Bee Quiz

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

If   \(\displaystyle\int f(x) \cos x \:dx=\frac 1 2 [f(x)]^2 +C\)   and  \(f(0)=0\)  then  \(f'(0)=\)  ________

(a) 1                            (b)  -1

(c) 0                            (d) 5

A fair coin is tossed at a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 heads, then the probability of getting exactly one head is 

________

(A)  \(\frac {1} {64}\)

(B)  \(\frac {1} {32}\)

(C)  \(\frac {1} {16}\)

(D)  \(\frac {1} {8}\)

The transformation due to reflection of (x,y) through the origin is described by the matrix

_____  

(A)   \(\begin{pmatrix}
-1 & 0 \\
0 & -1
\end{pmatrix}\)                              (C)  \(\begin{pmatrix}
0 & -1 \\
-1 & 0
\end{pmatrix}\)

(B)   \(\begin{pmatrix}
-1 & 0 \\
0 & 1
\end{pmatrix}\)                                  (D)   \(\begin{pmatrix}
1 & 0 \\
0 & -1
\end{pmatrix}\)

A gas satisfies the relation \(PV^{5/3}=K\),where P is pressure ,V is volume and K is constant.

The dimension of constant K are_________

(A) \([ML^4 T^{-2}]\)

(B) \([ML^2 T^{-2}]\)

(C) \([ML^6 T^{-2}]\)

(D) \([ML T^{-2}]\)

The Value of the sum  \(\displaystyle \sum_{n=1}^{13} (i^n +i^{n+1})\)   where  \(i=\sqrt{-1}\)  equals __________

(A)  i

(B) i-1

(C) -i 

(D) 0

which of the following products are formned on hydrolysis of \(NaO_2\)?

(A) NaoH                    (B) \(H_2O_2\)

(C) \(O_2\)                          (D) \(H_2O\)

(a) A,D                          (b) A,C,D

(c) A,B,D                        (d) A,B,C

If  \(\sec 2 \theta =p+\tan 2 \theta\)  then the value of  \(\sin ^2 \theta\)   in terms of p is given by _________

(A)  \(\frac {(p-1)^2} {2 (p^2+1)}\)

(B) \(\frac 1 2 \Big( \frac {p-1} {p+1}\Big) ^2\)

(C) \(\frac {p^2-1} {2(p^2+1)}\)

(D) \(\frac {p^2-1} {2(p+1)^2}\)

A hollow convex lens made of glass will behave like a 

(a) Convex lens 

(b) concave lens 

(c) glass plate 

(d) mirror

(A)  0

(B)  -16

(C) 16

(D)  -11

The number of common tangents to the circles \(x^2+y^2=4\)  and \(x^2+y^2-6x-8y-24=0\)   is__________

(A) 3

(B) 4

(C) 2

(D) 1

The number of ways of dividing 20 persons  into 10 couples  _____

(A)  \(\frac {20!} {2^{10}}\)

(B) \(^{20} C_{10}\)

(C) \(\frac {20!} {(2!)^9}\)

(D) None of these

What is the hybridisation state of benzyl carbonium ion

(A)  \(sp^3\)

(B) \(sp^2\)

(C) \(spd^2\)

(D) \(sp^2d\)

A ray of light incident at an angle  \(\theta\)  on a refracting face of a prism emerges from the other face normally.If the angle of the prism is \(5^0\)   and  the prism is made of a material of refractive index 1.5,the angle of incidence is

(A) \(7.5^0\)

(B) \(5^0\)

(C) \(15^0\)

(D) \(2.5^0\)

A ray of light incident at an angle  \(\theta\)  on a refracting face of a prism emerges from the other face normally.If the angle of the prism is \(5^0\)   and  the prism is made of a material of refractive index 1.5,the angle of incidence is

(A) \(7.5^0\)

(B) \(5^0\)

(C) \(15^0\)

(D) \(2.5^0\)