JEE Main & Advanced Sample Paper

done JEE Main Sample Paper-24 Total Questions - 90   

• question_answer1)
  If \[\int\limits_{0}^{2\pi }{\frac{1}{1+{{\tan }^{4}}x}=\frac{\pi }{k}}\] where \[k\in N\], then k equals
  A)
   1                    
  done clear
  B)
   2
  done clear
  C)
   3                                
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer2)
  Consider the matrix \[A\left( \begin{matrix}    3 & -2  \\    4 & -1  \\ \end{matrix} \right)\]. Then all possible values of \[\lambda \] such that the determinant of \[B=A-\lambda \,I\] is 0, where \[I=\left( \begin{matrix}   1 & 0  \\    0 & 1  \\ \end{matrix} \right)\]and \[i=\sqrt{-1}\]
  A)
   \[1\pm 2\,i\]                             
  done clear
  B)
   \[2\pm 3\,i\]
  done clear
  C)
   \[3\pm 4\,i\]                             
  done clear
  D)
   \[5\pm 6\,i\]
  done clear
  View Answer play_arrow

• question_answer3)
  If \[\vec{a}=5\,\vec{i}-\vec{j}+\vec{k}\,;\vec{b}=2\hat{i}-3\hat{j}-\hat{k}\,;\,\vec{c}=-3\hat{i}+\hat{j}+\hat{k}\]and \[\vec{d}=2\vec{j}+\vec{k}\], then the value of \[\vec{d}.\left( \vec{a}\times \left\{ \vec{b}\times (\vec{c}\times \vec{d}) \right\} \right)\] equals
  A)
   98                               
  done clear
  B)
   99
  done clear
  C)
   100                             
  done clear
  D)
   102
  done clear
  View Answer play_arrow

• question_answer4)
  If \[\ell n\left( e-1){{e}^{xy}}+{{x}^{2}} \right)={{x}^{2}}+{{y}^{2}}\], then \[\frac{dy}{dx}\] at (1, 0) is equal to
  A)
   0                    
  done clear
  B)
   1
  done clear
  C)
   2                                
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer5)
  Let \[A={{[{{a}_{ij}}]}_{3\times 3}},B={{[{{b}_{ij}}]}_{3\times 3}}\] where \[{{b}_{i\,j}}={{3}^{i-j}}{{a}_{i\,j}}\] and \[C={{[{{c}_{i\,j}}]}_{3\times 3}},\] where \[{{c}_{i\,j}}={{4}^{i-j}}{{b}_{i\,j}}\] be any three matrices. If det. \[A=2\], then det. B \[+\] del. C is equal to
  A)
   4                                
  done clear
  B)
   3
  done clear
  C)
   2                                
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer6)
  For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
  A)
   \[\frac{11}{2}\]                                    
  done clear
  B)
   6
  done clear
  C)
   \[\frac{13}{2}\]                                    
  done clear
  D)
   \[\frac{5}{2}\]
  done clear
  View Answer play_arrow

• question_answer7)
  The locus of the foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola \[{{y}^{2}}=4ax\] is
  A)
   \[x({{x}^{2}}+{{y}^{2}})=a{{y}^{2}}=0\]           
  done clear
  B)
   \[y({{x}^{2}}+{{y}^{2}})=a{{x}^{2}}=0\]
  done clear
  C)
   \[x({{x}^{2}}-{{y}^{2}})+a{{y}^{2}}=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}+a{{y}^{2}}=0\]
  done clear
  View Answer play_arrow

• question_answer8)
  Number of distinct real solutions of the equation \[{{x}^{7}}+14{{x}^{5}}+16{{x}^{3}}+30-420=0\] is equal to
  A)
   0                    
  done clear
  B)
   1
  done clear
  C)
   2                                
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer9)
  The eccentricity of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] whose length of conjugate axis is equal to half of the distance between the focus is
  A)
   \[\frac{4}{3}\]                                     
  done clear
  B)
   \[\frac{4}{\sqrt{3}}\]
  done clear
  C)
   \[\frac{2}{\sqrt{3}}\]                            
  done clear
  D)
   \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer10)
  If three vectors \[\vec{a},\vec{b},\vec{c}\] are such that \[\vec{a},\ne 0\] and \[\vec{a}\times \vec{b}=2\vec{a}\times \vec{c}\], \[\left| {\vec{a}} \right|=\left| {\vec{b}} \right|=1,\,\left| {\vec{b}} \right|=4\] and the angle between \[\vec{b},\,\vec{c}\] is \[{{\cos }^{-1}}\frac{1}{4}\] then \[\vec{b}-2\vec{c}=\lambda \vec{a}\] where \[\lambda (\lambda >0)\] is equal to
  A)
   2                                
  done clear
  B)
   4
  done clear
  C)
   \[\frac{1}{2}\]                         
  done clear
  D)
   \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer11)
  If \[f(x)=a\cos (\pi x)+b,\,\,f'\left( \frac{1}{2} \right)=\pi \] and \[\int\limits_{\frac{1}{2}}^{\frac{3}{2}}{f(x)dx=\frac{2}{\pi }+1}\], then the value of \[\frac{-12}{\pi }({{\sin }^{-1}}a+{{\cos }^{-1}}b)\] is equal to
  A)
   6                                
  done clear
  B)
   4
  done clear
  C)
   2                                
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer12)
  The equation to the locus of the middle point of the portion of the tangent to the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\] included between the co-ordinate axes is the curve
  A)
   \[9{{x}^{2}}+16{{y}^{2}}=4{{x}^{2}}{{y}^{2}}\]         
  done clear
  B)
   \[16{{x}^{2}}+9{{y}^{2}}=4{{x}^{2}}{{y}^{2}}\]
  done clear
  C)
   \[3{{x}^{2}}+4{{y}^{2}}=4{{x}^{2}}{{y}^{2}}\]          
  done clear
  D)
   \[9{{x}^{2}}+16{{y}^{2}}={{x}^{2}}{{y}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer13)
  Let P (a,b,c) be any point on the plane\[3x+2y+z=7\] then the least value of \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\], is
  A)
   7                                
  done clear
  B)
   14
  done clear
  C)
   \[\frac{7}{2}\]                                     
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer14)
  If \[\vec{a}=\hat{i}+\hat{j}+\hat{k}\],  \[\vec{b}=\hat{i}-\hat{j}+\hat{k}\], \[\vec{c}=\hat{i}+2\hat{j}-\hat{k}\]then the value of \[\left| \begin{matrix}    \vec{a}.\vec{a} & \vec{a}.\vec{b} & \vec{a}.\vec{c}  \\    \vec{a}.\vec{b} & \vec{b}.\vec{b} & \vec{b}.\vec{c}  \\    \vec{a}.\vec{c} & \vec{b}.\vec{c} & \vec{c}.\vec{c}  \\ \end{matrix} \right|\] is equal to
  A)
   18                               
  done clear
  B)
   16
  done clear
  C)
   10                               
  done clear
  D)
   8
  done clear
  View Answer play_arrow

• question_answer15)
  The  point  of intersection  of the  curve arg \[(2z-8\,i)\] and arg \[(3z+1-3\,i)=\frac{\pi }{4}\] is
  A)
   \[\frac{4}{3}(1+2\,i)\]              
  done clear
  B)
   \[\frac{4}{3}(1-2\,i)\]
  done clear
  C)
   \[\frac{-4}{3}(1+2\,i)\]             
  done clear
  D)
   \[\frac{1}{2}(4+3\,i)\]
  done clear
  View Answer play_arrow

• question_answer16)
  TP and TQ are tangents to the parabola \[{{y}^{2}}=4ax\] at P and Q. If the chord PQ passes through the fixed point [-a, b] then the locus of T is
  A)
   \[ay=2b(x-b)\]              
  done clear
  B)
   \[bx=2a(y-a)\]
  done clear
  C)
   \[by=2a(x-a)\]              
  done clear
  D)
   \[ab=2b(y-b)\]
  done clear
  View Answer play_arrow

• question_answer17)
  The distance of the plane passing through the point P (1, 1, 1) and perpendicular to the line \[\frac{x-1}{3}=\frac{y-1}{0}=\frac{z-1}{4}\] from the origin is
  A)
   \[\frac{3}{4}\]                                     
  done clear
  B)
   \[\frac{4}{3}\]
  done clear
  C)
   \[\frac{7}{5}\]                                     
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer18)
  If the ellipse \[4{{x}^{2}}+9{{y}^{2}}=36\] and the hyperbola \[{{\alpha }^{2}}{{x}^{2}}-{{y}^{2}}=4\] intersects orthogonally, then the value of \[\alpha \] can be
  A)
   5                                
  done clear
  B)
   4
  done clear
  C)
   3                                
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer19)
  The upper \[\left( \frac{3}{4} \right)\]th portion of a vertical pole subtends an angle \[{{\tan }^{-1}}\left( \frac{3}{5} \right)\] at a point in the horizontal plane through its foot and at a distance 40m. from the foot. The height of vertical pole is
  A)
   20m                            
  done clear
  B)
   40m
  done clear
  C)
   60 m                           
  done clear
  D)
   80 m
  done clear
  View Answer play_arrow

• question_answer20)
  The least value of the volume of parallelepiped formed by the vectors \[{{\vec{V}}_{1}}=\hat{i}+\hat{j}\], \[{{\vec{V}}_{2}}=\hat{i}+(2\cos ec\alpha )\hat{j}+\hat{k}\] and \[{{\vec{V}}_{3}}=\hat{j}+(2\cos ec\alpha )\,\hat{k}\] where \[\alpha \in (0,\pi )\], is
  A)
   16                               
  done clear
  B)
   9
  done clear
  C)
   5                                
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer21)
  Consider the following statements

  P: Suman is brilliant

  Q: Suman is rich

  R: Suman is honest

  The negation of the statement 'Suman is brilliant and dishonest if and only if Suman is rich9 can be expressed as
  A)
   \[\sim \left( Q\leftrightarrow (\operatorname{P}\wedge \sim R) \right)\]          
  done clear
  B)
   \[\sim Q\leftrightarrow \sim \operatorname{P}\wedge R\]
  done clear
  C)
   \[\sim (P\wedge \sim R)\leftrightarrow Q\]              
  done clear
  D)
   \[\sim P\wedge (Q\leftrightarrow \sim R)\]
  done clear
  View Answer play_arrow

• question_answer22)
  Let \[a+b+c=s\] and \[\left| \begin{matrix}    s+c & a & b  \\    c & s+a & b  \\    c & a & s+b  \\ \end{matrix} \right|\] is equal to 54, then the value of s is
  A)
   2                                
  done clear
  B)
   3
  done clear
  C)
   4                                
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer23)
  If \[\underset{x\to 1}{\mathop{\lim }}\,\frac{a{{x}^{2}}+bx+c}{{{(x-1)}^{2}}}=2\] then which of the following relation is correct?
  A)
   \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=12\]  
  done clear
  B)
   \[a+c=b\]
  done clear
  C)
   \[{{a}^{2}}+{{c}^{2}}=2b\]           
  done clear
  D)
   \[{{b}^{2}}=2({{a}^{2}}+{{c}^{2}})\]
  done clear
  View Answer play_arrow

• question_answer24)
  If the circle \[{{x}^{2}}+{{y}^{2}}+4x+22y+c=0\] bisects  the circumference of the circle \[{{x}^{2}}+{{y}^{2}}-2x+8y-d=0\] then \[(c+b)\] equals
  A)
   50                               
  done clear
  B)
   52
  done clear
  C)
   54                               
  done clear
  D)
   56
  done clear
  View Answer play_arrow

• question_answer25)
  Let P be a variable point on the ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] with foci at \[{{S}_{1}}\] and \[{{S}_{2}}\]. If A is the area of triangle \[P{{S}_{1}}\,{{S}_{2}}\], then the maximum value of A is
  A)
   12                               
  done clear
  B)
   24
  done clear
  C)
   36                               
  done clear
  D)
   48
  done clear
  View Answer play_arrow

• question_answer26)
  Let \[g(x)\] be a differentiable function on R and\[\int\limits_{\sin \,t}^{1}{{{x}^{2}}g(x)dx=(1-\sin \,t)}\], where \[t\in \left( 0,\frac{\pi }{2} \right)\]. Then the value of \[g\left( \frac{1}{\sqrt{2}} \right)\] equals
  A)
   \[\frac{1}{2}\]                         
  done clear
  B)
   \[\frac{1}{\sqrt{2}}\]
  done clear
  C)
   2                                
  done clear
  D)
   1          
  done clear
  View Answer play_arrow

• question_answer27)
        Let \[f(x)=\int\limits_{0}^{{{x}^{2}}}{\frac{{{t}^{2}}-1}{{{e}^{t}}+1}dt}\] If a is the Point of local maxima and b and \[c(b>c)\] are the points of the local minima, then
  A)
   \[a+b+c=1\]               
  done clear
  B)
   \[a+b=c\]
  done clear
  C)
   \[a+c=b\]                    
  done clear
  D)
   \[b+c=a\]
  done clear
  View Answer play_arrow

• question_answer28)
  Let \[\vec{a}=\hat{i}-2\hat{j}+3\hat{k};\,\vec{b}=\hat{i}+\hat{j}-4\hat{k};\vec{c}=4\hat{i}-3\hat{j}+6\hat{k};\]\[\vec{d}=3\hat{i}-6\hat{j}-5\hat{k}\] then the value of \[\left( \vec{a}\times \vec{b} \right).\left( \vec{c}\times \vec{d} \right)\]is equal to
  A)
   214                             
  done clear
  B)
   342
  done clear
  C)
   392                             
  done clear
  D)
   476
  done clear
  View Answer play_arrow

• question_answer29)
  Consider two lines \[{{L}_{1}}:\frac{x-7}{3}=\frac{y-7}{2}=\frac{z-3}{1}\] and\[{{L}_{2}}:\frac{x-1}{2}=\frac{y+1}{4}=\frac{z+1}{3}\]. lf a line L whose direction ratios are \[\left\langle 2,2,1 \right\rangle \] intersect the lines \[{{L}_{1}}\]and \[{{L}_{2}}\] at A and B then the distance AB is
  A)
   18                               
  done clear
  B)
   24
  done clear
  C)
   36                               
  done clear
  D)
   50
  done clear
  View Answer play_arrow

• question_answer30)
  If P is the affix of z in the Argand diagram and P moves so that \[\frac{z-i}{z-1}\] is always purely imaginary, then the locus of z is a circle whose radius is [Note: \[i=\sqrt{-1}\]]
  A)
   \[\frac{1}{2}\]                                     
  done clear
  B)
   \[\frac{1}{\sqrt{2}}\]
  done clear
  C)
   \[\frac{1}{2\sqrt{2}}\]                          
  done clear
  D)
   \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer31)
  A radio station has two channels. One is AM at 1020 kHz and the other FM at \[89.5\] MHz. For good results you will use.
  A)
  longer antenna for the AM channel and shorter for the FM
  done clear
  B)
   shorter antenna for the AM channel and longer for the FM
  done clear
  C)
   Same length antenna will work for both
  done clear
  D)
   information given is not enough to say which one to use for which.
  done clear
  View Answer play_arrow

• question_answer32)
  When p-n junction is forward biased.
  A)
  depletion layer reduces and barrier height increases.
  done clear
  B)
  depletion layer increases and barrier height reduces
  done clear
  C)
  depletion layer reduces and barrier height reduces
  done clear
  D)
   depletion layer increases and barrier height increases.
  done clear
  View Answer play_arrow

• question_answer33)
  In an inelastic collision, an electron excites a hydrogen atom from its ground state to a M-shell state. A second electron collides instantaneously with the excited hydrogen atom in the M-state and ionizes it. At least how much energy the second electron transfers to the atom in the M-state?
  A)
   \[+3.4\,\,eV\]               
  done clear
  B)
   \[+1.51\,\,eV\]
  done clear
  C)
   \[-3.4\,eV\]                               
  done clear
  D)
   \[-1.51\,eV\]
  done clear
  View Answer play_arrow

• question_answer34)
  \[{{K}_{\alpha }}\] and \[{{K}_{\beta }}\], X-rays are emitted when there is a transition of electron between the levels
  A)
   \[n=2\] to \[n=1\] and \[n=3\] to \[n=1\] respectively
  done clear
  B)
   \[n=2\] to \[n=1\] and \[n=3\] to \[n=2\] respectively
  done clear
  C)
   \[n=3\] to \[n=2\] and \[n=4\] to \[n=2\] respectively
  done clear
  D)
   \[n=3\] to \[n=2\] and \[n=4\] to \[n=3\] respectively
  done clear
  View Answer play_arrow

• question_answer35)
  In Young?s double slit experiment (slit distance d) monochromatic light of wavelength \[\lambda \], is used and the fringe pattern observed at a distance L from the slits. The angular position of the bright fringes are
  A)
   \[{{\sin }^{-1}}\left( \frac{n\lambda }{d} \right)\]                      
  done clear
  B)
   \[{{\sin }^{-1}}\left( \frac{n+\frac{1}{2}\lambda }{d} \right)\]
  done clear
  C)
   \[{{\sin }^{-1}}\left( \frac{n\lambda }{L} \right)\]          
  done clear
  D)
   \[{{\sin }^{-1}}\left( \frac{\left( n+\frac{1}{2} \right)\lambda }{L} \right)\]
  done clear
  View Answer play_arrow

• question_answer36)
  The least angle of deviation for a glass prism is equal to its refracting angle. The refractive index of glass is \[1.5\]. Then the angle of prism is:
  A)
   \[2{{\cos }^{-1}}\left( \frac{3}{4} \right)\]        
  done clear
  B)
   \[{{\sin }^{-1}}\left( \frac{3}{4} \right)\]
  done clear
  C)
   \[2{{\sin }^{-1}}\left( \frac{3}{2} \right)\]         
  done clear
  D)
   \[{{\cot }^{-1}}\left( \frac{3}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer37)
  The electric field of a plane electromagnetic wave varies    with    time    of    amplitude \[2\,V{{m}^{-1}}\] propagating along Z-axis. The average energy density of the magnetic field is (in \[J{{m}^{-3}}\])
  A)
   \[13.29\times {{10}^{-12}}\]               
  done clear
  B)
   \[8.85\times {{10}^{-12}}\]
  done clear
  C)
   \[17.72\times {{10}^{-12}}\]               
  done clear
  D)
   \[4.43\times {{10}^{-12}}\]
  done clear
  View Answer play_arrow

• question_answer38)
  An inductor of 2H and a resistance of \[10\,\Omega \] are connected in series with a battery of 5V. The initial rate of change of current is:
  A)
   \[0.5\,A{{s}^{-1}}\]                            
  done clear
  B)
   \[2.0\,A{{s}^{-1}}\]
  done clear
  C)
   \[2.5\,A{{s}^{-1}}\]                            
  done clear
  D)
   \[0.25\,A{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer39)
  A coil of inductance 300 mH and resistance \[2\,\Omega \] is connected to a source of voltage 2V. The current reaches half of its steady state value is:
  A)
   \[0.05\] s                                  
  done clear
  B)
   \[0.1\] s
  done clear
  C)
   \[0.15\] s                                  
  done clear
  D)
   \[0.3\] s
  done clear
  View Answer play_arrow

• question_answer40)
  In a coil when current changes from 10A to 2A in time \[0.1\] s induced emf is \[3.28\] V. What is self-inductance of coil?
  A)
   4H                              
  done clear
  B)
   \[0.4\] H
  done clear
  C)
   \[0.04\]H                                 
  done clear
  D)
   5H
  done clear
  View Answer play_arrow

• question_answer41)
  A magnet N-S is suspended from a spring and when it oscillates, the magnet moves in and out of the coil C. The coil is connected to a galvanometer G Then, as the magnet oscillates.
  A)
   G shows no deflection                  
  done clear
  B)
   G shows deflection to the left and right but the amplitude steadily decreases.
  done clear
  C)
   G shows deflection to the left and right with constant amplitude
  done clear
  D)
   G shows deflection on one side.
  done clear
  View Answer play_arrow

• question_answer42)
  The heat produced in \[4\,\Omega \] resistance is 10 cal. The heat produced in \[10\,\Omega \] resistance will be:
  A)
   25 cal                          
  done clear
  B)
   14 cal
  done clear
  C)
   10 cal                          
  done clear
  D)
   20 cal
  done clear
  View Answer play_arrow

• question_answer43)
  The current \[{{i}_{1}}\] and \[{{i}_{2}}\]through the resistors \[{{R}_{1}}(=10\,\Omega )\] and \[{{R}_{2}}(=30\,\Omega )\] on the circuit diagram with \[{{E}_{1}}=3\,V\], \[{{E}_{2}}=3\,V\] and \[{{E}_{3}}=2\,V\] are respectively
  A)
   \[0.2\] A, \[0.1\] A         
  done clear
  B)
   \[0.4\] A, \[0.2\] A
  done clear
  C)
   \[0.1\] A, \[0.2\] A         
  done clear
  D)
   \[0.2\] A, \[0.4\] A
  done clear
  View Answer play_arrow

• question_answer44)
  A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities remain unchanged?
  A)
   The charge on the capacitor
  done clear
  B)
   The stored energy in the capacitor
  done clear
  C)
   The potential difference between the plates.
  done clear
  D)
   the electric field in the capacitor.
  done clear
  View Answer play_arrow

• question_answer45)
  Two concentric hollow spherical shells have radii r and \[R(R>>r)\]. A charge Q is distributed on them such that the surface charge densities are equal. The electric potential at the centre is :
  A)
   \[\frac{Q(R+r)}{4\pi {{\varepsilon }_{0}}({{R}^{2}}+{{r}^{2}})}\]    
  done clear
  B)
   \[\frac{Q({{R}^{2}}+{{r}^{2}})}{4\pi {{\varepsilon }_{0}}(R+r)}\]
  done clear
  C)
   \[\frac{Q}{(R+r)}\]                   
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer46)
  A wave has velocity v in medium P and velocity 2v in medium Q. If the wave is incident in medium P at an angle of \[{{30}^{o}}\], then the angle of refraction will be:
  A)
   \[{{30}^{o}}\]                                   
  done clear
  B)
   \[{{45}^{o}}\]
  done clear
  C)
   \[{{60}^{o}}\]                                   
  done clear
  D)
   \[{{90}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer47)
  From an inclined plane two particles are projected with same speed at same angle \[\theta \], one up and other down the plane as shown in figure, which of the following statements is correct?
  A)
   The time of flight of each particle is the same
  done clear
  B)
   The particels will collide the plane with same speed.
  done clear
  C)
   Both the particles strike the plane perpendicular.
  done clear
  D)
   the particles will not collide in mid air even if projected simultaneously and time of flight of each particle is greater then the time of collision.
  done clear
  View Answer play_arrow

• question_answer48)
  A rocket is sent vertically up with a velocity v less than the escape velocity from the earth. Taking  M and R as the mass and radius of the earth, the maximum height h attained by the rocket is given by the following expression.
  A)
   \[{{v}^{2}}{{R}^{2}}/(2GR-Mv)\]     
  done clear
  B)
   \[{{v}^{2}}{{R}^{2}}/(2GM+{{v}^{2}}R)\]
  done clear
  C)
   \[{{v}^{2}}{{R}^{2}}/(2GM-{{v}^{2}}R)\]
  done clear
  D)
   \[{{v}^{2}}{{R}^{2}}/(2Gv+RM)\]
  done clear
  View Answer play_arrow

• question_answer49)
  A vessel contains oil (density \[0.8\,\,gc{{m}^{-3}}\]) over mercury (density \[13.6\,\,gc{{m}^{-3}}\]). A homogeneous sphere floats with half volume immersed in mercury and the other half in oil. The density of the material of the sphere in gem"3 is :
  A)
   \[12.8\]                                    
  done clear
  B)
   \[7.2\]
  done clear
  C)
   \[6.4\]                                      
  done clear
  D)
   \[3.3\]
  done clear
  View Answer play_arrow

• question_answer50)
  A wire fixed at the upper end stretches by length 1 by applying a force F. The work done in stretching is:
  A)
   \[\frac{F}{2\,l}\]                                   
  done clear
  B)
   \[Fl\]
  done clear
  C)
   \[2F\,l\]                                    
  done clear
  D)
   \[\frac{F\,l}{2}\]
  done clear
  View Answer play_arrow

• question_answer51)
  A black body at high temperature T radiates energy at the rate of U (in \[W{{m}^{-2}}\]). When the temperature T falls to half (i.e. \[\frac{T}{2}\]), The radiated energy (in \[W{{m}^{-2}}\]) will be:
  A)
   \[\frac{U}{8}\]                         
  done clear
  B)
   \[\frac{U}{16}\]
  done clear
  C)
   \[\frac{U}{4}\]                                     
  done clear
  D)
   \[\frac{U}{2}\]
  done clear
  View Answer play_arrow

• question_answer52)
  The displacement y of a particle is given by, \[y=4{{\cos }^{2}}\left( \frac{1}{2} \right)\sin (1000\,\,t)\]. This expression may be considered to be a result of the superposition of how many simple harmonic motions?
  A)
   2                                
  done clear
  B)
   3
  done clear
  C)
   1                                
  done clear
  D)
   none
  done clear
  View Answer play_arrow

• question_answer53)
  A 10 kg stone is suspended with a rope of breaking strength 30 kg-wt. The minimum time in which the stone can be raised through a height 10m starting from rest is (Taking: \[g=10\,Nk{{g}^{-1}}\])
  A)
   \[0.5\] s                                   
  done clear
  B)
   1 s
  done clear
  C)
   \[\sqrt{\frac{2}{3}}\] s                          
  done clear
  D)
   2 s 
  done clear
  View Answer play_arrow

• question_answer54)
  A hoop of radius r and mass m rotating with an angular velocity \[\omega {{\,}_{0}}\] is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
  A)
   \[\frac{r\omega {{\,}_{0}}}{4}\]                                   
  done clear
  B)
   \[\frac{r\omega {{\,}_{0}}}{3}\]
  done clear
  C)
   \[\frac{r\omega {{\,}_{0}}}{2}\]
  done clear
  D)
   \[r\omega {{\,}_{0}}\]
  done clear
  View Answer play_arrow

• question_answer55)
  Two blocks of equal masses m are released from the top of a smooth fixed wedge as shown in the figure. The acceleration of the centre of mass of the two blocks is :
  A)
   g                                 
  done clear
  B)
   \[\frac{g}{2}\]
  done clear
  C)
   \[\frac{3g}{4}\]                        
  done clear
  D)
   \[\frac{g}{\sqrt{2}}\]
  done clear
  View Answer play_arrow

• question_answer56)
  Consider an elliptically shaped rail PQ in the vertical plane with \[OP=3\] m and \[OQ=4\]m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see figure). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is \[(n\times 10)\,J\]. The value of n is: (Take acceleration due to gravity \[=10\,\,m{{s}^{-2}}\])
  A)
   50 J                            
  done clear
  B)
   100J
  done clear
  C)
   \[5\times {{10}^{2}}\] J                      
  done clear
  D)
   200 J
  done clear
  View Answer play_arrow

• question_answer57)
  A bob of mass m, suspended by a string of length\[{{l}_{1}}\], is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length\[{{l}_{2}}\], which initially at rest. Both the string are massless and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio \[\frac{{{l}_{1}}}{{{l}_{2}}}\] is:
  A)
   1                    
  done clear
  B)
   3
  done clear
  C)
   4                                
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer58)
  A body thrown vertically up to reach its maximum height in t second, the total time from the time of projection to reach a point at half of its maximum height while returning (in sec) is:
  A)
   \[\sqrt{2}\,t\]                            
  done clear
  B)
   \[\left( 1+\frac{1}{\sqrt{2}} \right)t\]  
  done clear
  C)
   \[\frac{3\,t}{2}\]                                  
  done clear
  D)
   \[\frac{t}{\sqrt{2}}\]
  done clear
  View Answer play_arrow

• question_answer59)
  Let \[[{{\varepsilon }_{0}}]\] denotes the dimensional formula of the permittivity of vacuum. If \[M=\] mass, \[L=\] length, \[T=\] time and \[A=\] electric current, then
  A)
   \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{2}}A]\]
  done clear
  B)
   \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\]
  done clear
  C)
   \[[{{\varepsilon }_{0}}]=[{{M}^{-2}}{{L}^{2}}{{T}^{-1}}{{A}^{-2}}]\]
  done clear
  D)
   \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}{{A}^{-1}}]\]
  done clear
  View Answer play_arrow

• question_answer60)
  Second law of thermodynamics is equivalent to :
  A)
   In general no engine has a efficiency of 100%
  done clear
  B)
   Random motion cannot be completely ordered 
  done clear
  C)
   Heat cannot be fully converted into work
  done clear
  D)
   All the above.
  done clear
  View Answer play_arrow

• question_answer61)
  Electrode potential for Zn electrode varies according to the equation.   \[{{E}_{z{{n}^{2+}}\left| Zn \right.}}=E_{Z{{n}^{2+}}\left| Zn \right.}^{o}-\frac{0.059}{2}\log \frac{1}{[Z{{n}^{2+}}]}\]. The graph of \[{{E}_{Z{{n}^{2+}}\left| zn \right.}}vs\log [Z{{n}^{2+}}]\]
  A)
          
  done clear
  B)
       
  done clear
  C)
           
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer62)
  The edge lengths of the unit cells in terms of the radius of spheres constituting fee ,bcc and simple cubic unit cell are respectively -
  A)
   \[2r,\frac{4r}{\sqrt{3}},2\sqrt{2}\]         
  done clear
  B)
   \[\frac{4r}{\sqrt{3}},2\sqrt{2},2r\]
  done clear
  C)
   \[2r,2\sqrt{2}r,\frac{4r}{\sqrt{3}}\]        
  done clear
  D)
   \[2\sqrt{2r},\frac{4r}{\sqrt{3}},2r\]
  done clear
  View Answer play_arrow

• question_answer63)
  For a given reaction A \[\to \] Product, rate is \[1\times {{10}^{-4}}M{{s}^{-1}}\]when \[[A]=0.01\] M and rate is \[1.41\times {{10}^{-4}}M{{s}^{-1}}\]when \[[A]=0.02\] M. Hence, rate law is:
  A)
   \[-\frac{d[A]}{dt}=\frac{k}{4}[A]\]        
  done clear
  B)
   \[-\frac{d[A]}{dt}=k{{[A]}^{1/2}}\]
  done clear
  C)
   \[-\frac{d[A]}{dt}=\frac{k}{4}[A]\]        
  done clear
  D)
   \[-\frac{d[A]}{dt}=k{{[A]}^{1/2}}\]
  done clear
  View Answer play_arrow

• question_answer64)
  A buffer solution is prepared in which the concentration of \[N{{H}_{3}}\] is \[0.30\] M and the concentration of \[N{{H}_{4}}^{+}\] is \[0.20\] M. If the equilibrium constant, \[{{K}_{b}}\] for \[N{{H}_{3}}\] equals\[1.8\times {{10}^{-5}}\], what is the pH of this solution? \[(\log 2.7=0.433)\].
  A)
   \[9.08\]                                    
  done clear
  B)
   \[9.43\]
  done clear
  C)
   \[11.72\]                                  
  done clear
  D)
   \[8.73\]
  done clear
  View Answer play_arrow

• question_answer65)
  A and B will be respectively:
  A)
   \[CuO,Cu{{(OH)}_{2}}\]          
  done clear
  B)
   \[Cu{{(OH)}_{2}}(CuO\]
  done clear
  C)
   \[Cu,\,CuO\]                             
  done clear
  D)
   \[CuO,Cu\]
  done clear
  View Answer play_arrow

• question_answer66)
  Borax structure contains:
  A)
   two \[B{{O}_{4}}\] groups and two \[B{{O}_{3}}\] groups
  done clear
  B)
  \[N{{a}_{2}}{{B}_{4}}{{O}_{2}},\,\,10{{H}_{2}}O\] \[\{N{{a}_{2}}[{{B}_{4}}{{O}_{5}}{{(OH)}_{4}}]\,8{{H}_{2}}O\}\]  four \[B{{O}_{4}}\] groups only
  done clear
  C)
   four \[B{{O}_{3}}\] groups only
  done clear
  D)
   three \[B{{O}_{4}}\] and one \[B{{O}_{3}}\] groups
  done clear
  View Answer play_arrow

• question_answer67)
  A complex cation is formed by Pt (in some oxidation state) with ligands (in proper number so that coordination number of Pt becomes six). Which of the following can be its correct IUPAC name
  A)
   Diaquaethylenediaminedithiocyanato-S platinum(IV) ion
  done clear
  B)
   Diaquaethylenediammedithiocyanato-S- platinate(IV) ion
  done clear
  C)
   Diaquaethylenediaminedithiocyanato-S-platinum(ll) ion
  done clear
  D)
   Diaquabis (ethylenediamine) dithiocyanate-S-platinum(IV) ion
  done clear
  View Answer play_arrow

• question_answer68)
  1 g sample of alkaline earth metal react completely with \[4.08\,g{{H}_{2}}S{{O}_{4}}\] and yield an ionic product \[MS{{O}_{4}}\]. Then find out the atomic mass of Alkaline earth metal (M)?
  A)
   9                                
  done clear
  B)
   24
  done clear
  C)
   40                               
  done clear
  D)
   87
  done clear
  View Answer play_arrow

• question_answer69)
  At Boyle's temperature, the graph of z v/s P is drawn select correct graph.
  A)
         
  done clear
  B)
    
  done clear
  C)
        
  done clear
  D)
    
  done clear
  View Answer play_arrow

• question_answer70)
  Which does not represent correct method?    
  A)
   \[C{{r}_{2}}{{O}_{3}}+2Al\xrightarrow{{}}A{{l}_{2}}{{O}_{3}}+2Fe\]: Thermite process
  done clear
  B)
   \[Ni{{(CO)}_{4}}\xrightarrow{{}}Ni+4Co\]: Mond process
  done clear
  C)
   \[Ni{{(CO)}_{4}}\xrightarrow{{}}2Ag+C{{O}_{2}}+\frac{1}{2}{{O}_{2}}\]: Van Arkel
  done clear
  D)
   \[Zr{{l}_{4}}\xrightarrow{{}}Zr+2{{l}_{2}}\]    : Van Arkel
  done clear
  View Answer play_arrow

• question_answer71)
  Number of 2 centre-2-electron bond in \[{{B}_{2}}{{H}_{6}}\].
  A)
   1                    
  done clear
  B)
   2
  done clear
  C)
   3                                
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer72)
  Among the following statements which is INCORRECT ;
  A)
   In the preparation of compounds of Xe, Bartlett had taken \[{{O}_{2}}P\,t{{F}_{6}}\] as a base compound because both \[{{O}_{2}}\] and Xe have almost same ionisation enthalpy.
  done clear
  B)
   Nitrogen does not show allotropy.
  done clear
  C)
   A brown ring is formed in the ring test for \[N{{O}_{3}}^{-}\] ion. It is due to the formation of \[{{[Fe{{({{H}_{2}}O)}_{5}}(NO)]}^{2+}}\]
  done clear
  D)
   On heating with concentrated NaOH solution in an inert atmosphere of \[C{{O}_{2}}\], red phosphorus gives \[P{{H}_{3}}\] gas.
  done clear
  View Answer play_arrow

• question_answer73)
  If for the equilibrium: \[N{{H}_{2}}COON{{H}_{4}}(s)\overset{{}}{leftrightarrows}\]          \[{{N}_{2}}(g)+3{{H}_{2}}(g)+CO(g)+\frac{1}{2}{{O}_{2}}(g)\]the value of Kp at 800 K is \[27\times {{2}^{\lambda /2}}\] and the equilibrium pressure is 22 atm value of \[\lambda \] is:
  A)
   12                               
  done clear
  B)
   21
  done clear
  C)
   10                               
  done clear
  D)
   11
  done clear
  View Answer play_arrow

• question_answer74)
  Which of the following is not correctly matched?
  A)
   Sodium (ethylene diammetetraacetato) chromate(ll)- Na,[Cr(CH3COO)/en)]
  done clear
  B)
   Dichloridobis (efhane-l, 2-diamine)cobalt (lll) ion-\[{{[Co{{(Cl)}_{2}}{{(en)}_{2}}]}^{+}}\]
  done clear
  C)
   Tris(bipyridyl)iron(U)ion-\[[Fe(N{{H}_{4}}C-{{C}_{5}}-{{C}_{5}}{{H}_{6}}N)B{{r}_{2}}]\]
  done clear
  D)
   Ammineaquadibromido copper(ll)-\[[Cu(N{{H}_{3}})\,\,({{H}_{2}}O)\,\,B{{r}_{2}}]\]
  done clear
  View Answer play_arrow

• question_answer75)
  In which of the following transitions does not emit photons?
  A)
   \[2{{p}_{x}}\xrightarrow{{}}3{{p}_{x}}\]        
  done clear
  B)
   \[4s\xrightarrow{{}}3{{d}_{{{x}^{2}}-{{y}^{2}}}}\]
  done clear
  C)
   \[2{{p}_{x}}\xrightarrow{{}}3{{p}_{y}}\]        
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer76)
  Which of the following statements are correct:

  [A] Principle of chromatographic operation is adsorption.

  [B] For adsorption \[\Delta G<O,\Delta S<O,\Delta H<O\]

  [C] Freundlich adsorption isotherm equation \[\frac{x}{m}=K{{p}^{-n}}\]

  [D] Zeolites are used as catalyst in petrochemical industries during craking.

  [E] In chemical adsorption, multilayer may be formed on adsorbent.

  A)
   A, B, D, E                   
  done clear
  B)
   E, C, D
  done clear
  C)
   A, B, D                       
  done clear
  D)
   B, C, E 
  done clear
  View Answer play_arrow

• question_answer77)
  Which of the following statement(s) for crystal having schottky defect is incorrect.
  A)
   Schottky defect arises due to absence of cations & anion from positions which they are expected to occupy.
  done clear
  B)
   The density of crystal having schottky defect is smaller than that of perfect crystal.
  done clear
  C)
   Schottky defect are more common in co valent compound with higher co-ordination number.
  done clear
  D)
   The crystal having schottky defect is electrically neutral as a whole.
  done clear
  View Answer play_arrow

• question_answer78)
  In the ostwahTs process, nitric acid is prepared by the catalytic oxidation of:
  A)
   \[{{N}_{2}}\]                                      
  done clear
  B)
   \[N{{H}_{3}}\]
  done clear
  C)
   \[{{N}_{2}}{{O}_{5}}\]                                 
  done clear
  D)
   \[N{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer79)
  The vapour pressure of the solution of two liquids \[A({{p}^{o}}=80\,mm)\] and \[B({{p}^{o}}=120\,mm)\] is found to be 100 mm when \[{{x}_{A}}=0.4\]. The result shows that
  A)
   solution exhibits ideal behaviour
  done clear
  B)
   solution shows positive deviations
  done clear
  C)
   solution shows negative deviations
  done clear
  D)
   solution will show positive deviations for lower concentration and negative deviations for higher concentrations.
  done clear
  View Answer play_arrow

• question_answer80)
  The thermal stability of hydrides of oxygen family is in order:
  A)
   \[{{H}_{2}}Po<{{H}_{2}}Te<{{H}_{2}}Se<{{H}_{2}}S<{{H}_{2}}O\]
  done clear
  B)
   \[{{H}_{2}}Po<{{H}_{2}}O<{{H}_{2}}Te<{{H}_{2}}Se<{{H}_{2}}S\]
  done clear
  C)
   \[{{H}_{2}}S<{{H}_{2}}O<{{H}_{2}}Te<{{H}_{2}}Se<{{H}_{2}}Po\]
  done clear
  D)
   \[{{H}_{2}}O<{{H}_{2}}S<{{H}_{2}}Te<{{H}_{2}}Se<{{H}_{2}}Po\]
  done clear
  View Answer play_arrow

• question_answer81)
  Which of the following is a non reducing sugar?
  A)
   \[OHC{{H}_{2}}-\underset{\begin{smallmatrix}  || \\  O \end{smallmatrix}}{\mathop{C}}\,-{{(CHOH)}_{3}}-C{{H}_{2}}OH\]
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
     
  done clear
  View Answer play_arrow

• question_answer82)
  Which of the following is nucleophilic addition reaction:
  A)
   \[C{{H}_{3}}COCl\xrightarrow{C{{H}_{3}}MgBr(1eq.)}C{{H}_{3}}COC{{H}_{3}}\]
  done clear
  B)
   \[C{{H}_{3}}COCl\xrightarrow{{{l}_{2}}/O{{H}^{-}}/\Delta }C{{H}_{3}}CO{{O}^{-}}+CH\,{{l}_{3}}\]
  done clear
  C)
   \[PhCHO\xrightarrow{KCN/{{H}^{\oplus }}}PhCH(OH)(CN)\]
  done clear
  D)
   \[C{{H}_{3}}C\equiv CMgBr\xrightarrow{C{{H}_{3}}Br}C{{H}_{3}}C\equiv CC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer83)
  Arrange the following compounds in decreasing order of reactivity for hydrolysis reaction:

  (I)  \[{{C}_{6}}{{H}_{5}}COOC{{H}_{3}}\]

  (II)

  (III)

  (IV)

  A)
   \[II>IV>I>III\]             
  done clear
  B)
   \[II>IV>III>I\]
  done clear
  C)
   \[I>II>III>IV\]             
  done clear
  D)
   \[IV>III>II>I\]
  done clear
  View Answer play_arrow

• question_answer84)
  A carbonyl compound on reaction with dilute NaOH gives 2-ethyl-3-hydroxy hexanal. The carbonyl compound is:
  A)
   propanal                     
  done clear
  B)
   propanone
  done clear
  C)
   butanal                        
  done clear
  D)
   butanone
  done clear
  View Answer play_arrow

• question_answer85)
  Which of the following is insoluble in NaOH:
  A)
                              
  done clear
  B)
   
  done clear
  C)
            
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer86)
  The major product obtained on acid catalyzed hydration of 3-Phenylbut-l-ene is:  
  A)
   3-Phenyl butane-2-ol     
  done clear
  B)
   2-Phenyl butane-2-ol
  done clear
  C)
   2-Phenyl butane-3-ol 
  done clear
  D)
   2-Phenyl butan-1 ?ol
  done clear
  View Answer play_arrow

• question_answer87)
  Which of the following is a C-4 epimer of D-glucose :
  A)
              
  done clear
  B)
   
  done clear
  C)
                         
  done clear
  D)
    
  done clear
  View Answer play_arrow

• question_answer88)
  The acidic strength order is          
  A)
   \[1>2>3>4\]               
  done clear
  B)
   \[1>4>2>3\]
  done clear
  C)
   \[1>2>4>3\]               
  done clear
  D)
   \[1>3>4>2\]
  done clear
  View Answer play_arrow

• question_answer89)
  Polymer obtained by the given compound is
  A)
   Urea formaldehyde resin
  done clear
  B)
   Phenol formaldehyde resin
  done clear
  C)
   Alkyl resin
  done clear
  D)
   Melamine formaldehyde resin
  done clear
  View Answer play_arrow

• question_answer90)
  Which of the following statement is not true?
  A)
   Some disinfectants can be used as antiseptics at low concentration
  done clear
  B)
   Sulphadizine is a synthetic antimalarial
  done clear
  C)
   Ampicillin is a natural antibiotic
  done clear
  D)
   Aspirin is both analgesic and antipyretic
  done clear
  View Answer play_arrow