Question

**If \(B_E\) represents equatorial magnetic field and \(B_A\) represents axial magnetic field due to a bar magnet. **

**Which of the following relationships between \(B_E\) and \(B_A\) is correct? **

**(a) \(B_E=2B_A\)**

**(b) \(B_A=2B_E\)**

**(c) \(B_E=4B_A\)**

**(d) \(B_A=4B_E\)**

Answer

Answer is : b

Your answer : b

Your answer : b

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Question

**If \(9\times 3=36;11\times 7=81 \) then \(5\times 13=?\)**

**(a) 65 **

**(b) 66**

**(c) 81**

**(d) 51**

Answer

Answer is : c

Your answer : c

Your answer : c

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Question

If a natural number \('\alpha'\) is divided by 7, the remainder is 5. If a natural number \('\beta'\) is divided by 7 , the remainder is 3. The remainder is 'r' if \(\alpha+\beta\) is divided by 7. Find the value of \(\frac{3r+5}{4}.\)

(a) 2 (b) 7

(c) 8 (d) 11

Answer

Answer is : a

Your answer : d

Your answer : d

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Question

**Find the principal values of \(\cos^{-1}\Bigl(\frac{1}{2}\Bigr)\)**

**(a) \(-\frac{\pi}{3}\)**

**(b) \(\frac{\pi}{3}\)**

**(c) \(\frac{\pi}{2}\)**

**(d) \(\frac{2\pi}{3}\)**

Answer

Answer is : b

Your answer : b

Your answer : b

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Question

If \(|a|=8,|b|=3\) and \(|a\times b|=12,\) then find the angle between a and b.

a. \(\frac{\pi}{3}\)

b. \(\frac{\pi}{6}\)

c. \(\frac{\pi}{4}\)

d. None of these

Answer

Answer is : b

Your answer : d

Your answer : d

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Question

Two masses \(m_1\) and \(m_2\) connected by a spring of spring constant k rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is

(a) \(T=2\pi \sqrt{\frac{1}{k}\Big(\frac{m_1m_2}{m_1+m_2}\Big)}\)

(b) \(T=2\pi \sqrt{k\Big(\frac{m_1+m_2}{m_1m_2}\Big)}\)

(c) \(T=2\pi \sqrt{\frac{m_1}{k}}\)

(d) \(T=2\pi \sqrt{\frac{m_2}{k}}\)

Answer

Answer is : a

Your answer : c

Your answer : c

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Question

The flux linked with a coil at any instant t given by \(\phi =10t^2-50 t+250\) then, induced emf at \(t=3 s\) is

(a) -10 V

(b) 10 V

(c) 190 V

(d) -190 V

Answer

Answer is : a

Your answer : b

Your answer : b

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Question

The flux linked with a coil at any instant t given by \(\phi =10t^2-50 t+250\) then, induced emf at \(t=3 s\) is

(a) -10 V

(b) 10 V

(c) 190 V

(d) -190 V

Answer

Answer is : a

Your answer : c

Your answer : c

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Question

**The number of commutative binary operations that can be defined on a set of \(2\) elements is **

**(a) \(8\)**

**(b) \(6\)**

**(c) \(4\)**

**(d) \(2\) **

Answer

Answer is : d

Your answer : c

Your answer : c

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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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