PYQ Vault

JEE Mains 2025 (24 Jan, Shift 2), Paper 1 (B.E./B.Tech) question paper

75 questions · 300 marks · 180 minutes · +4 per correct answer, -1 per wrong one

Every question in the order it was set, free to read. Tap an option to check it, or open the answer and worked solution. Answers open as you go; sign in free to keep opening them.

Sit it as a timed mock

Physics

25 questions

  1. 1
    Young's double slit interference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be :

    Tap an option to check your answer.

  2. 2
    Arrange the following in the ascending order of wavelength ( λ\lambda ) : (A) Microwaves (λ1)\left( \lambda_{1} \right) (B) Ultraviolet rays (λ2)\left( \lambda_{2} \right) (C) Infrared rays (λ3)\left( \lambda_{3} \right) (D) X-rays (λ4)\left( \lambda_{4} \right) Choose the most appropriate answer from the options given below :-

    Tap an option to check your answer.

  3. 3
    Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason(R). Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight- line path. Reason (R) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

    Tap an option to check your answer.

  4. 4
    A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

    Tap an option to check your answer.

  5. 5
    A long straight wire of a circular cross-section with radius ' aa ' carries a steady current II. The current II is a uniformly distributed across this cross-section The plot of magnitude of magnetic field BB with distance rr from the centre of the wire is given by

    Tap an option to check your answer.

  6. 6
    Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason(R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statement, choose the correct answer from the options given below :

    Tap an option to check your answer.

  7. 7
    Configuration(1) Configuration(2) In the first configuration (1) as shown in the figure, four identical charges (q0)\left( q_{0} \right) are kept at the corners A,B,CA,B,C and DD of square of side length ' aa '. In the second configuration (2), the same charges are shifted to mid points G,E,HG,E,H and F , of the square, If K=14πε0K =\frac{1}{4\pi\varepsilon_{0}}, the difference between the potential energies of configuration (2) and (1) is given by :

    Tap an option to check your answer.

  8. 8
    The position vector of a moving body at any instant of time is given as r→=(5t2i^−5tj^)m\overrightarrow{r}=\left( 5t^{2}\widehat{i}- 5t\widehat{j} \right)m. The magnitude and direction of velocity at t=2 st= 2\text{ }s is,

    Tap an option to check your answer.

  9. 9
    A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t1t_{1} and t2t_{2}, respectively, then

    Tap an option to check your answer.

  10. 10
    Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

    Tap an option to check your answer.

  11. 11
    N equally spaced charges each of value q , are placed on a circle of radius RR. The circle rotates about its axis with an angular velocity ω\omega as shown in the figure. A bigger Amperian loop BB encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, IA−IBI_{A}-I_{B}, for the given Amperian loops is

    Tap an option to check your answer.

  12. 12
    In photoelectric effect, the stopping potential (Vo)\left( V_{o} \right) v/sv/s frequency ( v ) curve is plotted. ( h is the Planck's constant and ϕ0\phi_{0} is work function of metal) (A) V0v/svV_{0}v/sv is linear (B) The slope of V0v/svV_{0}v/sv curve =ϕ0 h=\frac{\phi_{0}}{\text{ }h} (C) h constant is related to the slope of V0v/svV_{0}v/sv line (D) The value of electric charge of electron is not required to determine h using the V0v/svV_{0}v/sv curve. (E) The work function can be estimated without knowing the value of hh. Choose the correct answer from the options given below :

    Tap an option to check your answer.

  13. 13
    The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit)

    Tap an option to check your answer.

  14. 14
    A photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is 2 cm×2 cm2\text{ }cm \times 2\text{ }cm and the area of the landscape photographed is 400 km2400{\text{ }km}^{2}. The focal length of the lens in the drone camera is :

    Tap an option to check your answer.

  15. 15
    The output of the circuit is low (zero) for : (A) X=0,Y=0X = 0,Y = 0 (B) X=0,Y=1X = 0,Y = 1 (C) X=1,Y=0X = 1,Y = 0 (D) X=1,Y=1X = 1,Y = 1 Choose the correct answer from the options given below :

    Tap an option to check your answer.

  16. 16
    The temperature of a body in air falls from 40∘C40^{\circ}C to 24∘C24^{\circ}C in 4 minutes. The temperature of the air is 16∘C16^{\circ}C. The temperature of the body in the next 4 minutes will be :

    Tap an option to check your answer.

  17. 17
    The energy EE and momentum pp of a moving body of mass mm are related by some equation. Given that c represents the speed of light, identify the correct equation.

    Tap an option to check your answer.

  18. 18
    A small uncharged conducting sphere is placed in contact with an identical sphere but having 4×10−84 \times10^{- 8} C charge and then removed to a distance such that the force of repulsion between them is 9×10−3 N9 \times10^{- 3}\text{ }N. The distance between them is (Take 14πε0\frac{1}{4\pi\varepsilon_{0}} as 9×1099 \times10^{9} in SI units)

    Tap an option to check your answer.

  19. 19
    A particle oscillates along the x -axis according to the law, x(t)=x0sin⁡2(t2)x(t) =x_{0}\sin^{2}\left( \frac{t}{2} \right) where x0=1 mx_{0}= 1\text{ }m. The kinetic energy (K) of the particle as a function of xx is correctly represented by the graph.

    Tap an option to check your answer.

  20. 20
    In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of P1P_{1} and P2P_{2} are orthogonal to each other. The polarizer P3P_{3} covers both the slits with its transmission axis at 45∘45^{\circ} to those of P1P_{1} and P2P_{2}. An unpolarized light of wavelength λ\lambda and intensity I0I_{0} is incident on P1P_{1} and P2P_{2}. The intensity at a point after P3P_{3} where the path difference between the light waves from s1s_{1} and s2s_{2} is λ3\frac{\lambda}{3}, is

    Tap an option to check your answer.

  21. 21
    A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is _______\_\_\_\_\_\_\_ . [Take mass of electron m0=9×10−31 kgm_{0}= 9 \times10^{- 31}\text{ }kg, charge of electron ∣q0∣=1.6×10−19C\left| q_{0} \right|= 1.6 \times10^{- 19}C,  μ0=4π×10−7 N A2,1 ns=10−9 s]\left. \ \mu_{0}= 4\pi\times10^{- 7}\frac{\text{ }N}{{\text{ }A}^{2}},1\text{ }ns =10^{- 9}\text{ }s \right\rbrack
  22. 22
    A string of length LL is fixed at one end and carries a mass of M at the other end. The mass makes (3π)\left( \frac{3}{\pi} \right) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is ______\_\_\_\_\_\_ ML.
  23. 23
    The ratio of the power of a light source S1S_{1} to that the light source S2S_{2} is 2 . S1S_{1} is emitting 2×10152 \times10^{15} photons per second at 600 nm . If the wavelength of the source S2S_{2} is 300 nm , then the number of photons per second emitted by S2S_{2} is ______\_\_\_\_\_\_ ×1014\times10^{14}.
  24. 24
    The increase in pressure required to decrease the volume of a water sample by 0.2%0.2\% is P×105Nm−2P \times10^{5}Nm^{- 2}. Bulk modulus of water is 2.15×109Nm−22.15 \times10^{9}Nm^{- 2}. The value of PP is _____\_\_\_\_\_
  25. 25
    Acceleration due to gravity on the surface of earth is ' gg '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is _____\_\_\_\_\_ g.

Chemistry

25 questions

  1. 26
    Based on the data given below:
    ECr2O72−/Cr3+0=1.33 VECl2/Cl(−)0=1.36 VEMnO4−/Mn2+0=1.51 VECr3+/Cr0=−0.74 V\begin{matrix} E_{Cr_{2}O_{7}^{2 -}/Cr^{3 +}}^{0}= 1.33\text{ }V & E_{Cl_{2}/Cl^{( - )}}^{0}= 1.36\text{ }V \\ E_{MnO_{4}^{-}/Mn^{2 +}}^{0}= 1.51\text{ }V & E_{Cr^{3 +}/Cr}^{0}= - 0.74\text{ }V \end{matrix}
    the strongest reducing agent is :

    Tap an option to check your answer.

  2. 27
    Given below are two statements : Statement (I): The plot of t1/2t_{1/2} against [R]0[R]_{0} in the first figure is valid for a first order reaction. Statement (II): The plot of log⁡[R][R]0\log\frac{[R]}{[R]_{0}} against time in the second figure, with slope =k2.303=\frac{k}{2.303}, is valid for a first order reaction. In the light of the above statements, choose the correct answer from the options given below :

    Tap an option to check your answer.

  3. 28
    For reaction The correct order of set of reagents for the above conversion is :

    Tap an option to check your answer.

  4. 29
    For hydrogen atom, the orbital/s with lowest energy is/are : (A) 4 s (B) 3px3p_{x} (C) 3dx2−y23d_{x^{2}-y^{2}} (D) 3 dz23{\text{ }d}_{z^{2}} (E) 4pz4p_{z} Choose the correct answer from the options given below :

    Tap an option to check your answer.

  5. 30
    In the given structure, number of sp and sp2sp^{2} hybridized carbon atoms present respectively are :

    Tap an option to check your answer.

  6. 31
    Which of the following mixing of 1 M base and 1 M acid leads to the largest increase in temperature?

    Tap an option to check your answer.

  7. 32
    Given below are two statements: Statement(I) : Experimentally determined oxygen-oxygen bond lengths in the O3O_{3} are found to be same and the bond length is greater than that of a O=OO = O (double bond) but less than that of a single (O−O)(O - O) bond. Statement (II) : The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond (O=O)(O = O) but more than that of a single bond (O−O)(O - O). In the light of the above statements, choose the correct answer from the options given below:

    Tap an option to check your answer.

  8. 33
    Find the compound 'A' from the following reaction sequences.
    A→aqua−regiaB  →(1)KNO2[NH4OH](2)AcOHyellow ppt A\overset{aqua - regia}{\rightarrow}B\text{~ }\underset{\left( 2 \right)AcOH}{\overset{\left( 1 \right)KNO_{2}\lbrack NH_{4}OH\rbrack}{\rightarrow}}\text{yellow ppt~}

    Tap an option to check your answer.

  9. 34
    For the reaction,
    H2( g)+I2( g)⇌2HI( g)H_{2}(\text{ }g) +I_{2}(\text{ }g) \rightleftharpoons 2HI(\text{ }g)
    Attainment of equilibrium is predicted correctly by:

    Tap an option to check your answer.

  10. 35
    Match List-I with List-II.
    List-I (Transition metal ion)List-II (Spin-only magnetic moment, B.M.)
    (A)
    Ti3+Ti^{3 +}
    		(I)3.87
    (B)
    V2+V^{2 +}
    		(II)0.00
    (C)
    Ni2+Ni^{2 +}
    		(III)1.73
    (D)Sc3+Sc^{3 +}(IV)2.84
    Choose the correct answer from the options given below :

    Tap an option to check your answer.

  11. 36
    The elemental composition of a compound is 54.2%54.2\% C, 9.2%9.2\% H and 36.6%O36.6\% O. If the molar mass of the compound is 132 g mol−1132\text{ }g{\text{ }mol}^{- 1}, the molecular formula of the compound is : [Given : The relative atomic mass of C:H:O=C:H:O = 12:1:16]12:1:16\rbrack

    Tap an option to check your answer.

  12. 37
    When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be :

    Tap an option to check your answer.

  13. 38
    The conditions and consequence that favours the t2 g 3,eg 1t_{2\text{ }g}\ ^{3},e_{g}\ ^{1} configuration in a metal complex are :

    Tap an option to check your answer.

  14. 39
    Identify correct statement/s : (A) −OCH3-OCH_{3} and −NHCOCH3-NHCOCH_{3} are activating group (B) -CN and -OH are meta directing group (C) -CN and −SO3H-SO_{3}H are meta directing group (D) Activating groups act as ortho - and para directing groups (E) Halides are activating groups Choose the correct answer from the options given below :

    Tap an option to check your answer.

  15. 40
    Given below are two statements : Statement (I): The first ionization energy of Pb is greater than that of Sn Statement(II) : The first ionization energy of Ge is greater than that of Si . In the light of the above statements, choose the correct answer from the options given below :

    Tap an option to check your answer.

  16. 41
    S( g)+32O2( g)→SO3( g)+2x kcal SO2( g)+12O2( g)→SO3( g)+ykcal\begin{matrix} & S(\text{ }g) +\frac{3}{2}O_{2}(\text{ }g) \rightarrow SO_{3}(\text{ }g) + 2x\text{~kcal~} \\ & SO_{2}(\text{ }g) +\frac{1}{2}O_{2}(\text{ }g) \rightarrow SO_{3}(\text{ }g) + ykcal \end{matrix}
    The heat of formation of SO2( g)SO_{2}(\text{ }g) is given by :

    Tap an option to check your answer.

  17. 42
    Match List-I with List-II List-I (A) RCN→(i)SnCl2, HCl(ii)H3O+RCHORCN\underset{(ii)H_{3}O^{+}}{\overset{(i)SnCl_{2},\ HCl}{\rightarrow}}RCHO (B) C6H5COCl→H2Pd−BaSO4C6H5CHOC_{6}H_{5}COCl\underset{Pd - BaSO_{4}}{\overset{H_{2}}{\rightarrow}}C_{6}H_{5}CHO (C) C6H5CH3→(i)CrO2Cl2, CS2(ii)H3O+C6H5CHOC_{6}H_{5}CH_{3}\underset{(ii)H_{3}O^{+}}{\overset{(i)CrO_{2}Cl_{2},\ CS_{2}}{\rightarrow}}C_{6}H_{5}CHO (D) C6H6→CO, HClanhydrous AlCl3/CuClC6H5CHOC_{6}H_{6}\underset{anhydrous\ AlCl_{3}/CuCl}{\overset{CO,\ HCl}{\rightarrow}}C_{6}H_{5}CHO List-II (I) Etard reaction (II) Gattermann-Koch reaction (III) Rosenmund reduction (IV) Stephen reaction Choose the correct answer from the options given below :

    Tap an option to check your answer.

  18. 43
    The structure of the major product formed in the following reaction is : →AgCN\overset{AgCN}{\rightarrow} Major product

    Tap an option to check your answer.

  19. 44
    Match List-I with List-II. List-I List-II (A) Adenine (I) (B) Cytosine (II) (C) Thymine (III) (D) Uracil (IV) Choose the correct answer from the options given below :

    Tap an option to check your answer.

  20. 45
    The successive 5 ionisation energies of an element are 800,2427,3658,25024800,2427,3658,25024 and 32824 kJ/mol32824\text{ }kJ/mol, respectively. By using the above values predict the group in which the above element is present :

    Tap an option to check your answer.

  21. 46
    The observed and normal masses of compound MX2MX_{2} are 65.6 and 164 respectively. The percent degree of ionisation of MX2MX_{2} is _____\_\_\_\_\_ %. (Nearest integer)
  22. 47
    The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is ____\_\_\_\_ .
  23. 48
    Consider a complex reaction taking place in three steps with rate constants k1,k2k_{1},k_{2} and k3k_{3} respectively. The overall rate constant kk is given by the expression k=k1k3k2k =\sqrt{\frac{k_{1}k_{3}}{k_{2}}}. If the activation energies of the three steps are 60,30 and 10 kJ mol−110\text{ }kJ{\text{ }mol}^{- 1} respectively, then the overall energy of activation in kJmol−1kJmol^{- 1} is ______\_\_\_\_\_\_ . (Nearest integer)
  24. 49
    The hydrocarbon (X) with molar mass 80 g mol−180\text{ }g{\text{ }mol}^{- 1} and 90%90\% carbon has ______\_\_\_\_\_\_ degree of unsaturation.
  25. 50
    In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide (AgBr)(AgBr). The percentage of Bromine in the organic compound is ______\_\_\_\_\_\_ × 10−1%\times \ 10^{- 1}\% (Nearest integer). (Given : Molar mass of Ag is 108 and Br is 80 g mol−180\text{ }g{\text{ }mol}^{- 1} )

Mathematics

25 questions

  1. 51
    The equation of the chord, of the ellipse x225+y216=1\frac{x^{2}}{25}+\frac{y^{2}}{16}= 1, whose mid-point is (3,1)(3,1) is :

    Tap an option to check your answer.

  2. 52
    The function f:(−∞,∞)→(−∞,1)f:( - \infty,\infty) \rightarrow ( - \infty,1), defined by f(x)=2x−2−x2x+2−xf(x) =\frac{2^{x}-2^{-x}}{2^{x}+2^{-x}} is :

    Tap an option to check your answer.

  3. 53
    If α>β>γ>0\alpha > \beta > \gamma > 0, then the expression
    cot⁡−1{β+(1+β2)(α−β)}+cot⁡−1{γ+(1+γ2)(β−γ)}\cot^{- 1}\left\{ \beta +\frac{\left( 1 +\beta^{2} \right)}{(\alpha - \beta)} \right\}+\cot^{- 1}\left\{ \gamma +\frac{\left( 1 +\gamma^{2} \right)}{(\beta - \gamma)} \right\}
    +cot⁡−1{α+(1+α2)(γ−α)}+\cot^{- 1}\left\{ \alpha +\frac{\left( 1 +\alpha^{2} \right)}{(\gamma - \alpha)} \right\} is equal to:

    Tap an option to check your answer.

  4. 54
    Let f:(0,∞)→Rf:(0,\infty) \rightarrow R be a function which is differentiable at all points of its domain and satisfies the condition x2f′(x)=2xf(x)+3x^{2}f^{'}(x) = 2xf(x) + 3, with f(1)=4f(1) = 4. Then 2f(2)2f(2) is equal to:

    Tap an option to check your answer.

  5. 55
    Let
    A={x∈(0,π)−{π2}:log⁡(2/π)∣sin⁡x∣+log⁡(2/π)∣cos⁡x∣=2}A =\left\{ x \in (0,\pi) -\left\{ \frac{\pi}{2} \right\}:\log_{(2/\pi)}|\sin x| +\log_{(2/\pi)}|\cos x| = 2 \right\}
    And B={x≥0:x(x−4)−3∣x−2∣+6=0}\mathbf{B = \{ x \geq 0:}\sqrt{x}(\sqrt{x}- 4) - 3|\sqrt{x}- 2| + 6 = 0\}. Then n(A∪B)n(A \cup B) is equal to:

    Tap an option to check your answer.

  6. 56
    Let the position vectors of three vertices of a triangle be 4p→+q→−3r→,−5p→+q→+2r→4\overrightarrow{p}+\overrightarrow{q}- 3\overrightarrow{r}, - 5\overrightarrow{p}+\overrightarrow{q}+ 2\overrightarrow{r} and 2p→−q→+2r→2\overrightarrow{p}-\overrightarrow{q}+ 2\overrightarrow{r}. If the position vectors of the orthocenter and the circumcenter of the triangle are p→+q→+r→4\frac{\overrightarrow{p}+\overrightarrow{q}+\overrightarrow{r}}{4} and αp→+βq→+γr→\alpha\overrightarrow{p}+\beta\overrightarrow{q}+\gamma\overrightarrow{r} respectively, then α+2β+5γ\alpha+ 2\beta+ 5\gamma is equal to:

    Tap an option to check your answer.

  7. 57
    Let [x]\lbrack x\rbrack denote the greatest integer function, and let mm and nn respectively be the numbers of the points, where the function f(x)=[x]+∣x−2∣f(x) = \lbrack x\rbrack + |x - 2|, −2<x<3- 2 < x < 3, is not continuous and not differentiable. Then m+nm + n is equal to:

    Tap an option to check your answer.

  8. 58
    Let the points (112,α)\left( \frac{11}{2},\alpha \right) lie on or inside the triangle with sides x+y=11,x+2y=16x + y = 11,x + 2y = 16 and 2x+3y=292x + 3y = 29. Then the product of the smallest and the largest values of α\alpha is equal to :

    Tap an option to check your answer.

  9. 59
    In an arithmetic progression, if S40=1030S_{40}= 1030 and S12=57S_{12}= 57, then S30−S10S_{30}-S_{10} is equal to:

    Tap an option to check your answer.

  10. 60
    If 7=5+17(5+α)+172(5+2α)+173(5+3α)+⋯7 = 5 + \frac{1}{7}(5+\alpha) + \frac{1}{7^{2}}(5+2\alpha) + \frac{1}{7^{3}}(5+3\alpha) + \cdots upto ∞\infty, then the value of α\alpha is:

    Tap an option to check your answer.

  11. 61
    If the system of equations
    x+2y−3z=22x+λy+5z=514x+3y+μz=33\begin{matrix} & x+ 2y- 3z= 2 \\ & 2x+\lambda y+ 5z= 5 \\ & 14x+ 3y+\mu z= 33 \end{matrix}
    has infinitely many solutions, then λ+μ\lambda+\mu is equal to:

    Tap an option to check your answer.

  12. 62
    Let (2,3)(2,3) be the largest open interval in which the function f(x)=2log⁡e(x−2)−x2+ax+1f(x) = 2\log_{e}(x- 2) -x^{2}+ax+ 1 is strictly increasing and (b, c) be the largest open interval, in which the function g(x)=(x−1)3(x+2−a)2g(x) = (x- 1)^{3}(x+ 2 -a)^{2} is strictly decreasing. Then 100(a+b−c)100(a+b-c) is equal to:

    Tap an option to check your answer.

  13. 63
    Suppose A and B are the coefficients of 30th30^{\text{th}} and 12th12^{\text{th}} terms respectively in the binomial expansion of (1+x)2n−1(1 +x)^{2n- 1}. If 2A=5B2A= 5B, then nn is equal to:

    Tap an option to check your answer.

  14. 64
    Let a→=3i^−j^+2k^,b→=a→×(i^−2k^)\overrightarrow{a}= 3\widehat{i}-\widehat{j}+ 2\widehat{k},\overrightarrow{b}=\overrightarrow{a}\times (\widehat{i}- 2\widehat{k}) and c→=b→×k^\overrightarrow{c}=\overrightarrow{b}\times\widehat{k}. Then the projection of c→−2j^\overrightarrow{c}- 2\widehat{j} on a→\overrightarrow{a} is:

    Tap an option to check your answer.

  15. 65
    For some a,ba,b, let
    f(x)=∣a+sin⁡xx1ba1+sin⁡xxba1b+sin⁡xx∣, x≠0f(x) =\left| \begin{matrix} a +\frac{\sin x}{x} & 1 & b \\ a & 1 +\frac{\sin x}{x} & b \\ a & 1 & b +\frac{\sin x}{x} \end{matrix} \right|,\ x \neq 0
    lim⁡x→0f(x)=λ+μa+vb\lim_{x \rightarrow 0} f(x) = \lambda + \mu a + vb. Then (λ+μ+v)2(\lambda + \mu + v)^{2} is equal to:

    Tap an option to check your answer.

  16. 66
    Group A consists of 7 boys and 3 girls, while group BB consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group AA and the remaining 3 from group BB, is equal to:

    Tap an option to check your answer.

  17. 67
    The area of the region enclosed by the curves y=ex,y=∣ex−1∣y=e^{x},y=\left| e^{x}- 1 \right| and yy-axis is:

    Tap an option to check your answer.

  18. 68
    The number of real solution(s) of the equation x2+3x+2=min⁡{∣x−3∣,∣x+2∣}x^{2}+ 3x+ 2 = \min\{|x- 3|,|x+ 2|\} is :

    Tap an option to check your answer.

  19. 69
    Let A=[aij]A=\left\lbrack a_{ij} \right\rbrack be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability P(E)P(E) is :

    Tap an option to check your answer.

  20. 70
    If the equation of the parabola with vertex V(32,3)V\left( \frac{3}{2},3 \right) and the directrix x+2y=0x + 2y = 0 is αx2+βy2−γxy−30x−60y+225=0\alpha x^{2}+ \beta y^{2}- \gamma xy - 30x - 60y + 225 = 0, then α+β+γ\alpha + \beta + \gamma is equal to:

    Tap an option to check your answer.

  21. 71
    Number of functions f:{1,2,…,100}→{0,1}f\mathbf{:\{ 1,2,\ldots,100\} \rightarrow \{ 0,1\}}, that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ____\_\_\_\_ .
  22. 72
    Let PP be the image of the point Q(7,−2,5)Q(7,-2,5) in the line L:x−12=y+13=z4L:\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4} and R(5,p,q)R(5,p,q) be a point on LL. Then the square of the area of △PQR\triangle PQR is
  23. 73
    Let y=y(x)y=y(x) be the solution of the differential equation 2cos⁡xdydx=sin⁡2x−4ysinx,x∈(0,π2)2\cos x\frac{dy}{dx}= \sin2x- 4ysinx,x\in\left( 0,\frac{\pi}{2} \right). If y(π3)=0y\left( \frac{\pi}{3} \right)= 0, then y′(π4)+y(π4)y^{'}\left( \frac{\pi}{4} \right)+y\left( \frac{\pi}{4} \right) is equal to _____\_\_\_\_\_ .
  24. 74
    Let H1:x2a2−y2b2=1H_{1}:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 and H2:−x2A2+y2B2=1H_{2}: -\frac{x^{2}}{A^{2}}+\frac{y^{2}}{B^{2}}= 1 be two hyperbolas having length of latus rectums 15215\sqrt{2} and 12512\sqrt{5} respectively. Let their eccentricities be e1=52e_{1}=\sqrt{\frac{5}{2}} and e2e_{2} respectively. If the product of the lengths of their transverse axes is 10010100\sqrt{10}, then 25e2225e_{2}^{2} is equal to _____\_\_\_\_\_
  25. 75
    If ∫2x2+5x+9x2+x+1dx=xx2+x+1+αx2+x+1+\int\frac{2x^{2}+ 5x+ 9}{\sqrt{x^{2}+x+ 1}}dx=x\sqrt{x^{2}+x+ 1}+\alpha\sqrt{x^{2}+x+ 1}+ βlog⁡e∣x+12+x2+x+1∣+C\beta\log_{e}\left| x +\frac{1}{2}+\sqrt{x^{2}+ x + 1} \right|+C, where C is the constant of integration, then α+2β\alpha+ 2\beta is equal to ____\_\_\_\_

Want the real exam feel? Sit this paper with a 180-minute timer and get your score straight away.

Sit it as a timed mock