Bee Quiz

The minimum distance between a point on the curve \(y=e^x\) and a point on the curve \(y=\log _ex\) is

(a) \(\frac{1}{\sqrt{2}}\)

(b) \(\sqrt{2}\)

(c) \(\sqrt{3}\)

(d) \(2\sqrt{2}\)

Let \(a=\hat{i}+\hat{j}+\hat{k},b=\hat{i}-\hat{j}+\hat{k},a\times b=b+\lambda \ a\ and\ a\cdot c=1,\) then which of the following is true

(a) \([a\ b\ c]=-\frac{8}{3}\ and\ \lambda=-\frac{1}{3}\)

(b)  \([a\ b\ c]=\frac{8}{3}\ and\ \lambda=-\frac{1}{3}\)

(c) \([a\ b\ c]=-\frac{8}{3}\ and\ \lambda=-\frac{2}{3}\)

(d) \([a\ b\ c]=-\frac{8}{3}\ and\ \lambda=\frac{2}{3}\)

According to Newton's law of cooling, the rate of cooling of a body  is proportional to  \((\triangle \theta)^n\), where \(\triangle \theta\) is the difference of the temperature of the body and the surroundings and n is equal to  ____

(a) 2                                         (b) 3

(c) 4                                         (d) 1

If  \(a>0\)  and discriminant of  \(ax^2+2bx+c\)  is -ve  then 

\(\begin{vmatrix}
a & b & ax+b\\
b & c & bx+c\\
ax+b &bx+c&0
\end{vmatrix}\)   is ______

(a) +ve                         (b) \((ac-b^2) ( a x^2+2bx+c)\)

(c) -ve                          (d) 0

In the real number system, the equation \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\) has

(a) no solution

(b) exactly two distinct solutions

(c) exactly four distinct solutions

(d) infinitely many solutions

The angle \(\alpha,\beta,\gamma\) of a triangle satisfy the equation \(2\sin\alpha + 3\cos\beta =3\sqrt 2\) and \(3\sin\beta+2\cos\alpha=1.\) Then, \(\gamma\) equal

(a) \(150^\circ\)

(b) \(120^\circ\)

(c) \(60^\circ\)

(d) \(30^\circ\)

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelength \(\lambda_1:\lambda_2\) emitted in the two cases is

(a) 7/5

(b) 27/20

(c) 27/5

(d) 20/7

The force F acting on a particle of mass m indicated by force-time graph shown below.

The change in momentum of the particle over the time interval from zero to 8 s is

(a) 24 Ns

(b) 20 Ns

(c) 12 Ns

(d) 6 Ns

Consider the following statements:

I. \(\lim\limits_{n\to\infty}\frac{2^n+(-2)^n}{2^n}\) does not exist

II. \(\lim\limits_{n\to\infty}\frac{3^n+(-3)^n}{4^n}\) does not exist

Then, 

(a) I is true and II is false

(b) I is false and II is true

(c) I and II are true

(d) Neither I nor II is true

In the figure, galvanometer \(G\) gives maximum deflection when 

(a) magnet is pushed into the coil

(b) magnet is rotated into the coil

(c) magnet is stationary at the centre of the coil

(d) number of turns in the coil is reduced 

The order of reactivity in nucleophilic substitution reaction is

(a) \(\text {CH}_3\text F\lt\text {CH}_3\text {Cl} \lt\text {CH}_3\text I\lt\text {CH}_3\text {Br} \)              (b) \(\text {CH}_3\text F\lt\text {CH}_3\text {Cl} \lt\text {CH}_3\text {Br}\lt\text {CH}_3\text {I} \)

(c) \(\text {CH}_3\text F\lt\text {CH}_3\text {Br} \lt\text {CH}_3\text {Cl}\lt\text {CH}_3\text {I} \)              (d) \(\text {CH}_3\text I\lt\text {CH}_3\text {Br} \lt\text {CH}_3\text {Cl}\lt\text {CH}_3\text {F} \)

A circular loop of radius \(R\) carrying a current \(l\) is placed in a uniform magnetic field \(B\) perpendicular to the loop. The force on the loop is

(a) \(2\pi RI B\)

(b) \(2\pi R I^2 B^3\)

(c) \(\pi R^2IB\)

(d) zero

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