Question

If \(\log _{10}a+\log _{10}b=\log_{10}(a+b)\) then

(a) \(a=\frac{b^2}{1-b}\)

(b) \(a=\frac{b}{1-b}\)

(c) \(a=\frac{b}{b-1}\)

(d) \(a=\frac{b}{a+b}\)

Answer

Answer is : c

Your answer : b

Your answer : b

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Question

**The wrong unit conversion among the following is **

**(a) \(1\) angstrom \(= 10^{-10} \text m \)**

**(b) \(1\) fermi \(= 10^{-15 }\text m \)**

**(c) \(1\) light year \(= 9.46 \times 10^{15}\text m \)**

**(d) \(1\) astronomical unit \(= 1.496 \times 10^{-11} \text m\)**

Answer

Answer is : d

Your answer : a

Your answer : a

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Question

**A railway engine is travelling along a circular railway track of radius 1500 metres with a speed of 66 km/hr. Find the angle turned by the engine in 10 seconds.**

**(a) \(10^\circ\)**

**(b) \(7^\circ\)**

**(c) \(11^\circ\)**

**(d) \(8^\circ\)**

Answer

Answer is : b

Your answer : b

Your answer : b

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Question

**A railway engine is travelling along a circular railway track of radius 1500 metres with a speed of 66 km/hr. Find the angle turned by the engine in 10 seconds.**

**(a) \(10^\circ\)**

**(b) \(7^\circ\)**

**(c) \(11^\circ\)**

**(d) \(8^\circ\)**

Answer

Answer is : b

Your answer : c

Your answer : c

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Question

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) \(2\sqrt{2}\)

Answer

Answer is : b

Your answer : b

Your answer : b

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Question

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

Answer

Answer is : b

Your answer : b

Your answer : b

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Question

**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**

Answer

Answer is : d

Your answer : c

Your answer : c

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Question

**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**

Answer

Answer is : c

Your answer : c

Your answer : c

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Question

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

Answer

Answer is : d

Your answer : a

Your answer : a

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Question

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) \(30^\circ\)

Answer

Answer is : d

Your answer : c

Your answer : c

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Question

**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**

Answer

Answer is : c

Your answer : a

Your answer : a

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Question

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

Answer

Answer is : c

Your answer : c

Your answer : c

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Question

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

Answer

Answer is : a

Your answer : b

Your answer : b

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Question

**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 **

Answer

Answer is : a

Your answer : a

Your answer : a

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Question

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

Answer

Answer is : b

Your answer : d

Your answer : d

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Question

**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**

Answer

Answer is : d

Your answer : d

Your answer : d

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Question

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

Answer

Answer is : d

Your answer : a

Your answer : a

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Question

**How many lines of symmetry does a rhombus have?**

**(a) 0 (b) 1**

**(c) 2 (d) 3**

Answer

Answer is : c

Your answer : c

Your answer : c

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Question

**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**

Answer

Answer is : b

Your answer : a

Your answer : a

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Question

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

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

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

Answer

Answer is : c

Your answer : c

Your answer : c

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Question

**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**

Answer

Answer is : b

Your answer : a

Your answer : a

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Question

**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) \(2(x-6)\)**

Answer

Answer is : b

Your answer : b

Your answer : b

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Question

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

Answer

Answer is : c

Your answer : b

Your answer : b

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Question

**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) \(-\frac {5} {6}\)**

Answer

Answer is : a

Your answer : b

Your answer : b

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Question

**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) \(-\frac {1} {xy}=C\)**

Answer

Answer is : b

Your answer : b

Your answer : b

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Question

**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) \(y=x\: e^{(x-1)}\)**

Answer

Answer is : a

Your answer : a

Your answer : a

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Question

**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 **

Answer

Answer is : c

Your answer : b

Your answer : b

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Question

**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**

Answer

Answer is : b

Your answer : a

Your answer : a

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Question

**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**

Answer

Answer is : a

Your answer : d

Your answer : d

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Question

** 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 **

Answer

Answer is : d

Your answer : b

Your answer : b

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