Bee Quiz

What are the zeroes of   \(f(x)=8x^3-2x^2-3x\)  ?

(a)  \(\{ -\frac 1 2 \:,\frac 3 4\:\}\)                   (b) \(\{ -\frac 3 4\: ,\frac 1 2\:\}\)

(c) \(\{ -\frac 1 2\: ,\frac 1 2\: ,\frac 3 4\:\}\)               (d) \(\{ -\frac 1 2\:,0\:,\frac 3 4\:\}\)

How many lines of symmetry does a rhombus have?

(a) 0                                          (b)  1

(c) 2                                           (d) 3

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in young's double-slit experiment is ______

(a) infinite                                 (b) five

(c) three                                    (d) zero

\(\frac {(n!)^2} {[(n-1)!]^2}=\)

(a)  \(2n\)                                    (b) \(n\)

(c)  \(n^2\)                                     (d)  \(n^4\)

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in young's double-slit experiment is ______

(a) infinite                                 (b) five

(c) three                                    (d) zero

If   \(\frac {n} {x^2-36}=\frac {1} {x-6} +\frac {1} {x+6}\)  then n = _______

(a)  \(x\)                              (b) \(2x\)

(c)  \(2(x+6)\)                   (d) \(2(x-6)\)

A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time is given by _________

(a)  \(\frac 1 2 \frac {mv^2} {T^2} t\)                                           (b)  \(\frac 1 2 \frac {mv^2} {T^2} t^2\)

(c)  \( \frac {mv^2} {T^2} t\)                                              (d) \(\frac {mv^2} {T^2} t^2\)

what is the sum of the infinite series? 

\(1-\frac {1} {5}+\frac {1} {25}-\frac{1} {125}+...........?\)

(a)  \(\frac 5 6\)                                   (b) \(\frac 1 5\)

(c)  \(\frac 6 5\)                                    (d)  \(-\frac {5} {6}\)

The solution of the differential equation   \(y\:dx+(x+x^2y)\:dy=0\)  is ______

(a)  \(\log y =Cx\)                                            (b)  \(-\frac {1} {xy}+\log y=C\)

(c)  \(\frac {1} {xy}+\log y=C\)                                      (d)  \(-\frac {1} {xy}=C\)

The solution of the Differential equation  \(\frac {dy} {dx}=\frac {x+y} {x}\)  satisfying the condition  \(y(1)=1\)  is ______

(a) \(y=x \ln x+x\)

(b)  \(y= \ln x+x\)

(c) \(y=x \ln x+x^2\)

(d) \(y=x\: e^{(x-1)}\)

Two lenses of power -15 D and +5D are in contact with each other. The focal length of the combination is ____

(a) +10 cm                                (b) -20 cm

(c) -10cm                                  (d) + 20 cm 

If the roots of the quadratic equation  \(x^2+px+q=0\)  are  \(\tan 30^0\)  and  \(\tan 15^0\)  respectively then the value of \(2+q-p\)   is _____

(a)  2                    (b) 3                   (c) 0                           (d) 1

The function  \(f(x)= \frac {x} {1-2^x}-\frac {x} {2}\)  is   _____

(a) An even but not odd function

(b) An odd but not even function

(c) A both even and odd function

(d) A neither even nor odd function

 A  wheel whose moment of inertia is  \(12kg\:m^2\) has an initial angular velocity of 40 rad/s.A constant torque of 20 Nm acts on the wheel. The time in which the wheel is accelerated to 100 rad/s is _____

(a) 72 second                                   (b) 16 second 

(c) 8 second                                      (d) 36 second 

If     \(\displaystyle\int_{0}^{\pi} x f(\sin x ) \: dx=A\int_{0}^{\frac {\pi} {2}} f(\sin x) \: dx\)  then  A is ____

(a)  \(\frac {\pi} {4}\)                              (b)  \(\pi\)

(c)  0                               (d)  \(2\pi\)

Let   \(f(x)=(x+|x|) |x|\)  then, for all x

(a)  \(f\)  is continuous

(b) \(f\)   is differentiable for some x

(c)  \(f^{'}\) is continuous

(d)  \(f^{''}\)  is continuous

Let \(\epsilon_0\)  denote the  dimenstional formula of the permittivity of vacuum .If M=mass,L= length ,T=time and A= electric current ,then ___________

(a)  \([\epsilon_0]=[M^{-1} L^2 T^{-1} A]\)

(b) \([\epsilon_0]=[M^{-1} L^{-3} T^{2} A]\)

(c) \([\epsilon_0]=[M^{-1} L^{-3} T^{4} A^2]\)

(d) \([\epsilon_0]=[M^{-1} L^2 T^{-1} A^{-2}]\)

\(x-5y=2\)  and  \(3x+y=6\)   , \((xy)^2\)  =  ______

(a) 0                                        (b) 1

(c) 4                                        (d) 9

\(\displaystyle\lim_{n\to\infty}\bigg[\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{n(n+1)}\bigg]\) is equal to

(a) 1                                       (b) - 1

(c) 0                                       (d) None of these

The electric potential at any point is \(V=-5x+3y+\sqrt{15z},\) then the magnitude of the electric field is

(a) \(3\sqrt 2\)

(b) \(4\sqrt 2\)

(c) \(5\sqrt 2\)

(d) \(7\)

sodium and copper have work functions 2.3eV and 4.5 eV respectively. Then the ratio of the wavelengths of  sodium compared to copper is nearest to ________

(a) 1:2                          (b) 4:1

(c) 2:1                          (c) 1:4

The velocity of a particle is \(v=v_0+gt+ft^2\)  .If its position is  \(x=0\)  at  \(t=0\) then its displacement after unit time \((t=1)\)  is ________

(a)  \(v_0+\frac {g} {2} +f\)                                                   (b) \(v_0+2g+3f\)

(c)  \(v_0+\frac {g} {2} +\frac f 2\)                                                   (d)  \(v_0+g+f\)

Six identical coins are arranged in a row, the number of ways in which the number of trials is equal to the number of heads is _____

(a)  9                                               (b)  20

(c)  40                                             (d)  120

If  \(f(x)=\frac {(3x+2)}{ (5x-3)} \)  then _____

(a)   \(f^{-1} (x)=-f(x)\)

(b) \(f^{-1} (x)=f(x)\)

(c)  \(fo (f(x))=-x\)

(d)  \(f^{-1} (x)=-\frac {1} {19}\:f(x)\)

The average depth of the Indian ocean is about 3000m. The value of fractional compression of water at the bottom of the ocean is _____

(given that bulk modulus of water  is   \(2.2\times 10^9 Nm^{-2}\)  ,\(g=9.8\) ,\(\rho_{H_2O}=1000kg.m^{-3}\) )

(a) \(3.4 \times 10^{-2}\)

(b) \(1.34\times 10^{-2}\)

(c) \(4.13\times 10^{-2}\)

(d)  \(13.4\times 10^{-2}\)

The value of     \(I=\displaystyle \int_{o}^{\frac {\pi} {2}} \frac {(\sin x +\cos x )^2} {\sqrt{1+\sin 2x}}\: dx\)    is _______

(a) 2                                  (b) 1

(c) 0                                   (d) 3

A body of mass m is accelerated niformly from rest to a speed V in a time T. The instantaneous power delivered to the dody as a function of time is given by ________

(a)  \(\frac 1 2 \frac {mv^2} {T^2} t\)

(b)  \(\frac 1 2 \frac {mv^2} {T^2} t^2\)

(c) \( \frac {mv^2} {T^2} t\)

(d)  \( \frac {mv^2} {T^2} t^2\)

The axis of  a parabola is long the line  \(y=x\)  and the distances of its vertex and focus from origin are  \(\sqrt{2} \)  and   \(2\sqrt{2} \)  respectively.If vertex and focus both lie in the first quadrant.Then the equation of the parabola is ______

(a) \((x+y)^2=(x-y-2)\)

(b) \((x-y)^2=(x-y-2)\)

(c) \((x-y)^2=4(x+y-2)\)

(d) \((x-y)^2=8(x+y-2)\)

Let \(f:[0,2]\to R\)  be  function which is continuous on [0,2] and is differentiable on (0,2) with \(f(0)=1\)  .Let  \(F(x)=\displaystyle\int_{0}^{x^2} f(\sqrt{t}) dt\)   for  \(x\in [0,2]\)  . If  \(F'(x)=f'(x)\)  for all  \(x\in (0,2)\)  then F(2) equals 

(a) \(e^2-1\)

(b) \(e^4-1\)

(c) \(e-1\)

(d)  \(e^4\)

One mole of an ideal gas undergoes a process   \(P=P_0\Big[ 1+ \Big( \frac {2V_0} {V}\Big)^2\Big]^{-1}\)   where  \(P_0,V_0\)  are constants.Change in temperature  of the gas when volume is changed from  \(V=V_0\)  to \(V=2V_0\)  is _______

(a) \(\frac {4} {5} \frac {P_0V_0} {nR}\)

(b) \(\frac {3} {4} \frac {P_0V_0} {nR}\)

(c) \(\frac {2} {3} \frac {P_0V_0} {nR}\)

(d) \(\frac {7} {9} \frac {P_0V_0} {nR}\)