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) \(a=\frac{b}{a+b}\)
Topic image not updated
More information not updated
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 \(= 1.496 \times 10^{-11} \text m\)
Topic image not updated
More information not updated
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) \(8^\circ\)
Topic image not updated
More information not updated
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) \(8^\circ\)
Topic image not updated
More information not updated
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) \(2\sqrt{2}\)
Topic image not updated
More information not updated
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) \([a\ b\ c]=-\frac{8}{3}\ and\ \lambda=\frac{2}{3}\)
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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) \(30^\circ\)
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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) \(\text {CH}_3\text I\lt\text {CH}_3\text {Br} \lt\text {CH}_3\text {Cl}\lt\text {CH}_3\text {F} \)
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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) \(\{ -\frac 1 2\:,0\:,\frac 3 4\:\}\)
Topic image not updated
More information not updated
How many lines of symmetry does a rhombus have?
(a) 0 (b) 1
(c) 2 (d) 3
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
\(\frac {(n!)^2} {[(n-1)!]^2}=\)
(a) \(2n\) (b) \(n\)
(c) \(n^2\) (d) \(n^4\)
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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) \(2(x-6)\)
Topic image not updated
More information not updated
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) \(\frac {mv^2} {T^2} t^2\)
Topic image not updated
More information not updated
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) \(-\frac {5} {6}\)
Topic image not updated
More information not updated
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) \(-\frac {1} {xy}=C\)
Topic image not updated
More information not updated
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) \(y=x\: e^{(x-1)}\)
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated
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
Topic image not updated
More information not updated