2008 · Shift 0

88 questions · JEE Main

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JEE Main
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2008 · Shift 0

2008 · Shift 0

88 questions · JEE Main

Chemistry29 questions Mathematics27 questions Physics32 questions

Q1.In the following sequence of reactions, the alkene affords the compound ‘B’ $C H_{3} - C H = C H - C H_{3}$ $O_{3}$ A $Z n ⟶ H_{2} O$ B The compound B is
Chemistry · Hydrocarbons · MCQ
Q2.Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains
Chemistry · Hydrocarbons · MCQ
Q3.The hydrocarbon which can react with sodium in liquid ammonia is
Chemistry · Hydrocarbons · MCQ
Q4.The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is
Chemistry · Basics of Organic Chemistry · MCQ
Q5.For the following three reactions a, b and c, equilibrium constants are given: a. $C O$ (g) + $H_{2} O$ (g) $⇋$ $C O_{2}$ (g) + $H_{2}$ (g) ; K1 b. $C H_{4}$ (g) + $H_{2} O$ (g) $⇋$ $C O$ (g) + 3 $H_{2}$ (g) ; K2 c. $C H_{4}$ …
Chemistry · Chemical Equilibrium · MCQ
Q6.The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be
Chemistry · Ionic Equilibrium · MCQ
Q7.Four species are listed below i. $H C O_{3}^{-}$ ii. $H_{3} O^{+}$ iii. $H S O_{4}^{-}$ iv. $H S O_{3} F$ Which one of the following is the correct sequence of their acid strength?
Chemistry · Ionic Equilibrium · MCQ
Q8.The equilibrium constants KP1 and KP2 for the reactions X $⇋$ 2Y and Z $⇋$ P + Q, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total…
Chemistry · Chemical Equilibrium · MCQ
Q9.Standard entropy of $X_{2}$ , $Y_{2}$ and $X Y_{3}$ are 60, 40 and 50 JK−1 mol−1 , respectively. For the reaction, $\frac{1}{2} X_{2}$ + $\frac{3}{2} Y_{2} \to$ $X Y_{3}$ , $Δ H$ = -30 kJ, to be at equilibrium, the temperature will be :
Chemistry · Thermodynamics · MCQ
Q10.Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below: $\frac{1}{2} C l_{2} (g)$ $\frac{1}{2} Δ_{d i ss} H^{Θ}$ $C l (g) Δ_{e g} H^{Θ} C l^{-} (g) Δ_{H y d} H^{Θ} C l^{-} (a q)$ …
Chemistry · Thermodynamics · MCQ
Q11.Amount of oxalic acid present in a solution can be determined by its titration with $K M n O_{4}$ solution in the presence of $H_{2} S O_{4} .$ The titration gives unsatisfactory result when carried out in the presence of $H C l,$ because $H C l$ :
Chemistry · D and F Block Elements · MCQ
Q12.The treatment of $C H_{3} M g X$ with $C H_{3} C \equiv C - H$ produces
Chemistry · Hydrocarbons · MCQ
Q13.The absolute configuration of Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q14.The electrophile, $E^{\oplus}$ attacks the benzene ring to generate the intermediate $σ -$ complex. Of the following, which $σ -$ complex is lowest energy?
Chemistry · Basics of Organic Chemistry · MCQ
Q15. $α$ -D-(+)-glucose and $β$ -D-(+)-glucose are
Chemistry · Biomolecules · MCQ
Q16.Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives
Chemistry · Alcohols Phenols and Ethers · MCQ
Q17.The organic chloro compound, which shows complete stereochemical inversion during a SN2 reaction, is
Chemistry · Haloalkanes and Haloarenes · MCQ
Q18.The coordination number and the oxidation state of the element ‘E’ in the complex $[E (e n)_{2} (C_{2} O_{4})]$ $N O_{2}$ (where (en) is ethylene diamine) are, respectively,
Chemistry · Coordination Compounds · MCQ
Q19.In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $Δ_{o}$ be the highest?
Chemistry · Coordination Compounds · MCQ
Q20.Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being :
Chemistry · D and F Block Elements · MCQ
Q21.Which one of the following is the correct statement?
Chemistry · P Block Elements · MCQ
Q22.For a reaction $\frac{1}{2} A \to 2 B$ rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the expression
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q23.Given $E_{C r^{3 +} / C r}^{o}$ = -0.72 V; $E_{F e^{2 +} / F e}^{o}$ = -0.42V, The potential for the cell Cr | $C r^{3 +}$ (0.1M) || $F e^{2 +}$ (0.01 M) | Fe is
Chemistry · Electrochemistry · MCQ
Q24.The vapour pressure of water at 20oC is 17.5 mm Hg. If 18 g of glucose ( $C_{6} H_{12} O_{6}$ ) is added to 178.2 g of water at 20oC, the vapour pressure of the resulting solution will be
Chemistry · Solutions · MCQ
Q25.At 80oC, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture solution of ‘A’ and ‘B’ boils at 80oC and 1 atm pressure, the amount of ‘A’ in the mixture is (1 atm = 760 mm Hg)
Chemistry · Solutions · MCQ
Q26.Which of the following pair of species have the same bond order?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q27.The bond dissociation energy of B - F in $B F_{3}$ is 646 kJ mol-1 whereas that of C - F in $C F_{4}$ is 515 kj mol-1. The correct reason for higher B - F bond dissociation energy as compared to that of C - F is
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q28.The ionization enthalpy of hydrogen atom is 1.312 × 106 J mol−1. The energy required to excite the electron in the atom from n = 1 to n = 2 is
Chemistry · Structure of Atom · MCQ
Q29.Which one of the following constitutes a group of the isoelectronic species?
Chemistry · Structure of Atom · MCQ
Q30.The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
Mathematics · Statistics · MCQ
Q31.Let $f (x) = {(x - 1) sin \frac{1}{x - 1} 0 i f x e 1 i f x = 1$ Then which one of the following is true?
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Let $f : N \to Y$ be a function defined as f(x) = 4x + 3 where Y = { y $\in$ N, y = 4x + 3 for some x $\in$ N }. Show that f is invertible and its inverse is
Mathematics · Functions · MCQ
Q33.A die is thrown. Let $A$ be the event that the number obtained is greater than $3.$ Let $B$ be the event that the number obtained is less than $5.$ Then $P (A \cup B)$ is :
Mathematics · Probability · MCQ
Q34.It is given that the events $A$ and $B$ are such that $P (A) = \frac{1}{4}, P (A ∣ B) = \frac{1}{2}$ and $P (B ∣ A) = \frac{2}{3} .$ Then $P (B)$ is :
Mathematics · Probability · MCQ
Q35.The solution of the differential equation $\frac{d y}{d x} = \frac{x + y}{x}$ satisfying the condition $y (1) = 1$ is :
Mathematics · Differential Equations · MCQ
Q36.The area of the plane region bounded by the curves $x + 2 y^{2} = 0$ and $x + 3 y^{2} = 1$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q37.The value of $2 \int \frac{s i n x d x}{s i n ( x - \frac{π}{4} )}$ is
Mathematics · Indefinite Integrals · MCQ
Q38.Let $a, b, c$ be any real numbers. Suppose that there are real numbers $x, y, z$ not all zero such that $x = cy + b z, y = a z + c x,$ and $z = b x + a y .$ Then $a^{2} + b^{2} + c^{2} + 2 ab c$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q39.Let $A$ be $a 2 \times 2$ matrix with real entries. Let $I$ be the $2 \times 2$ identity matrix. Denote by tr $(A)$ , the sum of diagonal entries of $a$ . Assume that $a^{2} = I .$ Statement-1 : If $A e I$ and $A e - I$ , then det $(A) = - 1$ …
Mathematics · Matrices and Determinants · MCQ
Q40.Suppose the cubic $x^{3} - p x + q$ has three distinct real roots where $p > 0$ and $q > 0$ . Then which one of the following holds?
Mathematics · Application of Derivatives · MCQ
Q41.How many real solutions does the equation $x^{7} + 14 x^{5} + 16 x^{3} + 30 x - 560 = 0$ have?
Mathematics · Application of Derivatives · MCQ
Q42.The value of $co t (cos e c^{- 1} \frac{5}{3} + tan^{- 1} \frac{2}{3})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q43.The non-zero vectors are $a, b$ and $c$ are related by $a = 8 b$ and $c = - 7 b .$ Then the angle between $a$ …
Mathematics · Vector Algebra · MCQ
Q44.A parabola has the origin as its focus and the line $x = 2$ as the directrix. Then the vertex of the parabola is at :
Mathematics · Parabola · MCQ
Q45.A focus of an ellipse is at the origin. The directrix is the line $x = 4$ and the eccentricity is $\frac{1}{2}$ . Then the length of the semi-major axis is :
Mathematics · Ellipse · MCQ
Q46.The point diametrically opposite to the point $P (1, 0)$ on the circle $x^{2} + y^{2} + 2 x + 4 y - 3 = 0$ is :
Mathematics · Circle · MCQ
Q47.The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q48.The first two terms of a geometric progression add up to 12. the sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is
Mathematics · Sequences and Series · MCQ
Q49.How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
Mathematics · Permutations and Combinations · MCQ
Q50.In a shop there are five types of ice-cream available. A child buys six ice-cream. Statement - 1: The number of different ways the child can buy the six ice-cream is $^{10} C_{5}$ . Statement - 2: The number of different ways the child can…
Mathematics · Permutations and Combinations · MCQ
Q51.The quadratic equations $x^{2} - 6 x + a = 0$ and $x^{2} - c x + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q52.STATEMENT - 1 : For every natural number $n \geq 2, \frac{1}{1} + \frac{1}{2} + ........ + \frac{1}{n} > n .$ STATEMENT - 2 : For every natural number $n \geq 2,$ , $n (n + 1) < n + 1.$
Mathematics · Quadratic Equation and Inequalities · MCQ
Q53.Let R be the real line. Consider the following subsets of the plane $R \times R$ : $S = {(x, y) : y = x + 1 an d 0 < x < 2} T = {(x, y) : x - y i s an int e g er}$ , Which one…
Mathematics · Sets and Relations · MCQ
Q54.The conjugate of a complex number is $\frac{1}{i - 1}$ then that complex number is :
Mathematics · Complex Numbers · MCQ
Q55.If the straight lines $\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and $\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2}$ intersects at a point, then the integer…
Mathematics · 3D Geometry · MCQ
Q56.The line passing through the points $(5, 1, a)$ and $(3, b, 1)$ crosses the $y z$ -plane at the point $(0, \frac{17}{2}, - \frac{- 13}{2})$ . Then
Mathematics · 3D Geometry · MCQ
Q57.In the circuit below, $A$ and $B$ represent two inputs and $C$ represents the output. The circuit represents Includes diagram
Physics · Electronic Devices · MCQ
Q58.Suppose an electron is attracted towards the origin by a force $\frac{k}{r}$ where $^{'} k^{'}$ is a constant and $^{'} r^{'}$ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $n^{t h}$ orbital…
Physics · Atoms and Nuclei · MCQ
Q59.This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two statements: Statement- 1: Energy is released when heavy nuclei undergo fission or light nuclei…
Physics · Atoms and Nuclei · MCQ
Q60.A student measures the focal length of a convex lens by putting an object pin at a distance $^{'} u^{'}$ from the lens and measuring the distance $^{'} v^{'}$ of the image pin. The graph between $^{'} u^{'}$ and $^{'} v^{'}$ plotted by the student should look like
Physics · Geometrical Optics · MCQ
Q61.In an experiment, electrons are made to pass through a narrow slit of width $^{'} d^{'}$ comparable to their de Broglie wavelength. They are detected on a screen at a distance $^{'} D^{'}$ from the slit (see figure). Which of the following graphs can be… Includes diagram
Physics · Dual Nature of Radiation · MCQ
Q62.An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by
Physics · Units and Measurements · MCQ
Q63.Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 c m^{2}$ and length $= 20 c m$ . If one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is $(μ_{0} = 4 π \times 10^{- 7} T m A^{- 1})$ …
Physics · Electromagnetic Induction · MCQ
Q64.A horizontal overhead powerline is at height of $4 m$ from the ground and carries a current of $100 A$ from east to west. The magnetic field directly below it on the ground is $(μ_{0} = 4 π \times 10^{- 7} T m A^{- 1})$ …
Physics · Magnetics · MCQ
Q65.Relative permittivity and permeability of a material $ε_{r}$ and $μ_{r},$ respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
Physics · Magnetic Properties of Matter · MCQ
Q66.A $5 V$ battery with internal resistance $2Ω$ and a $2 V$ battery with internal resistance $1Ω$ are connected to a $10Ω$ resistor as shown in the figure. The current in the $10Ω$ resistor is Includes diagram
Physics · Current Electricity · MCQ
Q67.Consider a block of conducting material of resistivity $^{'} ρ^{'}$ shown in the figure. Current $^{'} I^{'}$ enters at $^{'} A^{'}$ and leaves from $^{'} D^{'}$ . We apply superposition principle to find voltage $^{'} Δ V^{'}$ developed between $^{'} B^{'}$ and $^{'} C^{'}$ . The… Includes diagram
Physics · Current Electricity · MCQ
Q68.A body is at rest at $x = 0.$ At $t = 0,$ it starts moving in the positive $x$ -direction with a constant acceleration. At the same instant another body passes through $x = 0$ moving in the positive $x$ direction with a constant speed. The…
Physics · Motion in A Straight Line · MCQ
Q69.Consider a block of conducting material of resistivity $^{'} ρ^{'}$ shown in the figure. Current $^{'} I^{'}$ enters at $^{'} A^{'}$ and leaves from $^{'} D^{'}$ . We apply superposition principle to find voltage $^{'} Δ V^{'}$ developed between $^{'} B^{'}$ and $^{'} C^{'}$ . The… Includes diagram
Physics · Current Electricity · MCQ
Q70.A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11 k m s^{- 1},$ the escape velocity from the surface of the planet…
Physics · Gravitation · MCQ
Q71.Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resister $R$ is Includes diagram
Physics · Current Electricity · MCQ
Q72.A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E (r)$ produced by the shell in the range $0 \leq r < \infty,$ where $r$ is…
Physics · Electrostatics · MCQ
Q73.A parallel plate capacitor with air between the plates has capacitance of $9 pF .$ The separation between its plates is $^{'} d^{'} .$ The space between the plates has dielectric constant $k_{1} = 3$ and thickness $\frac{d}{3}$ while the other one has…
Physics · Capacitor · MCQ
Q74.A wave travelling along the $x$ -axis is described by the equation $y (x, t) = 0.005$ $cos (α x - β t) .$ If the wavelength and the time period of the wave are $0.08 m$ and $2.0 s$ , respectively, then $α$ and $β$ …
Physics · Waves · MCQ
Q75.While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $18 c m$ during winter. Repeating the same experiment during summer, she measures the column…
Physics · Waves · MCQ
Q76.A jar is filled with two non-mixing liquids $1$ and $2$ having densities $ρ_{1}$ and $ρ_{2}$ respectively. A solid ball, made of a material of density $ρ_{3}$ , is dropped in the jar. It comes to equilibrium in the position… Includes diagram
Physics · Properties of Matter · MCQ
Q77.A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?
Physics · Properties of Matter · MCQ
Q78.A thin rod of length $^{'} L^{'}$ is lying along the $x$ -axis with its ends at $x = 0$ and $x = L$ . Its linear density (mass/length) varies with $x$ as $k (\frac{x}{L})^{n},$ where $n$ can be zero or any positive number. If the…
Physics · Center of Mass · MCQ
Q79.An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_{1}$ and contains ideal gas at pressure $P_{1}$ and temperature $T_{1}$ . The other chamber has volume $V_{2}$ and…
Physics · Heat and Thermodynamics · MCQ
Q80.The speed of sound in oxygen $(O_{2})$ at a certain temperature is $460 m s^{- 1} .$ The speed of sound in helium $(H e)$ at the same temperature will be (assume both gases to be ideal)
Physics · Heat and Thermodynamics · MCQ
Q81.A spherical solid ball of volume $V$ is made of a material of density $ρ_{1}$ . It is falling through a liquid of density $ρ_{2} (ρ_{2} < ρ_{1})$ . Assume that the liquid applies a viscous force on the ball…
Physics · Properties of Matter · MCQ
Q82.This question contains Statement - $1$ and Statement - $2$ . of the four choices given after the statements, choose the one that best describes the two statements. Statement - $1$ : For a mass $M$ kept at the center of a cube of side $^{'} a^{'}$ ,…
Physics · Gravitation · MCQ
Q83.Consider a uniform square plate of side $^{'} a^{'}$ and mass $^{'} m^{'}$ . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
Physics · Rotational Motion · MCQ
Q84.An athlete in the olympic games covers a distance of $100 m$ in $10 s .$ His kinetic energy can be estimated to be in the range
Physics · Work Power and Energy · MCQ
Q85.A block of mass $0.50 k g$ is moving with a speed of $2.00 m s^{- 1}$ on a smooth surface. It strike another mass of $1.0 k g$ and then they move together as a single body. The energy loss during the collision is :
Physics · Center of Mass · MCQ
Q86.Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while…
Physics · Units and Measurements · MCQ
Q87.A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recorded as
Physics · Units and Measurements · MCQ
Q88.The dimension of magnetic field in M, L, T and C (coulomb) is given as
Physics · Units and Measurements · MCQ

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2008 · Shift 0

88 questions · JEE Main

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Papers
2008 · Shift 0

2008 · Shift 0

88 questions · JEE Main

Chemistry29 questions Mathematics27 questions Physics32 questions

Q1.In the following sequence of reactions, the alkene affords the compound ‘B’ $C H_{3} - C H = C H - C H_{3}$ $O_{3}$ A $Z n ⟶ H_{2} O$ B The compound B is
Chemistry · Hydrocarbons · MCQ
Q2.Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains
Chemistry · Hydrocarbons · MCQ
Q3.The hydrocarbon which can react with sodium in liquid ammonia is
Chemistry · Hydrocarbons · MCQ
Q4.The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is
Chemistry · Basics of Organic Chemistry · MCQ
Q5.For the following three reactions a, b and c, equilibrium constants are given: a. $C O$ (g) + $H_{2} O$ (g) $⇋$ $C O_{2}$ (g) + $H_{2}$ (g) ; K1 b. $C H_{4}$ (g) + $H_{2} O$ (g) $⇋$ $C O$ (g) + 3 $H_{2}$ (g) ; K2 c. $C H_{4}$ …
Chemistry · Chemical Equilibrium · MCQ
Q6.The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be
Chemistry · Ionic Equilibrium · MCQ
Q7.Four species are listed below i. $H C O_{3}^{-}$ ii. $H_{3} O^{+}$ iii. $H S O_{4}^{-}$ iv. $H S O_{3} F$ Which one of the following is the correct sequence of their acid strength?
Chemistry · Ionic Equilibrium · MCQ
Q8.The equilibrium constants KP1 and KP2 for the reactions X $⇋$ 2Y and Z $⇋$ P + Q, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total…
Chemistry · Chemical Equilibrium · MCQ
Q9.Standard entropy of $X_{2}$ , $Y_{2}$ and $X Y_{3}$ are 60, 40 and 50 JK−1 mol−1 , respectively. For the reaction, $\frac{1}{2} X_{2}$ + $\frac{3}{2} Y_{2} \to$ $X Y_{3}$ , $Δ H$ = -30 kJ, to be at equilibrium, the temperature will be :
Chemistry · Thermodynamics · MCQ
Q10.Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below: $\frac{1}{2} C l_{2} (g)$ $\frac{1}{2} Δ_{d i ss} H^{Θ}$ $C l (g) Δ_{e g} H^{Θ} C l^{-} (g) Δ_{H y d} H^{Θ} C l^{-} (a q)$ …
Chemistry · Thermodynamics · MCQ
Q11.Amount of oxalic acid present in a solution can be determined by its titration with $K M n O_{4}$ solution in the presence of $H_{2} S O_{4} .$ The titration gives unsatisfactory result when carried out in the presence of $H C l,$ because $H C l$ :
Chemistry · D and F Block Elements · MCQ
Q12.The treatment of $C H_{3} M g X$ with $C H_{3} C \equiv C - H$ produces
Chemistry · Hydrocarbons · MCQ
Q13.The absolute configuration of Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q14.The electrophile, $E^{\oplus}$ attacks the benzene ring to generate the intermediate $σ -$ complex. Of the following, which $σ -$ complex is lowest energy?
Chemistry · Basics of Organic Chemistry · MCQ
Q15. $α$ -D-(+)-glucose and $β$ -D-(+)-glucose are
Chemistry · Biomolecules · MCQ
Q16.Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives
Chemistry · Alcohols Phenols and Ethers · MCQ
Q17.The organic chloro compound, which shows complete stereochemical inversion during a SN2 reaction, is
Chemistry · Haloalkanes and Haloarenes · MCQ
Q18.The coordination number and the oxidation state of the element ‘E’ in the complex $[E (e n)_{2} (C_{2} O_{4})]$ $N O_{2}$ (where (en) is ethylene diamine) are, respectively,
Chemistry · Coordination Compounds · MCQ
Q19.In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $Δ_{o}$ be the highest?
Chemistry · Coordination Compounds · MCQ
Q20.Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being :
Chemistry · D and F Block Elements · MCQ
Q21.Which one of the following is the correct statement?
Chemistry · P Block Elements · MCQ
Q22.For a reaction $\frac{1}{2} A \to 2 B$ rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the expression
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q23.Given $E_{C r^{3 +} / C r}^{o}$ = -0.72 V; $E_{F e^{2 +} / F e}^{o}$ = -0.42V, The potential for the cell Cr | $C r^{3 +}$ (0.1M) || $F e^{2 +}$ (0.01 M) | Fe is
Chemistry · Electrochemistry · MCQ
Q24.The vapour pressure of water at 20oC is 17.5 mm Hg. If 18 g of glucose ( $C_{6} H_{12} O_{6}$ ) is added to 178.2 g of water at 20oC, the vapour pressure of the resulting solution will be
Chemistry · Solutions · MCQ
Q25.At 80oC, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture solution of ‘A’ and ‘B’ boils at 80oC and 1 atm pressure, the amount of ‘A’ in the mixture is (1 atm = 760 mm Hg)
Chemistry · Solutions · MCQ
Q26.Which of the following pair of species have the same bond order?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q27.The bond dissociation energy of B - F in $B F_{3}$ is 646 kJ mol-1 whereas that of C - F in $C F_{4}$ is 515 kj mol-1. The correct reason for higher B - F bond dissociation energy as compared to that of C - F is
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q28.The ionization enthalpy of hydrogen atom is 1.312 × 106 J mol−1. The energy required to excite the electron in the atom from n = 1 to n = 2 is
Chemistry · Structure of Atom · MCQ
Q29.Which one of the following constitutes a group of the isoelectronic species?
Chemistry · Structure of Atom · MCQ
Q30.The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
Mathematics · Statistics · MCQ
Q31.Let $f (x) = {(x - 1) sin \frac{1}{x - 1} 0 i f x e 1 i f x = 1$ Then which one of the following is true?
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Let $f : N \to Y$ be a function defined as f(x) = 4x + 3 where Y = { y $\in$ N, y = 4x + 3 for some x $\in$ N }. Show that f is invertible and its inverse is
Mathematics · Functions · MCQ
Q33.A die is thrown. Let $A$ be the event that the number obtained is greater than $3.$ Let $B$ be the event that the number obtained is less than $5.$ Then $P (A \cup B)$ is :
Mathematics · Probability · MCQ
Q34.It is given that the events $A$ and $B$ are such that $P (A) = \frac{1}{4}, P (A ∣ B) = \frac{1}{2}$ and $P (B ∣ A) = \frac{2}{3} .$ Then $P (B)$ is :
Mathematics · Probability · MCQ
Q35.The solution of the differential equation $\frac{d y}{d x} = \frac{x + y}{x}$ satisfying the condition $y (1) = 1$ is :
Mathematics · Differential Equations · MCQ
Q36.The area of the plane region bounded by the curves $x + 2 y^{2} = 0$ and $x + 3 y^{2} = 1$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q37.The value of $2 \int \frac{s i n x d x}{s i n ( x - \frac{π}{4} )}$ is
Mathematics · Indefinite Integrals · MCQ
Q38.Let $a, b, c$ be any real numbers. Suppose that there are real numbers $x, y, z$ not all zero such that $x = cy + b z, y = a z + c x,$ and $z = b x + a y .$ Then $a^{2} + b^{2} + c^{2} + 2 ab c$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q39.Let $A$ be $a 2 \times 2$ matrix with real entries. Let $I$ be the $2 \times 2$ identity matrix. Denote by tr $(A)$ , the sum of diagonal entries of $a$ . Assume that $a^{2} = I .$ Statement-1 : If $A e I$ and $A e - I$ , then det $(A) = - 1$ …
Mathematics · Matrices and Determinants · MCQ
Q40.Suppose the cubic $x^{3} - p x + q$ has three distinct real roots where $p > 0$ and $q > 0$ . Then which one of the following holds?
Mathematics · Application of Derivatives · MCQ
Q41.How many real solutions does the equation $x^{7} + 14 x^{5} + 16 x^{3} + 30 x - 560 = 0$ have?
Mathematics · Application of Derivatives · MCQ
Q42.The value of $co t (cos e c^{- 1} \frac{5}{3} + tan^{- 1} \frac{2}{3})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q43.The non-zero vectors are $a, b$ and $c$ are related by $a = 8 b$ and $c = - 7 b .$ Then the angle between $a$ …
Mathematics · Vector Algebra · MCQ
Q44.A parabola has the origin as its focus and the line $x = 2$ as the directrix. Then the vertex of the parabola is at :
Mathematics · Parabola · MCQ
Q45.A focus of an ellipse is at the origin. The directrix is the line $x = 4$ and the eccentricity is $\frac{1}{2}$ . Then the length of the semi-major axis is :
Mathematics · Ellipse · MCQ
Q46.The point diametrically opposite to the point $P (1, 0)$ on the circle $x^{2} + y^{2} + 2 x + 4 y - 3 = 0$ is :
Mathematics · Circle · MCQ
Q47.The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q48.The first two terms of a geometric progression add up to 12. the sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is
Mathematics · Sequences and Series · MCQ
Q49.How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
Mathematics · Permutations and Combinations · MCQ
Q50.In a shop there are five types of ice-cream available. A child buys six ice-cream. Statement - 1: The number of different ways the child can buy the six ice-cream is $^{10} C_{5}$ . Statement - 2: The number of different ways the child can…
Mathematics · Permutations and Combinations · MCQ
Q51.The quadratic equations $x^{2} - 6 x + a = 0$ and $x^{2} - c x + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q52.STATEMENT - 1 : For every natural number $n \geq 2, \frac{1}{1} + \frac{1}{2} + ........ + \frac{1}{n} > n .$ STATEMENT - 2 : For every natural number $n \geq 2,$ , $n (n + 1) < n + 1.$
Mathematics · Quadratic Equation and Inequalities · MCQ
Q53.Let R be the real line. Consider the following subsets of the plane $R \times R$ : $S = {(x, y) : y = x + 1 an d 0 < x < 2} T = {(x, y) : x - y i s an int e g er}$ , Which one…
Mathematics · Sets and Relations · MCQ
Q54.The conjugate of a complex number is $\frac{1}{i - 1}$ then that complex number is :
Mathematics · Complex Numbers · MCQ
Q55.If the straight lines $\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and $\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2}$ intersects at a point, then the integer…
Mathematics · 3D Geometry · MCQ
Q56.The line passing through the points $(5, 1, a)$ and $(3, b, 1)$ crosses the $y z$ -plane at the point $(0, \frac{17}{2}, - \frac{- 13}{2})$ . Then
Mathematics · 3D Geometry · MCQ
Q57.In the circuit below, $A$ and $B$ represent two inputs and $C$ represents the output. The circuit represents Includes diagram
Physics · Electronic Devices · MCQ
Q58.Suppose an electron is attracted towards the origin by a force $\frac{k}{r}$ where $^{'} k^{'}$ is a constant and $^{'} r^{'}$ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $n^{t h}$ orbital…
Physics · Atoms and Nuclei · MCQ
Q59.This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two statements: Statement- 1: Energy is released when heavy nuclei undergo fission or light nuclei…
Physics · Atoms and Nuclei · MCQ
Q60.A student measures the focal length of a convex lens by putting an object pin at a distance $^{'} u^{'}$ from the lens and measuring the distance $^{'} v^{'}$ of the image pin. The graph between $^{'} u^{'}$ and $^{'} v^{'}$ plotted by the student should look like
Physics · Geometrical Optics · MCQ
Q61.In an experiment, electrons are made to pass through a narrow slit of width $^{'} d^{'}$ comparable to their de Broglie wavelength. They are detected on a screen at a distance $^{'} D^{'}$ from the slit (see figure). Which of the following graphs can be… Includes diagram
Physics · Dual Nature of Radiation · MCQ
Q62.An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by
Physics · Units and Measurements · MCQ
Q63.Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 c m^{2}$ and length $= 20 c m$ . If one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is $(μ_{0} = 4 π \times 10^{- 7} T m A^{- 1})$ …
Physics · Electromagnetic Induction · MCQ
Q64.A horizontal overhead powerline is at height of $4 m$ from the ground and carries a current of $100 A$ from east to west. The magnetic field directly below it on the ground is $(μ_{0} = 4 π \times 10^{- 7} T m A^{- 1})$ …
Physics · Magnetics · MCQ
Q65.Relative permittivity and permeability of a material $ε_{r}$ and $μ_{r},$ respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
Physics · Magnetic Properties of Matter · MCQ
Q66.A $5 V$ battery with internal resistance $2Ω$ and a $2 V$ battery with internal resistance $1Ω$ are connected to a $10Ω$ resistor as shown in the figure. The current in the $10Ω$ resistor is Includes diagram
Physics · Current Electricity · MCQ
Q67.Consider a block of conducting material of resistivity $^{'} ρ^{'}$ shown in the figure. Current $^{'} I^{'}$ enters at $^{'} A^{'}$ and leaves from $^{'} D^{'}$ . We apply superposition principle to find voltage $^{'} Δ V^{'}$ developed between $^{'} B^{'}$ and $^{'} C^{'}$ . The… Includes diagram
Physics · Current Electricity · MCQ
Q68.A body is at rest at $x = 0.$ At $t = 0,$ it starts moving in the positive $x$ -direction with a constant acceleration. At the same instant another body passes through $x = 0$ moving in the positive $x$ direction with a constant speed. The…
Physics · Motion in A Straight Line · MCQ
Q69.Consider a block of conducting material of resistivity $^{'} ρ^{'}$ shown in the figure. Current $^{'} I^{'}$ enters at $^{'} A^{'}$ and leaves from $^{'} D^{'}$ . We apply superposition principle to find voltage $^{'} Δ V^{'}$ developed between $^{'} B^{'}$ and $^{'} C^{'}$ . The… Includes diagram
Physics · Current Electricity · MCQ
Q70.A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11 k m s^{- 1},$ the escape velocity from the surface of the planet…
Physics · Gravitation · MCQ
Q71.Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resister $R$ is Includes diagram
Physics · Current Electricity · MCQ
Q72.A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E (r)$ produced by the shell in the range $0 \leq r < \infty,$ where $r$ is…
Physics · Electrostatics · MCQ
Q73.A parallel plate capacitor with air between the plates has capacitance of $9 pF .$ The separation between its plates is $^{'} d^{'} .$ The space between the plates has dielectric constant $k_{1} = 3$ and thickness $\frac{d}{3}$ while the other one has…
Physics · Capacitor · MCQ
Q74.A wave travelling along the $x$ -axis is described by the equation $y (x, t) = 0.005$ $cos (α x - β t) .$ If the wavelength and the time period of the wave are $0.08 m$ and $2.0 s$ , respectively, then $α$ and $β$ …
Physics · Waves · MCQ
Q75.While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $18 c m$ during winter. Repeating the same experiment during summer, she measures the column…
Physics · Waves · MCQ
Q76.A jar is filled with two non-mixing liquids $1$ and $2$ having densities $ρ_{1}$ and $ρ_{2}$ respectively. A solid ball, made of a material of density $ρ_{3}$ , is dropped in the jar. It comes to equilibrium in the position… Includes diagram
Physics · Properties of Matter · MCQ
Q77.A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?
Physics · Properties of Matter · MCQ
Q78.A thin rod of length $^{'} L^{'}$ is lying along the $x$ -axis with its ends at $x = 0$ and $x = L$ . Its linear density (mass/length) varies with $x$ as $k (\frac{x}{L})^{n},$ where $n$ can be zero or any positive number. If the…
Physics · Center of Mass · MCQ
Q79.An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_{1}$ and contains ideal gas at pressure $P_{1}$ and temperature $T_{1}$ . The other chamber has volume $V_{2}$ and…
Physics · Heat and Thermodynamics · MCQ
Q80.The speed of sound in oxygen $(O_{2})$ at a certain temperature is $460 m s^{- 1} .$ The speed of sound in helium $(H e)$ at the same temperature will be (assume both gases to be ideal)
Physics · Heat and Thermodynamics · MCQ
Q81.A spherical solid ball of volume $V$ is made of a material of density $ρ_{1}$ . It is falling through a liquid of density $ρ_{2} (ρ_{2} < ρ_{1})$ . Assume that the liquid applies a viscous force on the ball…
Physics · Properties of Matter · MCQ
Q82.This question contains Statement - $1$ and Statement - $2$ . of the four choices given after the statements, choose the one that best describes the two statements. Statement - $1$ : For a mass $M$ kept at the center of a cube of side $^{'} a^{'}$ ,…
Physics · Gravitation · MCQ
Q83.Consider a uniform square plate of side $^{'} a^{'}$ and mass $^{'} m^{'}$ . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
Physics · Rotational Motion · MCQ
Q84.An athlete in the olympic games covers a distance of $100 m$ in $10 s .$ His kinetic energy can be estimated to be in the range
Physics · Work Power and Energy · MCQ
Q85.A block of mass $0.50 k g$ is moving with a speed of $2.00 m s^{- 1}$ on a smooth surface. It strike another mass of $1.0 k g$ and then they move together as a single body. The energy loss during the collision is :
Physics · Center of Mass · MCQ
Q86.Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while…
Physics · Units and Measurements · MCQ
Q87.A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recorded as
Physics · Units and Measurements · MCQ
Q88.The dimension of magnetic field in M, L, T and C (coulomb) is given as
Physics · Units and Measurements · MCQ