : h_{2}$ …
Physics · Rotational Motion · Numerical
Q82.An infinite plane sheet of charge having uniform surface charge density $+ σ_{s} C / m^{2}$ is placed on $x$ - $y$ plane. Another infinitely long line charge having uniform linear charge density $+ λ_{e} C / m$ …
Physics · Electrostatics · Numerical
Q83.A hydrogen atom changes its state from $n = 3$ to $n = 2$ . Due to recoil, the percentage change in the wave length of emitted light is approximately $1 \times 1 0^{- n}$ . The value of $n$ is . [Given Rhc $= 13.6 eV, hc = 1242 eV nm, h = 6.6 \times 1 0^{- 34} J s$ …
Physics · Atoms and Nuclei · Numerical
Q84.A soap bubble is blown to a diameter of $7 cm$ . $36960 erg$ of work is done in blowing it further. If surface tension of soap solution is 40 dyne/ $cm$ then the new radius is cm Take $(π = \frac{22}{7})$ …
Physics · Properties of Matter · Numerical
Q85.An elastic spring under tension of $3 N$ has a length $a$ . Its length is $b$ under tension $2 N$ . For its length $(3 a - 2 b)$ , the value of tension will be N.
Physics · Properties of Matter · Numerical
Q86.The magnetic field existing in a region is given by $B = 0.2 (1 + 2 x) \hat{k}$ . A square loop of edge $50 cm$ carrying 0.5 A current is placed in $x$ - $y$ plane with its edges parallel to the $x$ - $y$ axes, as shown in figure.… Includes diagram
Physics · Magnetics · Numerical
Q87.Two forces $\overline{F}_{1}$ and $\overline{F}_{2}$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle…
Physics · Laws of Motion · Numerical
Q88.A alternating current at any instant is given by $i = [6 + 56 sin (100 π t + π /3)]$ A. The $r m s$ value of the current is A.
Physics · Alternating Current · Numerical
Q89.Twelve wires each having resistance $2Ω$ are joined to form a cube. A battery of $6 V$ emf is joined across point $a$ and $c$ . The voltage difference between $e$ and $f$ is V. Includes diagram
Physics · Current Electricity · Numerical
Q90.Two wavelengths $λ_{1}$ and $λ_{2}$ are used in Young's double slit experiment. $λ_{1} = 450 nm$ and $λ_{2} = 650 nm$ . The minimum order of fringe produced by $λ_{2}$ which overlaps with the fringe…
Physics · Wave Optics · Numerical