2017 · Shift 0

69 questions · JEE Main

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JEE Main
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2017 · Shift 0

2017 · Shift 0

69 questions · JEE Main

Chemistry24 questions Mathematics19 questions Physics26 questions

Q1.The major product obtained in the following reaction is : Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q2.Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?
Chemistry · Biomolecules · MCQ
Q3.The correct sequence of reagents for the following conversion will be : Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q4.Sodium salt of an organic acid ‘X’ produces effervescence with conc. $H_{2} S O_{4}$ . ‘X’ reacts with the acidified aqueous $C a C l_{2}$ solution to give a white precipitate which decolourises acidic solution of $K M n O_{4}$ . ‘X’ is :
Chemistry · Practical Organic Chemistry · MCQ
Q5.The major product obtained in the following reaction is : Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q6.Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolorize the colour of bromine?
Chemistry · Haloalkanes and Haloarenes · MCQ
Q7.3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :
Chemistry · Haloalkanes and Haloarenes · MCQ
Q8.The increasing order of the reactivity of the following halides for the SN1 reaction is : Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q9.Which of the following compounds will form significant amount of meta product during mono-nitration reaction?
Chemistry · Compounds Containing Nitrogen · MCQ
Q10.Which of the following molecules is least resonance stabilized?
Chemistry · Basics of Organic Chemistry · MCQ
Q11.On treatment of 100 mL of 0.1 M solution of $C o C l_{3}$ . 6 $H_{2} O$ with excess $A g N O_{3}$ ; 1.2 $\times$ 1022 ions are precipitated. The complex is :
Chemistry · Coordination Compounds · MCQ
Q12.In the following reactions, $Z n O$ is respectively acting as a/an : (a) $Z n O$ + $N a_{2} O$ $\to$ $N a_{2} Z n O_{2}$ (b) $Z n O$ + $C O_{2}$ $\to$ $Z n C O_{3}$
Chemistry · D and F Block Elements · MCQ
Q13.The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight which a 75 kg person would gain if all 1H atoms are replaced by 2H atoms is:
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q14.Two reactions $R_{1}$ and $R_{2}$ have identical pre-exponential factors. Activation energy of $R_{1}$ exceeds that of $R_{2}$ by 10 kJ mol–1. If $k_{1}$ and $k_{2}$ are rate constants for reactions $R_{1}$ and $R_{2}$ respectively at 300 K, then…
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q15.Which of the following reactions is an example of a redox reaction?
Chemistry · Redox Reactions · MCQ
Q16.pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is :
Chemistry · Ionic Equilibrium · MCQ
Q17.Given $E_{C l_{2} / C l^{-}}^{o}$ = 1.36 V, $E_{C r^{3 +} / C r}^{o}$ = - 0.74 V $E_{C r_{2} O_{7}^{2 -} / C r^{3 +}}^{o}$ = 1.33 V, $E_{M n O_{4}^{-} / M n^{2 +}}^{o}$ = 1.51 V Among the following, the strongest reducing agent is :
Chemistry · Electrochemistry · MCQ
Q18.Given, $C_{(g r a p hi t e)} + O_{2} \to C O_{2} (g)$ ; $Δ_{r} H^{o}$ = - 393.5 kJ mol-1 $H_{2} (g)$ + $\frac{1}{2} O_{2} (g) \to H_{2} O (l) Δ_{r} H^{o}$ = - 285.8 kJ mol-1 $C O_{2} (g)$ + $2 H_{2} O (l) \to C H_{4} (g)$ + $2 O_{2} (g) Δ_{r} H^{o}$ …
Chemistry · Thermodynamics · MCQ
Q19.The freezing point of benzene decreases by 0.450C when 0.2 g of acetic acid is added to 20g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be: (Kf for benzene = 5.12…
Chemistry · Solutions · MCQ
Q20.The group having isoelectronic species is:
Chemistry · Structure of Atom · MCQ
Q21. $Δ$ U is equal to :
Chemistry · Thermodynamics · MCQ
Q22.Which of the following species is not paramagnetic?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q23.The radius of the second Bohr orbit for hydrogen atom is: (Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1091 × 10-31 kg; charge of electron (e) = 1.60210 × 10-19 C; permittivity of vacuum ( ${varepsilon _0}$ ) = 8.854185 ×…
Chemistry · Structure of Atom · MCQ
Q24.1 gram of a carbonate ( $M_{2} C O_{3}$ ) on treatment with excess $H C l$ produces 0.01186 mole of $C O_{2}$ . The molar mass of $M_{2} C O_{3}$ in g mol–1 is:
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q25.Let $a$ , b, c $\in R$ . If $f$ (x) = ax2 + bx + c is such that $a$ + b + c = 3 and $f$ (x + y) = $f$ (x) + $f$ (y) + xy, $\forall x, y \in R,$ then $n = 1 \sum 10 f (n)$ is equal to
Mathematics · Functions · MCQ
Q26.A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party…
Mathematics · Permutations and Combinations · MCQ
Q27.If for a positive integer n, the quadratic equation $x (x + 1) + (x + 1) (x + 2) + .... + (x + \overline{n - 1}) (x + n)$ $= 10 n$ has two consecutive integral…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q28.If S is the set of distinct values of 'b' for which the following system of linear equations x + y + z = 1 x + ay + z = 1 ax + by + z = 0 has no solution, then S is :
Mathematics · Matrices and Determinants · MCQ
Q29.If $A = [2 - 4 - 3 1]$ , then adj(3A2 + 12A) is equal to
Mathematics · Matrices and Determinants · MCQ
Q30.Let $ω$ be a complex number such that 2 $ω$ + 1 = z where z = $- 3$ . If $111 1 - ω^{2} - 1 ω^{2} 1 ω^{2} ω^{7} = 3 k$ …
Mathematics · Complex Numbers · MCQ
Q31.The function $f : R \to [- \frac{1}{2}, \frac{1}{2}]$ defined as $f (x) = \frac{x}{1 + x ^{2}}$ , is
Mathematics · Functions · MCQ
Q32.If $5 (tan^{2} x - cos^{2} x) = 2 cos 2 x + 9$ , then the value of $cos 4 x$ is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q33.If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :
Mathematics · Probability · MCQ
Q34.For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = $\frac{1}{4}$ and P(All the three events occur simultaneously) = $\frac{1}{16}$ . Then the probability that…
Mathematics · Probability · MCQ
Q35.Let $a = 2 i + j - 2 k$ and $b = i + j$ . Let $c$ be a vector such that $c - a = 3$ , $(a \times b) \times c = 3$ …
Mathematics · Vector Algebra · MCQ
Q36.Let k be an integer such that the triangle with vertices (k, – 3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.If $(2 + sin x) \frac{d y}{d x} + (y + 1) cos x = 0$ and y(0) = 1, then $y (\frac{π}{2})$ is equal to :
Mathematics · Differential Equations · MCQ
Q38.The area (in sq. units) of the region ${(x, y) : x \geq 0, x + y \leq 3, x^{2} \leq 4 y an d y \leq 1 + x}$ is
Mathematics · Area Under the Curves · MCQ
Q39.Let $I_{n} = \int tan^{n} x d x, (n > 1) .$ If $I_{4} + I_{6}$ = $a tan^{5} x + b x^{5} + C$ , where C is a constant of integration, then the ordered pair $(a, b)$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q40.The integral $\frac{π}{4} \int \frac{3 π}{4} \frac{d x}{1 + c o s x}$ is equal to
Mathematics · Definite Integration · MCQ
Q41.Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :
Mathematics · Application of Derivatives · MCQ
Q42.If for $x \in (0, \frac{1}{4})$ , the derivatives of $tan^{- 1} (\frac{6 x x}{1 - 9 x ^{3}})$ is $x . g (x)$ , then $g (x)$ equals
Mathematics · Differentiation · MCQ
Q43. $x \to \frac{π}{2} lim \frac{c o t x - c o s x}{( π - 2 x ) ^{3}}$ equals
Mathematics · Limits Continuity and Differentiability · MCQ
Q44.A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy – time graph of the particle will look like:
Physics · Simple Harmonic Motion · MCQ
Q45.A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging lens of magnitude of focal length 20cm. A beam of parallel light falls on the diverging lens. The final image formed is:
Physics · Geometrical Optics · MCQ
Q46.In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least…
Physics · Wave Optics · MCQ
Q47.In a coil of resistance 100 $Ω$ , a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is: Includes diagram
Physics · Electromagnetic Induction · MCQ
Q48.When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 $Ω$ , it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range…
Physics · Current Electricity · MCQ
Q49.A magnetic needle of magnetic moment 6.7 $\times$ 10-2 A m2 and moment of inertia 7.5 $\times$ 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:
Physics · Magnetic Properties of Matter · MCQ
Q50.In the given circuit, the current in each resistance is: Includes diagram
Physics · Current Electricity · MCQ
Q51.Which of the following statements is false?
Physics · Current Electricity · MCQ
Q52.In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be: Includes diagram
Physics · Capacitor · MCQ
Q53.An electric dipole has a fixed dipole moment $p$ , which makes angle $θ$ with respect to x-axis. When subjected to an electric field $E_{1} \to = E i$ , it experiences a torque $T_{1} = τ k$ …
Physics · Electrostatics · MCQ
Q54.A capacitance of 2 $μ$ F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 $μ$ F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum…
Physics · Capacitor · MCQ
Q55.An electron beam is accelerated by a potential difference V to hit a metallic target to produce X–rays. It produces continuous as well as characteristic X-rays. If $λ$ min is the smallest possible wavelength of X-ray in the spectrum,…
Physics · Dual Nature of Radiation · MCQ
Q56.CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for nitrogen gas The correct relation between a and b is
Physics · Heat and Thermodynamics · MCQ
Q57.The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 $\times$ 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating,…
Physics · Heat and Thermodynamics · MCQ
Q58.An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and $α$ is its coefficient of linear expansion. Suppose we want to bring the cube to…
Physics · Heat and Thermodynamics · MCQ
Q59.A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75oC. T is given by:…
Physics · Heat and Thermodynamics · MCQ
Q60.The variation of acceleration due to gravity $g$ with distance d from centre of the earth is best represented by (R = Earth’s radius):
Physics · Gravitation · MCQ
Q61.A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :
Physics · Properties of Matter · MCQ
Q62.A slender uniform rod of mass M and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The… Includes diagram
Physics · Rotational Motion · MCQ
Q63.The moment of inertia of a uniform cylinder of length $l$ and radius R about its perpendicular bisector is $I$ . What is the ratio $\frac{l}{R}$ such that the moment of inertia is minimum?
Physics · Rotational Motion · MCQ
Q64.A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:
Physics · Work Power and Energy · MCQ
Q65.A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 = 10 ms–1. If, after 10 s, its energy is $\frac{1}{8} m v_{0}^{2}$ , the value of k will be:
Physics · Work Power and Energy · MCQ
Q66.A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?
Physics · Motion in A Straight Line · MCQ
Q67.The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 $\times$ 10-2 m rise of water, h = 1.45 $\times$ 10-2m Using g = 9.80 m/s2 and the simplified relation T…
Physics · Units and Measurements · MCQ
Q68.Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $λ_{1}$ / $λ_{2}$ , is given by: Includes diagram
Physics · Atoms and Nuclei · MCQ
Q69.A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $λ_{A}$ to $λ_{B}$ after the collision is:
Physics · Dual Nature of Radiation · MCQ

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2017 · Shift 0

69 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
2017 · Shift 0

2017 · Shift 0

69 questions · JEE Main

Chemistry24 questions Mathematics19 questions Physics26 questions

Q1.The major product obtained in the following reaction is : Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q2.Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?
Chemistry · Biomolecules · MCQ
Q3.The correct sequence of reagents for the following conversion will be : Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q4.Sodium salt of an organic acid ‘X’ produces effervescence with conc. $H_{2} S O_{4}$ . ‘X’ reacts with the acidified aqueous $C a C l_{2}$ solution to give a white precipitate which decolourises acidic solution of $K M n O_{4}$ . ‘X’ is :
Chemistry · Practical Organic Chemistry · MCQ
Q5.The major product obtained in the following reaction is : Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q6.Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolorize the colour of bromine?
Chemistry · Haloalkanes and Haloarenes · MCQ
Q7.3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :
Chemistry · Haloalkanes and Haloarenes · MCQ
Q8.The increasing order of the reactivity of the following halides for the SN1 reaction is : Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q9.Which of the following compounds will form significant amount of meta product during mono-nitration reaction?
Chemistry · Compounds Containing Nitrogen · MCQ
Q10.Which of the following molecules is least resonance stabilized?
Chemistry · Basics of Organic Chemistry · MCQ
Q11.On treatment of 100 mL of 0.1 M solution of $C o C l_{3}$ . 6 $H_{2} O$ with excess $A g N O_{3}$ ; 1.2 $\times$ 1022 ions are precipitated. The complex is :
Chemistry · Coordination Compounds · MCQ
Q12.In the following reactions, $Z n O$ is respectively acting as a/an : (a) $Z n O$ + $N a_{2} O$ $\to$ $N a_{2} Z n O_{2}$ (b) $Z n O$ + $C O_{2}$ $\to$ $Z n C O_{3}$
Chemistry · D and F Block Elements · MCQ
Q13.The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight which a 75 kg person would gain if all 1H atoms are replaced by 2H atoms is:
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q14.Two reactions $R_{1}$ and $R_{2}$ have identical pre-exponential factors. Activation energy of $R_{1}$ exceeds that of $R_{2}$ by 10 kJ mol–1. If $k_{1}$ and $k_{2}$ are rate constants for reactions $R_{1}$ and $R_{2}$ respectively at 300 K, then…
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q15.Which of the following reactions is an example of a redox reaction?
Chemistry · Redox Reactions · MCQ
Q16.pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is :
Chemistry · Ionic Equilibrium · MCQ
Q17.Given $E_{C l_{2} / C l^{-}}^{o}$ = 1.36 V, $E_{C r^{3 +} / C r}^{o}$ = - 0.74 V $E_{C r_{2} O_{7}^{2 -} / C r^{3 +}}^{o}$ = 1.33 V, $E_{M n O_{4}^{-} / M n^{2 +}}^{o}$ = 1.51 V Among the following, the strongest reducing agent is :
Chemistry · Electrochemistry · MCQ
Q18.Given, $C_{(g r a p hi t e)} + O_{2} \to C O_{2} (g)$ ; $Δ_{r} H^{o}$ = - 393.5 kJ mol-1 $H_{2} (g)$ + $\frac{1}{2} O_{2} (g) \to H_{2} O (l) Δ_{r} H^{o}$ = - 285.8 kJ mol-1 $C O_{2} (g)$ + $2 H_{2} O (l) \to C H_{4} (g)$ + $2 O_{2} (g) Δ_{r} H^{o}$ …
Chemistry · Thermodynamics · MCQ
Q19.The freezing point of benzene decreases by 0.450C when 0.2 g of acetic acid is added to 20g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be: (Kf for benzene = 5.12…
Chemistry · Solutions · MCQ
Q20.The group having isoelectronic species is:
Chemistry · Structure of Atom · MCQ
Q21. $Δ$ U is equal to :
Chemistry · Thermodynamics · MCQ
Q22.Which of the following species is not paramagnetic?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q23.The radius of the second Bohr orbit for hydrogen atom is: (Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1091 × 10-31 kg; charge of electron (e) = 1.60210 × 10-19 C; permittivity of vacuum ( ${varepsilon _0}$ ) = 8.854185 ×…
Chemistry · Structure of Atom · MCQ
Q24.1 gram of a carbonate ( $M_{2} C O_{3}$ ) on treatment with excess $H C l$ produces 0.01186 mole of $C O_{2}$ . The molar mass of $M_{2} C O_{3}$ in g mol–1 is:
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q25.Let $a$ , b, c $\in R$ . If $f$ (x) = ax2 + bx + c is such that $a$ + b + c = 3 and $f$ (x + y) = $f$ (x) + $f$ (y) + xy, $\forall x, y \in R,$ then $n = 1 \sum 10 f (n)$ is equal to
Mathematics · Functions · MCQ
Q26.A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party…
Mathematics · Permutations and Combinations · MCQ
Q27.If for a positive integer n, the quadratic equation $x (x + 1) + (x + 1) (x + 2) + .... + (x + \overline{n - 1}) (x + n)$ $= 10 n$ has two consecutive integral…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q28.If S is the set of distinct values of 'b' for which the following system of linear equations x + y + z = 1 x + ay + z = 1 ax + by + z = 0 has no solution, then S is :
Mathematics · Matrices and Determinants · MCQ
Q29.If $A = [2 - 4 - 3 1]$ , then adj(3A2 + 12A) is equal to
Mathematics · Matrices and Determinants · MCQ
Q30.Let $ω$ be a complex number such that 2 $ω$ + 1 = z where z = $- 3$ . If $111 1 - ω^{2} - 1 ω^{2} 1 ω^{2} ω^{7} = 3 k$ …
Mathematics · Complex Numbers · MCQ
Q31.The function $f : R \to [- \frac{1}{2}, \frac{1}{2}]$ defined as $f (x) = \frac{x}{1 + x ^{2}}$ , is
Mathematics · Functions · MCQ
Q32.If $5 (tan^{2} x - cos^{2} x) = 2 cos 2 x + 9$ , then the value of $cos 4 x$ is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q33.If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :
Mathematics · Probability · MCQ
Q34.For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = $\frac{1}{4}$ and P(All the three events occur simultaneously) = $\frac{1}{16}$ . Then the probability that…
Mathematics · Probability · MCQ
Q35.Let $a = 2 i + j - 2 k$ and $b = i + j$ . Let $c$ be a vector such that $c - a = 3$ , $(a \times b) \times c = 3$ …
Mathematics · Vector Algebra · MCQ
Q36.Let k be an integer such that the triangle with vertices (k, – 3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.If $(2 + sin x) \frac{d y}{d x} + (y + 1) cos x = 0$ and y(0) = 1, then $y (\frac{π}{2})$ is equal to :
Mathematics · Differential Equations · MCQ
Q38.The area (in sq. units) of the region ${(x, y) : x \geq 0, x + y \leq 3, x^{2} \leq 4 y an d y \leq 1 + x}$ is
Mathematics · Area Under the Curves · MCQ
Q39.Let $I_{n} = \int tan^{n} x d x, (n > 1) .$ If $I_{4} + I_{6}$ = $a tan^{5} x + b x^{5} + C$ , where C is a constant of integration, then the ordered pair $(a, b)$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q40.The integral $\frac{π}{4} \int \frac{3 π}{4} \frac{d x}{1 + c o s x}$ is equal to
Mathematics · Definite Integration · MCQ
Q41.Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :
Mathematics · Application of Derivatives · MCQ
Q42.If for $x \in (0, \frac{1}{4})$ , the derivatives of $tan^{- 1} (\frac{6 x x}{1 - 9 x ^{3}})$ is $x . g (x)$ , then $g (x)$ equals
Mathematics · Differentiation · MCQ
Q43. $x \to \frac{π}{2} lim \frac{c o t x - c o s x}{( π - 2 x ) ^{3}}$ equals
Mathematics · Limits Continuity and Differentiability · MCQ
Q44.A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy – time graph of the particle will look like:
Physics · Simple Harmonic Motion · MCQ
Q45.A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging lens of magnitude of focal length 20cm. A beam of parallel light falls on the diverging lens. The final image formed is:
Physics · Geometrical Optics · MCQ
Q46.In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least…
Physics · Wave Optics · MCQ
Q47.In a coil of resistance 100 $Ω$ , a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is: Includes diagram
Physics · Electromagnetic Induction · MCQ
Q48.When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 $Ω$ , it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range…
Physics · Current Electricity · MCQ
Q49.A magnetic needle of magnetic moment 6.7 $\times$ 10-2 A m2 and moment of inertia 7.5 $\times$ 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:
Physics · Magnetic Properties of Matter · MCQ
Q50.In the given circuit, the current in each resistance is: Includes diagram
Physics · Current Electricity · MCQ
Q51.Which of the following statements is false?
Physics · Current Electricity · MCQ
Q52.In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be: Includes diagram
Physics · Capacitor · MCQ
Q53.An electric dipole has a fixed dipole moment $p$ , which makes angle $θ$ with respect to x-axis. When subjected to an electric field $E_{1} \to = E i$ , it experiences a torque $T_{1} = τ k$ …
Physics · Electrostatics · MCQ
Q54.A capacitance of 2 $μ$ F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 $μ$ F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum…
Physics · Capacitor · MCQ
Q55.An electron beam is accelerated by a potential difference V to hit a metallic target to produce X–rays. It produces continuous as well as characteristic X-rays. If $λ$ min is the smallest possible wavelength of X-ray in the spectrum,…
Physics · Dual Nature of Radiation · MCQ
Q56.CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for nitrogen gas The correct relation between a and b is
Physics · Heat and Thermodynamics · MCQ
Q57.The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 $\times$ 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating,…
Physics · Heat and Thermodynamics · MCQ
Q58.An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and $α$ is its coefficient of linear expansion. Suppose we want to bring the cube to…
Physics · Heat and Thermodynamics · MCQ
Q59.A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75oC. T is given by:…
Physics · Heat and Thermodynamics · MCQ
Q60.The variation of acceleration due to gravity $g$ with distance d from centre of the earth is best represented by (R = Earth’s radius):
Physics · Gravitation · MCQ
Q61.A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :
Physics · Properties of Matter · MCQ
Q62.A slender uniform rod of mass M and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The… Includes diagram
Physics · Rotational Motion · MCQ
Q63.The moment of inertia of a uniform cylinder of length $l$ and radius R about its perpendicular bisector is $I$ . What is the ratio $\frac{l}{R}$ such that the moment of inertia is minimum?
Physics · Rotational Motion · MCQ
Q64.A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:
Physics · Work Power and Energy · MCQ
Q65.A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 = 10 ms–1. If, after 10 s, its energy is $\frac{1}{8} m v_{0}^{2}$ , the value of k will be:
Physics · Work Power and Energy · MCQ
Q66.A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?
Physics · Motion in A Straight Line · MCQ
Q67.The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 $\times$ 10-2 m rise of water, h = 1.45 $\times$ 10-2m Using g = 9.80 m/s2 and the simplified relation T…
Physics · Units and Measurements · MCQ
Q68.Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $λ_{1}$ / $λ_{2}$ , is given by: Includes diagram
Physics · Atoms and Nuclei · MCQ
Q69.A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $λ_{A}$ to $λ_{B}$ after the collision is:
Physics · Dual Nature of Radiation · MCQ