Question

**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**

Answer

Answer is : a

Your answer : c

Your answer : c

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

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

Answer

Answer is : c

Your answer : c

Your answer : c

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

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

(a) 0 (b) 1

(c) 4 (d) 9

Answer

Answer is : a

Your answer : a

Your answer : a

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

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

**(a) 1 (b) - 1**

**(c) 0 (d) None of these**

Answer

Answer is : a

Your answer : d

Your answer : d

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \(7\)**

Answer

Answer is : d

Your answer : c

Your answer : c

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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**

Answer

Answer is : c

Your answer : b

Your answer : b

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \(v_0+g+f\)**

Answer

Answer is : c

Your answer : c

Your answer : c

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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**

Answer

Answer is : b

Your answer : d

Your answer : d

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

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

Answer

Answer is : b

Your answer : a

Your answer : a

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \(13.4\times 10^{-2}\)**

Answer

Answer is : b

Your answer : b

Your answer : b

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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**

Answer

Answer is : a

Your answer : a

Your answer : a

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \( \frac {mv^2} {T^2} t^2\)**

Answer

Answer is : c

Your answer : b

Your answer : b

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \((x-y)^2=8(x+y-2)\)**

Answer

Answer is : d

Your answer : c

Your answer : c

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \(e^4\)**

Answer

Answer is : b

Your answer : c

Your answer : c

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

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

Answer

Answer is : a

Your answer : c

Your answer : c

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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**

Answer

Answer is : a

Your answer : a

Your answer : a

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \(\frac {1} {8}\)**

Answer

Answer is : B

Your answer : B

Your answer : B

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

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

**_____ **

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

0 & -1 \\

-1 & 0

\end{pmatrix}\)

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

Answer

Answer is : A

Your answer : B

Your answer : B

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \([ML T^{-2}]\)**

Answer

Answer is : A

Your answer : C

Your answer : C

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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**

Answer

Answer is : B

Your answer : C

Your answer : C

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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**

Answer

Answer is : d

Your answer : b

Your answer : b

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

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

Answer

Answer is : A

Your answer : D

Your answer : D

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**A hollow convex lens made of glass will behave like a **

**(a) Convex lens **

**(b) concave lens **

**(c) glass plate **

**(d) mirror**

Answer

Answer is : c

Your answer : c

Your answer : c

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**(A) 0**

**(B) -16**

**(C) 16**

**(D) -11**

Answer

Answer is : D

Your answer : C

Your answer : C

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

Answer

Answer is : 1

Your answer : 4

Your answer : 4

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

T**he 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**

Answer

Answer is : B

Your answer : C

Your answer : C

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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**

Answer

Answer is : D

Your answer : C

Your answer : C

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**What is the hybridisation state of benzyl carbonium ion**

**(A) \(sp^3\)**

**(B) \(sp^2\)**

**(C) \(spd^2\)**

**(D) \(sp^2d\)**

Answer

Answer is : B

Your answer : B

Your answer : B

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \(2.5^0\)**

Answer

Answer is : A

Your answer : A

Your answer : A

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated

Question

**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) \(2.5^0\)**

Answer

Answer is : A

Your answer : A

Your answer : A

Solution

Solution image not uploaded

Formula

Formula image not uploaded

More information

Topic image not updated

More information not updated