Question stringlengths 2 3k | label int64 0 1 |
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13. The value of $\int \frac{d x}{x^{2}\left(x^{4}+1\right)^{3 / 4}}$ is
(a) $\frac{x^{4}+1}{x^{4}}+c$
(b) $\left(x^{4}+1\right)^{\frac{1}{4}}+c$
(c) $-\left(x^{4}+1\right)^{\frac{1}{4}}+c$
(d) $-{\frac{x^{4}+1}{x^{4}}}^{\frac{1}{4}}+c$ | 1 |
5. A wave moving in a gas (a) must be longitudinal (b) may be longitudinal (c) must be transverse (d) may be transverse. | 1 |
What was the total amount of the rescue package given to Greece? | 0 |
How do I ask a girl out? | 0 |
8. Find the minimum value of
$$
\left(x_{1}-x_{2}\right)^{2}+\left(\frac{x_{1}^{2}}{20}-\sqrt{\left(17-x_{2}\right)\left(x_{2}-13\right)}\right)^{2}
$$
where $x_{1} \in R^{+}, x_{2} \in(13,17)$. | 1 |
Can imei number be changed? | 0 |
28. For a reaction, $A \rightleftharpoons P$, the plots of $[A]$ and $[P]$ with time at temperatures $T_{1}$ and $T_{2}$ are given below.
Time
+C$,
where $C$ is a constant of integration, then $f(x)$ is equal to
(a) $-4 x^{3}-1$
(b) $4 x^{3}+1$
(c) $-2 x^{3}-1$
(d) $-2 x^{3}+1$ | 1 |
4. If $a \in R$ and the equation $-3(x-[x])^{2}+2(x-[x])$ $+a^{2}=0$ (where, $[x]$ denotes the greatest integer $\leq x$ ) has no integral solution, then all possible values of $a$ lie in the interval
(2014 Main)
(a) $(-1,0) \cup(0,1)$
(b) $(1,2)$
(c) $(-2,-1)$
(d) $(-\infty,-2) \cup(2, \infty)$ | 1 |
34. In the commercial electrochemical process for aluminium extraction the electrolyte used is
(a) $\mathrm{Al}(\mathrm{OH})_{3}$ in $\mathrm{NaOH}$ solution
(b) an aqueous solution of $\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}$.
(c) a molten mixture of $\mathrm{Al}_{2} \mathrm{O}_{3}$ and $\mathrm{Na}_{3} \m... | 1 |
82. The solution of the differential equation
$$
\begin{aligned}
& \frac{x+\frac{x^{3}}{3!}+\frac{x^{5}}{5!}+\ldots}{1+\frac{x^{2}}{2!}+\frac{x^{4}}{4!}+\ldots}=\frac{d x-d y}{d x+d y} \text { is } \\
& \begin{array}{ll}
\text { a. } 2 y e^{2 x}=C e^{2 x}+1 & \text { b. } 2 y e^{2 x}=C e^{2 x}-1 \\
\text { c. } y e^{2... | 1 |
4. Each plate of a parallel plate capacitor has a charge $q$ on it. The capacitor is now connected to a battery. Now,
(a) the facing surfaces of the capacitor have equal and opposite charges
(b) the two plates of the capacitor have equal and opposite charges
(c) the battery supplies equal and opposite charges to the... | 1 |
Where did the last Resistance from the White movement occur? | 0 |
What are good gifts for a foreign visitor to bring when they're invited to someone's home in Bangladesh for the first time? | 0 |
What type of remains were found in the Narmada Valley? | 0 |
What type of party system is the United States? | 0 |
25. A man of mass $60 \mathrm{~kg}$ is standing on a platform executing SHM in the vertical plane. The displacement from the mean position varies as $y=0.5 \sin (2 \pi f t)$. The value of $f$, for which the man will feel weightlessness at the highest point, is ( $y$ in metre)
(a) $g / 4 \pi$
(b) $4 \pi g$
(c) $\frac{\s... | 1 |
Are TripAdvisor reviews more reliable than Yelp reviews? | 0 |
49. Let $(h, k)$ be a fixed point, where $h>0, k>0$. A straight line passing through this point cuts the positive directions of the coordinate axes at the points $P$ and $Q$. Find the minimum area of the $\triangle O P Q, O$ being the origin. | 1 |
When was the Battle of Plassey? | 0 |
3. $\lim _{n \rightarrow \infty} \frac{n^{p} \sin ^{2}(n!)}{n+1}, 0<p<1$, is equal to
a. 0
b. $\infty$
c. 1
d. None of these | 1 |
36. If $(\sqrt{3}) b x+a y=2 a b$ touches the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, then the eccentric angle of the point of contact is
a. $\frac{\pi}{6}$
b. $\frac{\pi}{4}$
c. $\frac{\pi}{3}$
d. $\frac{\pi}{2}$ | 1 |
When did Aspar die? | 0 |
15. One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?
... | 1 |
What is the Baluchistan conflict all about? | 0 |
34. The shape of $\left[\mathrm{CH}_{3}\right]^{+}$ is......... | 1 |
What do you think about ban on Rs. 500 and Rs. 1000 currency notes? | 0 |
10. Three resonant frequencies of string with both rigid ends are 90,150 and $210 \mathrm{~Hz}$. If the length of the string is $80 \mathrm{~cm}$, what is the speed of the transverse wave in the string?
(a) $45 \mathrm{~m} / \mathrm{s}$
(b) $75 \mathrm{~m} / \mathrm{s}$
(c) $48 \mathrm{~m} / \mathrm{s}$
(d) $80 \mathrm... | 1 |
What exactly is the ring in The Lord of the Rings? | 0 |
Is Being Egyptian engineer won't give you the chance to work in multinational companies in USA or Europe? Why? | 0 |
\section*{Problem 3.10}
Show by a chemical reaction with water that $\mathrm{Na}_{2} \mathrm{O}$ is a basic oxide and $\mathrm{Cl}_{2} \mathrm{O}_{7}$ is an acidic oxide. | 1 |
What is one reason that a homosexual would engage in heterosexual behavior? | 0 |
8. If $S_{1}, S_{2}, S_{3}, \ldots, S_{m}$ are the sums of $n$ terms of $m$ A.P.'s whose first terms are $1,2,3, \ldots, m$ and common differences are $1,3,5, \ldots$, ( $2 m-1$ ), respectively, show that
$$
S_{1}+S_{2}+\cdots+S_{m}=\frac{m n}{2}(m n+1)
$$ | 1 |
49. For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant $K$ in terms of change in entropy is described by
(a) With increase in temperature, the value of $K$ for exothermic reaction decreases because the entropy change of the system is... | 1 |
What is the best freelance page? | 0 |
62. Refer to Q. 61. For the given orbital in column 1, the only correct combination for any hydrogen like species is
(a) (2) (ii) (P)
(b) (1) (ii) (S)
(c) (4) (iv) (R)
(d) (3) (iii) (P) | 1 |
Ex. 31. An organic compound (A) contains $40 \%$ carbon, $6 \cdot 7 \%$ hydrogen and rest, oxygen. Its vapour density is 15 . On reacting with a concentrated solution of KOH , it gives two compounds, (B) and (C). When (B) is oxidised, the original compound (A) is obtained. When (C) is treated with concentrated HCl , it... | 1 |
9. Two compounds I and II are eluted by column chromatography( of I > II). Which one of the following is a correct statement?
(a) II moves slower and has higher $R_{f}$ value than I
(b) II moves faster and has higher $R_{f}$ value than I
(c) I moves faster and has higher $R_{f}$ value than II
(d) I moves slower a... | 1 |
14. The value of $n$ in the molecular formula $\mathrm{Be}_{n} \mathrm{Al}_{2} \mathrm{Si}_{6} \mathrm{O}_{18}$ is | 1 |
26. Isobutyl magnesium bromide with dry ether and ethyl alcohol gives :
(a)
```
CH3CHCH OH & CH CH CH2
CH3
```
CH3CHCH \& MgBr(OC NOTES
CH3
CH3CH, CH = CH2 \& Mg(OH)Br
CH3
CH3CHCH \& \& CH CH CH2OMgB
CH3 | 1 |
21. Four cubes of side $a$ each of mass $40 \mathrm{~g}, 20 \mathrm{~g}, 10 \mathrm{~g}$ and $20 \mathrm{~g}$ are arranged in $X Y$ plane as shown in the figure. The coordinates of COM of the combination with respect to point $O$ is
$ | 1 |
When will the general public be able to use India's IRNSS? | 0 |
What are animals whose body plans display bilateral symmetry called? | 0 |
2. Consider three quantities $x=E / B, y=\sqrt{1 / \mu_{0} \varepsilon_{0}}$ and $z=\frac{l}{C R}$. Here, $l$ is the length of a wire, $C$ is a capacitance and $R$ is a resistance. All other symbols have standard meanings.
(a) $x, y$ have the same dimensions.
(b) $y, z$ have the same dimensions.
(c) $z, x$ have the ... | 1 |
69. If $\mid 2 \sin \theta-\operatorname{cosec} \theta \geq 1$ and $\theta \neq \frac{n \pi}{2}, n \in I$, then
a. $\cos 2 \theta \geq 1 / 2$
b. $\cos 2 \theta \geq 1 / 4$
c. $\cos 2 \theta \leq 1 / 2$
d. $\cos 2 \theta \leq 1 / 4$ | 1 |
12. A capacitor becomes a perfect insulator for
(a) alternating current
(b) direct current
(c) both (a) and (b)
(d) None of these | 1 |
15. For the proces
$\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$
at $T=100^{\circ} \mathrm{C}$ and 1 atmosphere pressure, the correct choice is
(a) $\Delta S_{\text {system }}>0$ and $\Delta S_{\text {surroundings }}>0$
(b) $\Delta S_{\text {system }}>0$ and $\Delta S_{... | 1 |
How should one write an essay on myself? | 0 |
What should you do if the stock market crashes? | 0 |
3. For $x \in R$, let $[x]$ denote the greatest integer $\leq x$, then the sum of the series $\left[-\frac{1}{3}\right]+\left[-\frac{1}{3}-\frac{1}{100}\right]+\left[-\frac{1}{3}-\frac{2}{100}\right]+\ldots+\left[-\frac{1}{3}-\frac{99}{100}\right]$ is
(2019 Main, 12 April I)(a) -153
(b) -133
(c) -131
(d) -135 | 1 |
Problem 7.6 The value of $K_{p}$ for the reaction,
$\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{C}(\mathrm{s}) \stackrel{p}{\rightleftharpoons} 2 \mathrm{CO}(\mathrm{g})$
is 3.0 at 1000 K . If initially $P_{\mathrm{CO}_{2}}=0.48$ bar and $P_{C O}=0$ bar and pure graphite is present, calculate the equilibrium partial pressur... | 1 |
What is your least embarrassing moment ever? | 0 |
3. If $(5,12)$ and $(24,7)$ are the foci of a hyperbola passing through the origin, then
a. $e=\frac{\sqrt{386}}{12}$
b. $e=\frac{\sqrt{386}}{13}$
c. $L R=\frac{121}{6}$
d. $L R=\frac{121}{3}$ | 1 |
What was the situation on New Year’s Eve in the vicinity of MG road, Bengaluru on 31st, December, 2016? | 0 |
8. A train is moving on a straight track with speed $20 \mathrm{~ms}^{-1}$. It is blowing its whistle at the frequency of $1000 \mathrm{~Hz}$. The percentage change in the frequency heard by a person standing near the track as the train passes him is close to (speed of sound $=320 \mathrm{~ms}^{-1}$ )
(a) $12 \%$
(b) $... | 1 |
92 You can estimate your distance from a lightning stroke by counting the seconds between the flash you see and the thunder you later hear. By what integer should you divide the number of seconds to get the distance in kilometers? | 1 |
What pope launched the First crusade? | 0 |
Why did Microsoft choose core m3 and not core i3 for Surface Pro 4? | 0 |
35. In Fig. (i), a lens of focal length $10 \mathrm{~cm}$ is shown. It is cut into two parts and placed as shown in Fig. (ii). An object $A B$ of height $1 \mathrm{~cm}$ is placed at a distance of $7.5 \mathrm{~cm}$. The height of the image will be
 Find the time taken by the ball to strike the ground. | 1 |
45. The solution of the differential equation $2 x^{2} y \frac{d y}{d x}=\tan \left(x^{2} y^{2}\right)-2 x y^{2}$, given $y(1)=\sqrt{\frac{\pi}{2}}$, is
a. $\sin x^{2} y^{2}=e^{x-1}$
b. $\sin \left(x^{2} y^{2}\right)=x$
c. $\cos x^{2} y^{2}+x=0$
d. $\sin \left(x^{2} y^{2}\right)=e e^{x}$ | 1 |
36. Two identical vehicles are moving with same velocity $v$ towards an intersection as shown in figure. If the collision is completely inelastic, then
(a) the velocity of separation is zero
(b) the velocity of approach is $2 v \sin \frac{\theta}{2}$
(c) the common velocity after collision is $v \cos \frac{\theta}{2... | 1 |
What did the Bengali Renaissance resemble? | 0 |
Why are there very few men fighting for men's rights? | 0 |
Which of the two systems, reward or punishment is better understood? | 0 |
(b) Identify an element that would tend to lose two electrons.
. | 1 |
16. The radius of an ion in a body-centred cube of edge $a$ is
(a) $\frac{a}{2}$
(b) $\frac{\sqrt{2} a}{4}$
(c) $\frac{\sqrt{3} a}{4}$
(d) $a$ | 1 |
6. A linear harmonic oscillator of force constant $2 \times 10^{6} \mathrm{~N} / \mathrm{m}$ and amplitude $0.01 \mathrm{~m}$ has a total mechanical energy of $160 \mathrm{~J}$. Its
$(1989,2 \mathrm{M})$
(a) maximum potential energy is $100 \mathrm{~J}$
(b) maximum kinetic energy is $100 \mathrm{~J}$
(c) maximum po... | 1 |
42. Which of the following curves represent(s) a zero-order reaction?
(a)
(b)
$ is a continuous and bijective function on $R$. If $\forall t \in R$ area bounded by $y=f(x), x=a-t, x=a$ and $x$-axis is equal to area bounded by $y=f(x), x=a+t, x=a$ and $x$-axis, then prove that $\int_{-\lambda}^{\lambda} f^{-1}(x) d x=2 a \lambda$ (given that $f(a)=0$ ). | 1 |
Who developed the concept of emotional labor? | 0 |
The basal ganglia is thought to be the central location at which what are made? | 0 |
13. The normal to the curve $x=a(\cos \theta+\theta \sin \theta)$, $y=a(\sin \theta-\theta \cos \theta)$ at any point ' $\theta$ ' is such that
(a) it makes a constant angle with the $X$-axis
(b) it passes through the origin
(c) it is at a constant distance from the origin
(d) None of the above | 1 |
2. An example of a disproportionation reaction is:
(a) $2 \mathrm{MnO}_{4}+10 \mathrm{I}^{-}+16 \mathrm{H}^{+} \rightarrow 2 \mathrm{Mn}^{2+}+5 \mathrm{I}_{2}+8 \mathrm{H}_{2} \mathrm{O}$
(b) $2 \mathrm{NaBr}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{NaCl}+\mathrm{Br}_{2}$
(c) $2 \mathrm{KMnO}_{4} \rightarrow \mathrm{... | 1 |
8. In the options given below, let $E$ denote the rest mass energy of a nucleus and $n$ a neutron. The correct option is
(a) $E\left({ }_{92}^{236} \mathrm{U}\right)>E\left({ }_{53}^{137} \mathrm{I}\right)+E\left({ }_{39}^{97} \mathrm{Y}\right)+2 E(n)$
(b) $E\left({ }_{92}^{236} \mathrm{U}\right)<E\left({ }_{53}^{... | 1 |
What form of literature enjoyed the most widespread popularity during the Middle Ages? | 0 |
- Example 4 A piece of ice having a stone frozen in it floats in a glass vessel filled with water. How will the level of water in the vessel change when the ice melts?
Note : This is result (iii). | 1 |
3. $\frac{1}{\sqrt{(2-x)^{2}+1}}$ | 1 |
What is the difference between UI design and graphic design? | 0 |
Why is no one giving me an answer to my questions? | 0 |
3. $y=e^{\sin x^{2}}$ | 1 |
43. Value of $\frac{3+\cot 80^{\circ} \cot 20^{\circ}}{\cot 80^{\circ}+\cot 20^{\circ}}$ is equal to
a. $\cot 20^{\circ}$
b. $\tan 50^{\circ}$
c. $\cot 50^{\circ}$
d $\cot \sqrt{20^{\circ}}$ | 1 |
5. Monochromatic light is incident on a glass prism of angle $A$. If the refractive index of the material of the prism is $\mu$, a ray incident at an angle $\theta$, on the face $A B$ would get transmitted through the face $A C$ of the prism provided
(a) $\theta<\cos ^{-1} \mu \sin A+\sin ^{-1} \frac{1}{\mu}$
(b) $\... | 1 |
103 In Fig. 10-63, a thin uniform rod (mass 3.0 kg , length 4.0 m ) rotates freely about a horizontal axis $A$ that is perpendicular to the rod and passes through a point at distance $d=1.0 \mathrm{~m}$ from the end of the rod. The kinetic energy of the rod as it passes through the vertical position is 20 J . (a) What ... | 1 |
How can I lose weight slowly and naturally? | 0 |
-33 What multiple of the energy needed to escape from Earth gives the energy needed to escape from (a) the Moon and (b) Jupiter? | 1 |
What is the God of the Hebrew Bible called? | 0 |
When was the Behmani Sultanate established? | 0 |
How do I upload YouTube videos which have copyright issues if I want to monetize them? | 0 |
1. 1.5276 grams of $\mathrm{CdCl}_{2}$ was found to contain 0.9367 gram of Cd . Calculate the atomic weight of Cd .
(112.4 amu) | 1 |
41. One mole of a monoatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100 \mathrm{~K}$ and the universal gas constant $R=8.0 \mathrm{j} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$, the decrease in its internal energy in joule... | 1 |
6. Two wires $A$ and $B$ have equal lengths and are made of the same material, but diameter
of wire $A$ is twice that of wire $B$. Then, for a given load,
(a) the extension of $B$ will be ... | 1 |
20. A solution of copper sulphate $\left(\mathrm{CuSO}_{4}\right)$ is electrolysed for 10 minutes with a current of 1.5 amperes. The mass of copper deposited at the cathode (at. mass of $\mathrm{Cu}=63 \mathrm{u}$ ) is:
[Main Online April 25, 2013]
(a) $0.3892 \mathrm{~g}$
(b) $0.2938 \mathrm{~g}$
(c) $0.2398 \math... | 1 |
In what years did the Great Famine occur? | 0 |
31. The speed of sound of the whistle is
(a) $340 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$
(b) $360 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$
(c) $310 \mathrm{~m} / \mathrm{s}$ for passenger... | 1 |
What is Chyawanprash good for? | 0 |
Can I use my mobile phone while charging? | 0 |
What is the significance of symmetric components in a power system? | 0 |
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