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Example I. 32 Solve $\log _{2}(x-1)>4$. | 1 |
5. In a monoclinic unit cell, the relation of sides and angles are respectively:
[Main Online April 12, 2014]
(a) $\mathrm{a}=\mathrm{b} \neq \mathrm{c}$ and $\alpha=\beta=\gamma=90^{\circ}$
(b) $\mathrm{a} \neq \mathrm{b} \neq \mathrm{c}$ and $\alpha=\beta=\gamma=90^{\circ}$
(c) $\mathrm{a} \neq \mathrm{b} \neq \m... | 1 |
2. The values of $\theta$ lying between $\theta=0$ and $\theta=\theta / 2$ and satisfying the equation
$\left|\begin{array}{ccc}1+\sin ^{2} \theta & \cos ^{2} \theta & 4 \sin 4 \theta \\ \sin ^{2} \theta & 1+\cos ^{2} \theta & 4 \sin 4 \theta \\ \sin ^{2} \theta & \cos ^{2} \theta & 1+4 \sin 4 \theta\end{array}\right|... | 1 |
Is it possible to time travel to past? | 0 |
1. A block of mass 2 kg placed on a long frictionless horizontal table is pulled horizontally by a constant force F. It is found to move 10 m in the first two seconds. Find the magnitude of F. | 1 |
What was the religion of the Slavs? | 0 |
Would you rather watch Dr Strange or Fantastic Beasts? | 0 |
How can you use SSH to run a shell script? | 0 |
What is more plentiful in capital projects? | 0 |
What places in India have never been under British rule? | 0 |
1. Figure $(29-\mathrm{Q} 2)$ shows some of the electric field lines corresponding to an electric field. The figure suggests that
(a) $E_{A}>E_{B}>E_{C}$
(b) $E_{A}=E_{B}=E_{C}$
(c) $E_{A}... | 1 |
12. The coordination numbers of $\mathrm{Co}$ and $\mathrm{Al}$ in $\left[\mathrm{Co}(\mathrm{Cl})(\mathrm{en})_{2}\right] \mathrm{Cl}$ and
(en $=$ ethane-1, 2-diamine)
[Main April 12, 2019... | 1 |
Under this law what does this state that is required by employers? | 0 |
What are the best night out places in Pune? | 0 |
What government body is responsible for releasing the annual official economic report for Delhi? | 0 |
46. If the solubility product of silver oxalate is $1 \times 10^{-11}$, what will be the weight of $\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4$ in 2.5 litres of a saturated solution?
( 0.103 g ) | 1 |
21. $\frac{1}{\left(e^x-1\right)}\left[\right.$ Hint : Put $\left.e^x=t\right]$ | 1 |
How can I download movies without torrents? | 0 |
Why do girls have to make eye contact with me? | 0 |
Example 2.64 Prove that $\left(\frac{\cos A+\cos B}{\sin A-\sin B}\right)^{n}+\left(\frac{\sin A+\sin B}{\cos A-\cos B}\right)^{n}=2 \cot ^{n} \frac{A-B}{2}$ or 0 , accordingly as $n$ is even or odd. | 1 |
On what plain is New Delhi located? | 0 |
What does bandes dessinées mean? | 0 |
16. Let $f(n)=\left|\begin{array}{ccc}n & n+1 & n+2 \\ { }^{n} P_{n} & { }^{n+1} P_{n+1} & { }^{n+2} P_{n+2} \\ { }^{n} C_{n} & { }^{n+1} C_{n+1} & { }^{n+2} C_{n+2}\end{array}\right|$ where the symbols have their usual meanings. Then $f(n)$ is divisible by
a. $n^{2}+n+1$
b. $(n+1)$ !
c. $n$ !
d. none of these | 1 |
14. The eccentricity of locus of $P$ is
a. $\sqrt{\frac{2 e}{1-e}}$
b. $\sqrt{\frac{2 e}{1+e}}$
c. 1
d. none of these | 1 |
5.7 What role does adsorption play in heterogeneous catalysis? | 1 |
36. If $\vec{a}$ and $\vec{b}$ are unit vectors such that $(\vec{a}+\vec{b}) \cdot(2 \vec{a}+3 \vec{b}) \times(3 \vec{a}-2 \vec{b})=\overrightarrow{0}$, then angle between $\vec{a}$ and $\vec{b}$ is
a. 0
b. $\pi / 2$.
c. $\pi$
d. indeterminate | 1 |
How many million of tons went through Aghioi Theodoroi in 2010? | 0 |
58. Statement $-\mathbf{1}$ The endothermic reactions are favoured at lower temperature and the exothermic reactions are favoured at higher temperature.
Statement -2 When a system in equilibrium is disturbed by changing the temperature, it will tend to adjust itself so as to overcome the effect of change.
(a) If both... | 1 |
What was your "eureka" moment? | 0 |
7. A hydrogen atom and $\mathrm{Li}^{2+}$ ion are both in the second excited state. If $I_{\mathrm{H}}$ and $I_{\mathrm{Li}}$ are their respective electronic angular momenta, and $E_{\mathrm{H}}$ and $E_{\mathrm{Li}}$ their respective energies, then
(a) $I_{\mathrm{H}}>I_{\mathrm{Li}}$ and $\left|E_{\mathrm{H}}\right|>... | 1 |
71. $\mathrm{Fe}^{3+}$ is reduced to $\mathrm{Fe}^{2+}$ by using
(a) $\mathrm{H}_{2} \mathrm{O}_{2}$ in presence of $\mathrm{NaOH}$
(b) $\mathrm{Na}_{2} \mathrm{O}_{2}$ in water
(c) $\mathrm{H}_{2} \mathrm{O}_{2}$ in presence of $\mathrm{H}_{2} \mathrm{SO}_{4}$
(d) $\mathrm{Na}_{2} \mathrm{O}_{2}$ in presence of $... | 1 |
11. Which of the following function(s) has/have removable discontinuity at $x=1$ ?
a. $f(x)=\frac{1}{\ln |x|}$
c. $f(x)=2^{-2^{\frac{1}{1-x}}}$
d. $f(x)=\frac{\sqrt{x+1}-\sqrt{2 x}}{x^{2}-x}$
h. $f(x)=\frac{x^{2}-1}{x^{3}-1}$
?? | 1 |
Why do we say competition is better than comparison? | 0 |
Why would someone prefer a second edition to a first edition? | 0 |
69. If $y=\sin m x$, then the value of the determinant $\left|\begin{array}{lll}y & y_{1} & y_{2} \\ y_{3} & y_{4} & y_{5} \\ y_{6} & y_{7} & y_{8}\end{array}\right|$, where $y_{n}=\frac{d^{n} y}{d x^{n}}$, is
a. $m^{9}$
b. $m^{2}$
c. $m^{3}$
d. none of these | 1 |
How do I change the iPhone's battery? | 0 |
Who led the Nazis? | 0 |
13. Which of the following amines can be prepared by Gabriel phthalimide reaction?
(a) $n$-butylamine
(b) triethylamine
(c) $t$-butylamine
(d) neo-pentylamine | 1 |
9. A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to
(a) $t^{1 / 2}$
(b) $t^{3 / 4}$
(c) $t^{3 / 2}$
(d) $t^{2}$ | 1 |
Why don't more women have babies with semen from a sperm bank rather than having kids from guys who are good for nothing? | 0 |
How do I get unlimited data plan on Jio 4G sim? | 0 |
3. The strength of an aqueous $\mathrm{NaOH}$ solution is most accurately determined by titrating: (Note: consider that an appropriate indicator is used)
(a) Aq. $\mathrm{NaOH}$ in a pipette and aqueous oxalic acid in a burette
(b) Aq. $\mathrm{NaOH}$ in a burette and aqueous oxalic acid in a conical flask
(c) Aq. $\... | 1 |
10. Statement 1 : The point of intersection of the tangents at three distinct points $A, B, C$ on the parabola $y^{2}=4 x$ can be collinear.
Statement 2: If a line $L$ does not intersect the parabola $y^{2}=4 x$, then from every point of the line two tangents can be drawn to the parabola. | 1 |
Who are the modern-day descendants of Leonardo da Vinci? | 0 |
What are the differences between project management and business management? | 0 |
What is your review of There Will Be Blood (2007 movie)? | 0 |
Why do we need friends? | 0 |
Do people who are blind from birth have dreams? | 0 |
24. What is the correct IUPAC name of the following compound.
(A) 4-Hydroxyhex-1-en-6-al
(B) 1-Oxohex-5-en-3-ol
(C) 3-Hydroxyhex-5-enal
(D) 6-Oxohex-1-en-4-ol | 1 |
1. If $\cos ^{3} x \sin 2 x=\sum_{r=0}^{n} a_{r} \sin (r x), \forall x \in R$ then
(a) $n=5, a_{1}=\frac{1}{2}$
(b) $n=5, a_{1}=\frac{1}{4}$
(c) $n=5, a_{2}=\frac{1}{8}$
(d) $n=5, a_{2}=\frac{1}{4}$ | 1 |
2. Show that $|\vec{a}| \vec{b}+|\vec{b}| \vec{a}$ is a perpendicular to $|\vec{a}| \vec{b}-|\vec{b}| \vec{a}$, for any two non-zero vectors $\vec{a}$ and $\vec{b}$. | 1 |
Should "at" or "in" be used in this English sentence? | 0 |
When did France enter the American Revolution war? | 0 |
15. Figure $(10-\mathrm{Q} 6)$ shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of incline $\theta$ is related to the acceleration $a$ of the car as $a=g \tan \theta$. If the sphere is set in pure rolling on the incline, (a) it will continue pure rolling (b) it will slip down th... | 1 |
Example 3 Which is larger $(1.01)^{1000000}$ or 10,000 ? | 1 |
What are the best books in electronics? | 0 |
How does it feel to be a gay in New Zealand? | 0 |
17. Upon heating a litre of a $\frac{\mathrm{N}}{2} \mathrm{HCl}$ solution, $2 \cdot 675 \mathrm{~g}$ of hydrogen chloride is lost and the volume of the solution shrinks to 750 mL . Calculate (i) the normality of the resultant solution (ii) the number of milliequivalents of HCl in 100 mL of the original solution.
(0.56... | 1 |
What is cosmic background radiation and what is so exciting about it? | 0 |
24. If $\hat{i}-3 \hat{j}+5 \hat{k}$ bisects the angle between $\hat{a}$ and $-\hat{i}+2 \hat{j}+2 \hat{k}$, where $\hat{a}$ is a unit vector, then
a. $\hat{a}=\frac{1}{105}(41 \hat{i}+88 \hat{j}-40 \hat{k})$
b. $\hat{a}=\frac{1}{105}(41 \hat{i}+88 \hat{j}+40 \hat{k})$
c. $\hat{a}=\frac{1}{105}(-41 \hat{i}+88 \hat{j}-4... | 1 |
25. A mixture of 20 mL of $\mathrm{CO}, \mathrm{CH}_{4}$ and $\mathrm{N}_{2}$ was burnt in an excess of oxygen, resulting in reduction of 13 mL of volume. The residual gas was treated with KOH solution when there was a further reduction of 14 mL in volume. Calculate the volumes of CO and $\mathrm{CH}_{4}$ in the given ... | 1 |
1. Derivative of $\tan ^{-1}\left\{\frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}\right\}$ with respect to $\cos ^{-1} x^{2}$ is
a. $-1 / 2$
b. $1 / 2$
c. -1
d. 1 | 1 |
How can I simplify these expressions? | 0 |
The scope of federal power is not what? | 0 |
What are all the available options for government jobs after completing B.Tech in mechanical engineering? | 0 |
19. The figure shows a system consisting of (i) a ring of outer radius $3 R$ rolling clockwise without slipping on a horizontal surface with angular speed $\omega$ and (ii) an inner disc of radius $2 R$ rotating anti-clockwise with angular speed $\omega / 2$.
The ring and disc are separated by frictionless ball bearin... | 1 |
(i) the frequency of oscillations | 1 |
What does Stephen Hawking and Leonard Mlodinow pose as a better question that "Is there a God"? | 0 |
What is the best places in India to travel? | 0 |
- Example 10 A change of $8.0 \mathrm{~mA}$ in the emitter current brings a change of 7.9 $m A$ in the collector current. How much change in the base current is required to have the same change $7.9 \mathrm{~mA}$ in the collector current? Find the values of $\alpha$ and $\beta$. | 1 |
The neural groove is a hollow cord of cells with what in the center? | 0 |
5. The point $Q$ will be
a. $(1,-2)$
b. $\left(-\frac{1}{3},-\frac{2}{3}\right)$
c. $(-2,1)$
d. None of these | 1 |
8. The number of isomers of $\mathrm{C}_{6} \mathrm{H}_{14}$ is
(a) 4
(b) 5
(c) 6
(d) 7 | 1 |
Example 9 Solve $3 x+2 y>6$ graphically.
$\mathbf{Y}^{\prime} \quad$ Fig 6.7 | 1 |
Where do comics usually appear? | 0 |
7 To mop-clean a floor, a cleaning machine presses a circular mop of radius $R$ vertically down with a total force $F$ and rotates it with a constant angular speed about its axis. If the force $F$ is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is $\mu$, the torque app... | 1 |
5. $y^{2}=10 x$ | 1 |
2. Assertion : A particle is under SHM along the $x$-axis. Its mean position is $x=2$, amplitude is $A=2$ and angular frequency $\omega$. At $t=0$, particle is at origin, then $x$-co-ordinate versus time equation of the particle will be $x=-2 \cos \omega t+2$.
Reason: At $t=0$, particle is at rest. Directions : Choose... | 1 |
Who won the first presidential debate September 2016? | 0 |
What are Greater Swiss Mountain dogs good at? | 0 |
Does exercise help pass meth drug test? | 0 |
10. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r=\lambda_{1} / \lambda_{2}$ is given by
(a) $r=\frac{2}{3}$
(b) $r=\frac{3}{4}$
(c) $r=\frac{1}{3}$
(d) $r=\frac{4}{3}$
 coulombs and (b) electrons pass through any cross section across the wire's width? | 1 |
Who are journalists? | 0 |
10. A potentiometer wire $A B$ having length $L$ and resistance $12 r$ is joined to a cell $D$ of EMF $\varepsilon$ and internal resistance $r$. A cell $C$ having emf $\frac{\varepsilon}{2}$ and internal resistance $3 r$ is connected. The length $A J$ at which the galvanometer as shown in figure shows no deflection is
... | 1 |
17. In a Frank-Hertz experiment, an electron of energy $5.6 \mathrm{eV}$ passes through mercury vapour and emerges with an energy $0.7 \mathrm{eV}$. The minimum wavelength of photons emitted by mercury atoms is close to
(a) $250 \mathrm{~nm}$
(b) $2020 \mathrm{~nm}$
(c) $1700 \mathrm{~nm}$
(d) $220 \mathrm{~nm}$ | 1 |
13. Probability that A speaks truth is $\frac{4}{5}$. A coin is tossed. A reports that a head appears. The probability that actually there was head is
(A) $\frac{4}{5}$
(B) $\frac{1}{2}$
(C) $\frac{1}{5}$
(D) $\frac{2}{5}$ | 1 |
What is the best latest movie? | 0 |
If a Bollywood movie were made on the life and career of Dhirubhai Ambani, what would be its before interval scene? | 0 |
19. $\mathrm{A}+2 \mathrm{~B} \rightarrow \mathrm{C}$, the rate equation for this reaction is given as Rate $=k[\mathrm{~A}]$ $[B]$
If the concentration of $\mathrm{A}$ is kept the same but that of $\mathrm{B}$ is doubled what will happen to the rate itself?
(a) halved
(b) the same
(c) doubled
(d) quadrupled | 1 |
When did 458 million people live in the British Empire? | 0 |
3. Two particles of masses $1.0 \mathrm{~kg}$ and $2.0 \mathrm{~kg}$ are placed at a separation of $50 \mathrm{~cm}$. Assuming that the only forces acting on the particles are their mutual gravitation, find the initial accelerations of the two particles. | 1 |
1.363. A particle moves in the frame $K$ with a velocity $v$ at an angle $\theta$ to the $x$ axis. Find the corresponding angle in the frame $K^{\prime}$ moving with a velocity $V$ relative to the frame $K$ in the positive direction of its $x$ axis, if the $x$ and $x^{\prime}$ axes of the two frames coincide. | 1 |
Do I need to be good looking to ask out a girl? | 0 |
What are the best things in life? | 0 |
When did Ally Sloper first appear? | 0 |
Where should I buy my guitar? | 0 |
How does invalidating ₹500 and ₹1000 notes help us fight corruption and bring back black money? | 0 |
From where do zygotes derive their genetic information? | 0 |
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