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17. Evaluate for $m \in N$,
$$
\int\left(x^{3 m}+x^{2 n}+x^{m}\right)\left(2 x^{2 m}+3 x^{m}+6\right)^{1 / m} d x, x>0
$$
| 1
|
61. Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure $p_{i}$ and temperature $T_{1}$ are connected through a narrow pipe of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_{2}$. The final pressure $p_{f}$ is
(a) $2 p_{i}\left(\frac{T_{1}}{T_{1}+T_{2}}\right)$
(b) $2 p_{i}\left(\frac{T_{2}}{T_{1}+T_{2}}\right)$
(c) $2 p_{i}\left(\frac{T_{1} T_{2}}{T_{1}+T_{2}}\right)$
(d) $p_{i}\left(\frac{T_{1} T_{2}}{T_{1}+T_{2}}\right)$
(IIT 2016 Main)
[Hint: $p_{i}(2 V)=n R T, p_{f} V=n_{1} R T_{1}$
$$
\left.p_{f} V=n_{2} R T_{2} \text { and } n=n_{1}+n_{2}\right]
$$
| 1
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What are your favorite music genres?
| 0
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(a) What is the force acting on the loop?
| 1
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Do we need revised computer-user interface concepts?
| 0
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34. Match the following, choosing one item from column X and one from column Y.
| X | Y |
|------------------------------------------------------------------------------------------------------|---------------------------------------------------|
| (i) pyrolysis of alkanes | (a) elimination reaction |
| (ii) benzene+chloroethane | (b) saponification |
| (iii)$\begin{aligned} & \mathrm{CH}_3 \mathrm{COOC}_2 \mathrm{H}_5 \\ & +\mathrm{NaOH}\end{aligned}$ | (c) Wurtz reaction |
| (iv) preparation of alkanes | (d) Friedel-Crafts reaction |
| (v) phenol | |
| | (e) Reimer-Tiemann<br>+ CHCl3<br> (NaOH) reaction |
| (vi) $\mathrm{C}_2 \mathrm{H}_5 \mathrm{Br}+$ alc. KOH | (f) cracking |
| 1
|
5.166. Resorting to the Fresnel equations, demonstrate that light reflected from the surface of dielectric will be totally polarized if the angle of incidence $\theta_{1}$ satisfies the condition $\tan \theta_{1}=n$, where $n$ is the refractive index of the dielectric. What is in this case the angle between the reflected and refracted rays?
Fig. 5.30.
Fig. 5.31.
| 1
|
8. Digital signals
(i) do not provide a continuous set of values
(ii) represent values as discrete steps
(iii) can utilize binary system and
(iv) can utilize decimal as well as binary systems
Which of the above statements are true?
(a) (i) and (ii) only
(b) (ii) and (iii) only
(c) (i), (ii) and (iii) but not (iv)
(d) All of (i), (ii), (iii) and (iv)
| 1
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Problem 7.15
Classify the following species into Lewis acids and Lewis bases and show how these act as such:
(a) HO
(b) $\mathrm{F}^{-}$
(c) $\mathrm{H}^{+}$
(d) $\mathrm{BCl}_{3}$
| 1
|
Which courses I need to take/books to study for becoming a programmer from scratch?
| 0
|
When did cotations to English decisions gradually disappear?
| 0
|
7. When a sound wave travels from water to air, it
(a) bends towards normal
(b) bends away from normal
(c) may bend in any direction
(d) data insufficient
| 1
|
How do I use the Jio 4G sim in 3G cellphone?
| 0
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What is a portfolio manager?
| 0
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What do American girls like about Indian guys?
| 0
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6. A compound of formula $A_{2} B_{3}$ has the hep lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms:
[Main Jan. 10, 2019 (II)]
(a) hcp lattice - A, $\frac{2}{3}$ Tetrahedral voids - B
(b) hcp lattice - A, $\frac{1}{3}$ Tetrahedral voids - B
(c) hcp lattice - B, $\frac{2}{3}$ Tetrahedral voids - A
(d) hcp lattice - B, $\frac{1}{3}$ Tetrahedral voids - A
| 1
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Why do I see questions with basic grammatical mistakes on Quora but some of my questions are marked as "needing improvement"?
| 0
|
43. The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)
[Adv. 2013]
(a) $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2}$ and $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}{ }_{2}\right] \mathrm{Cl}$
(b) $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}$and $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}\right]^{+}$
(c) $\left[\mathrm{CoBr}_{2} \mathrm{Cl}_{2}\right]^{2-}$ and $\left[\mathrm{PtBr}_{2} \mathrm{Cl}_{2}\right]^{2-}$
(d) $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{NO}_{3}\right)\right] \mathrm{Cl}$ and $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}\right] \mathrm{Br}$
| 1
|
What was thought to be only good for children and those who could not read or write?
| 0
|
What is thermal conductivity?
| 0
|
How do I improve my physics?
| 0
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Can we ever act human again?
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What is salary of a private college professor?
| 0
|
24. A straight wire of length $l$ can slide on two parallel plastic rails kept in a horizontal plane with a separation $d$. The coefficient of friction between the wire and the rails is $\mu$. If the wire carries a current $i$, what minimum magnetic field should exist in the space in order to slide the wire on the rails.
| 1
|
What resulted from Europe's exploration of the New World?
| 0
|
When did the physical exchange of the drachma to euro take place?
| 0
|
51. Equation of the chord of contact of pair of tangents drawn to the ellipse $4 x^{2}+9 y^{2}=36$ from the point $(m, n)$ where $m . n=m+n, m, n$ being non-zero positive integers is
a. $2 x+9 y=18$
b. $2 x+2 y=1$
c. $4 x+9 y=18$
d. none of these
| 1
|
7. A reference frame attached to the earth
(a) is an inertial frame by definition
(b) cannot be an inertial frame because the earth is revolving round the sun
(c) is an inertial frame because Newton's laws are applicable in this frame
(d) cannot be an inertial frame because the earth is rotating about its own axis
| 1
|
How do I get over a girl that I like?
| 0
|
What would the boggart of a boggart be?
| 0
|
55. If $y \sqrt{x^{2}+1}=\log \left(\sqrt{x^{2}+1}-x\right)$, then $\left(x^{2}+1\right) \frac{d y}{d x}+x y+1=$
a. 0
b. 1
c. 2 .
d. None of these
| 1
|
What are the prerequisites for Android development?
| 0
|
89. The number of triangles that the four lines $y=x+3$, $y=2 x+3, y=3 x+2$ and $y+x=3$ form is
a. 4
b. 2
c. 3
d. 1
| 1
|
a. $\lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{4 n^2-1}}+\frac{1}{\sqrt{4 n^2-2^2}}+\cdots+\frac{1}{\sqrt{3 n^2}}\right)$
| 1
|
How can I improve my English Language?
| 0
|
3.8 Suggest a way to determine the $\Lambda_{m}^{\circ}$ value of water.
| 1
|
21. 25.4 g of iodine and 14.2 g of chlorine are made to react completely to yield a mixture of ICl and $\mathrm{ICl}_{3}$. Calculate the number of moles of ICl and $\mathrm{ICl}_{3}$ formed.
( 0.1 mole, 0.1 mole)
| 1
|
4. A particle executes simple harmonic motion with frequency $2.5 \mathrm{~Hz}$ and amplitude $2 \mathrm{~m}$. The speed of the particle $0.3 \mathrm{~s}$ after crossing, the equilibrium position is
(a) zero
(b) $2 \pi \mathrm{m} / \mathrm{s}$
(c) $4 \pi \mathrm{m} / \mathrm{s}$
(d) $\pi \mathrm{m} / \mathrm{s}$
| 1
|
What idea did Sigmund Freud bring to the table?
| 0
|
44. 5 g of bleaching powder was suspended in water and volume made up to half a litre. 20 mL of this suspension when acidified with acetic acid and treated with excess of KI solution, liberated $\mathrm{I}_{2}$ which required 20 mL of a $\mathrm{N} / 10$ hypo solution for titration. Calculate the percentage of available chlorine in bleaching powder.
[Hint: See Example 58.]
| 1
|
15. The number of radial nodes of $3 s$ and $2 p$ orbitals are respectively
(a) 2,0
(b) 0,2
(c) 1,2
(d) 2,1
| 1
|
$\bullet 50$ Light of wavelength 102.6 nm is emitted by a hydrogen atom. What are the (a) higher quantum number and (b) lower quantum number of the transition producing this emission? (c) What is the name of the series that includes the transition?
| 1
|
When someone vanishes something in the Potter universe, where does it go?
| 0
|
54. Which of the following compounds will react with ethanolic KCN?
(a) ethyl chloride
(b) acetyl chloride
(c) chlorobenzene
(d) benzaldehyde
| 1
|
Mark your answer as
(a) If Statement I is true, Statement II is true; Statement II is the correct explanation for Statement I
(b) If Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
(c) If Statement I is true; Statement II is false
(d) If Statement I is false; Statement II is true
23. Statement I In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Statement II In an elastic collision, the linear momentum of the system is conserved.
| 1
|
How do you prove the following equation?
| 0
|
What is the most interesting thing you have done in your life?
| 0
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What should I do to get into AIIMS?
| 0
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When was the Gallipoli Campaign?
| 0
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I am 15 years old and want to join the Secret Service. What advice do you have for me?
| 0
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5. As shown in the figure, two infinitely long, identical wires are bent by $90^{\circ}$ and placed in such a way that the segments $L P$ and $Q M$ are along the $X$-axis, while segments $P S$ and $Q N$ are parallel to the $Y$-axis. If $O P=O Q=4 \mathrm{~cm}$ and the magnitude of the magnetic field at $O$ is $10^{-4} \mathrm{~T}$ and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at $O$ will be (Take, $\mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$ )
(a) $40 \mathrm{~A}$, perpendicular out of the page
(b) $20 \mathrm{~A}$, perpendicular into the page
(c) $20 \mathrm{~A}$, perpendicular out of the page
(d) $40 \mathrm{~A}$, perpendicular into the page
| 1
|
What are some hacking hacks?
| 0
|
10. How can the following reaction be made to proceed in forward direction?
$\mathrm{B}(\mathrm{OH})_{3}+\mathrm{NaOH} \rightleftharpoons \mathrm{NaBO}_{2}+\mathrm{Na}\left[\mathrm{B}(\mathrm{OH})_{4}\right]+\mathrm{H}_{2} \mathrm{O}$
(a) addition of borax
(b) addition of cis -1,2-diol
(c) addition of $\mathrm{Na}_{2} \mathrm{HPO}_{4}$
(d) addition of trans -1,2-diol
| 1
|
How do you jailbreak an iPad?
| 0
|
How much does it cost to get hair transplant in India?
| 0
|
1. Among the sulphates of alkaline earth metals, the solubilities of $\mathrm{BeSO}_{4}$ and $\mathrm{MgSO}_{4}$ in water, respectively,
(a) poor and poor
(b) high and poor
(c) high and high
(d) poor and high
| 1
|
Why can't I get an answer with 1k upvotes?
| 0
|
What is will in property?
| 0
|
8. The velocity-time plot for a particle moving on a straight line is shown in the figure (3-Q4).
Figure 3-Q4
(a) The particle has a constant acceleration.
(b) The particle has never turned around.
(c) The particle has zero displacement.
(d) The average speed in the interval 0 to $10 \mathrm{~s}$ is the same as the average speed in the interval $10 \mathrm{~s}$ to $20 \mathrm{~s}$.
| 1
|
12. A conducting square loop of side $l$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. A uniform and constant magnetic field $B$ exists along the perpendicular to the plane of the loop as shown in figure (38-Q6). The current induced in the loop is
(a) $B l v / R$ clockwise
(c) $2 B l v / R$ anticlockwise
(b) $B l v / R$ anticlockwise
(d) zero.
| 1
|
Why do we use whipped cream in ice cream?
| 0
|
3. In comparison to the zeolite process for the removal of permanent hardness, the synthetic resins method is:
(a) less efficient as it exchanges only anions
(b) more efficient as it can exchange both cations as well as anions
(c) less efficient as the resins cannot be regenerated
(d) more efficient as it can exchange only cations
| 1
|
What are the most famous and historical studios for portraiture?
| 0
|
63. For an object placed in front of a mirror, magnification $(m)$ is given in Column I, Column II gives the possible nature of the mirror or that of image. Match appropriately.
| Column-I | | | Column - II |
| :--- | :--- | :--- | :--- |
| A. | $m=\frac{1}{4}$ | (p) | Concave mirror |
| B. | $m=-1$ | | |
| C. | $m=2$ | (q) | Convex mirror |
| D. | $m=1$ | (r) | Plane mirror |
| | | (s) | Real |
| 1
|
6. Find the lengths of transverse axis and conjugate axis, eccentricity, the coordinates of foci, vertices, lengths of the latus rectum and equations of the directrices of the following hyperbola: $16 x^{2}-9 y^{2}=-144$.
| 1
|
6. The current in a circuit with an external resistance of $3.75 \Omega$ is 0.5 A. When a resistance of $1 \Omega$ is introduced into the circuit, the current becomes $0.4 \mathrm{~A}$. The emf of the power source is
(a) $1 \mathrm{~V}$
(b) $2 \mathrm{~V}$
(c) $3 \mathrm{~V}$
(d) $4 \mathrm{~V}$
| 1
|
11. Let $a, b, c$, and $d$ be real numbers in a G.P. $u, v, w$, satisfy the system of equations
$u+2 v+3 w=6$
$4 u+5 v+6 w=12$
$6 u+9 \nu=4$
Show that the roots of the equation $\left(\frac{1}{u}+\frac{1}{v}+\frac{1}{w}\right) x^{2}+\left[(b-c)^{2}\right.$ $\left.+(c-a)^{2}+(d-b)^{2}\right] x+u+v+w=0$ and $20 x^{2}+10(a-d)^{2} x-9$ $=0$ are reciprocals of each other.
| 1
|
4. Let $A_{n}$ be the area enclosed by the $n$th orbit in a hydrogen atom. The graph of $\ln \left(A_{n} / A_{1}\right)$ against $\ln (n)$
(a) will pass through the origin
(b) will be a straight line with slope 4 (c) will be a monotonically increasing nonlinear curve (d) will be a circle.
| 1
|
11. The amphoteric hydroxide is :
(a) $\mathrm{Be}(\mathrm{OH})_{2}$
(b) $\mathrm{Ca}(\mathrm{OH})_{2}$
(c) $\mathrm{Mg}(\mathrm{OH})_{2}$
(d) $\mathrm{Sr}(\mathrm{OH})_{2}$
| 1
|
2.44 An ion with mass number 56 contains 3 units of positive charge and $30.4 \%$ more neutrons than electrons. Assign the symbol to this ion.
| 1
|
5. In how many ways can a strip of cloth with 5 stripes on it be colored with 3 different colours? Assume that the strip of cloth can be flipped over i.e do not count as different patterns that are equivalent if the cloth is turned around. As example following two strips are same
(a) 135
(b) 270
(c) 105
(d) None of these
| 1
|
6.120. Using the Hund rules, find the total angular momentum of the atom in the ground state whose partially filled subshell contains
(a) three $d$ electrons; (b) seven $d$ electrons.
| 1
|
1. If the line $a x+b y+c=0$ is a normal to the curve $x y=1$, then
a. $a>0, b>0$
b. $a>0, b<0$
c. $a<0, b>0$
d. $a<0, b<0$
e. None of these
| 1
|
52. The centre of a rectangular hyperbola lies on the line $y=2 x$. If one of the asymptotes is $x+y+c=0$, then the other asymptote is
a. $x-y-3 c=0$
b. $2 x-y+c=0$
c. $x-y-c=0$
d. none of these
Hence, equation of other asymptote is $x+y-3 c=0$.
| 1
|
6. A wooden block performs SHM on a frictionless surface with frequency $v_{0}$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\mathbf{E}$ is switched-on as shown, then the SHM of the block will be
(2011)
(a) of the same frequency and with shifted mean position
(b) of the same frequency and with the same mean position
(c) of changed frequency and with shifted mean position
(d) of changed frequency and with the same mean position
| 1
|
Who do you think won the second 2016 Presidential debate?
| 0
|
If my base salary is $150,000 in NYC, what will my take home after taxes and potential annual saving be?
| 0
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Can I get pregnant two days after my period ends?
| 0
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These civic ideas allowed what to come into being?
| 0
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What troops were uniquely successful in English service?
| 0
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What is causing contreversy as to the concept of sexual orientation?
| 0
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I sent a free Facebook message to a non-friend, so it will appear in their "others" folder. I need them to read it now. If I pay for the message now, will it move to their inbox folder?
| 0
|
What did he state was an invention of the modern state?
| 0
|
According to the constructivists, what is an example of a learned meta-emotion?
| 0
|
8. Consider a point $(a, b)$ in first quadrant with $b<a$, let P be the minimum perimeter of a triangle with one vertex at $(a, b)$, one on the $x$-axis, and one on the line $y=x$, then
(a) $p=\sqrt{10}$ if $a=2, b=1$
(b) $p=\sqrt{50}$ if $a=4, b=3$
(c) $p=\sqrt{20}$ if $a=3, b=2$
(d) $p=\sqrt{80}$ if $a=6, b=3$
| 1
|
How much money did the IMF and other Eurozone countries agree to give Greece in 2010?
| 0
|
5. If $\left(\sin ^{-1} x+\sin ^{-1} w\right)\left(\sin ^{-1} y+\sin ^{-1} z\right)=\pi^{2}$, then $D=\left|\begin{array}{ll}x^{N_{1}} & y^{N_{2}} \\ z^{N_{3}} & w^{N_{4}}\end{array}\right|\left(N_{1}, N_{2}, N_{3}, N_{4} \in N\right)$
a. has a maximum value of 2
h. has a minimum value of 0
c. 16 different $D$ are possible
d has a minimum value of -2
| 1
|
Is Hillary Clinton better than Donald Trump for Pakistan?
| 0
|
2. Consider the differential equation, $y^{2} d x+x-\frac{1}{y} d y=0$. If value of $y$ is 1 when $x=1$, then the value of $x$ for which $y=2$, is
(a) $\frac{5}{2}+\frac{1}{\sqrt{e}}$
(b) $\frac{3}{2}-\frac{1}{\sqrt{e}}$
(c) $\frac{1}{2}+\frac{1}{\sqrt{e}}$
(d) $\frac{3}{2}-\sqrt{e}$
| 1
|
16. The figure shows two paths for the change of state of a gas from $A$ to $B$. The ratio of molar heat capacities in path 1 and path 2 is
(a) $<1$
(b) $>1$
(c) 1
(d) Data insufficient
| 1
|
21. Equal volumes of two immiscible liquids of densities $\rho$ and $2 \rho$ are filled in a vessel as shown in figure. Two small holes are punched at depth $h / 2$ and $3 h / 2$ from the surface of lighter liquid. If $v_{1}$ and $v_{2}$ are the velocities of a flux at these two holes, then $v_{1} / v_{2}$ is 
(a) $\frac{1}{2 \sqrt{2}}$
(b) $\frac{1}{2}$
(c) $\frac{1}{4}$
(d) $\frac{1}{\sqrt{2}}$
| 1
|
14. To get output ' 1 ' at $R$, for the given logic gate circuit, the input values must be
(a) $X=0, Y=0$
(b) $X=1, Y=0$
(c) $X=1, Y=1$
(d) $X=0, Y=1$
| 1
|
42. In which of the following aqueous solutions is the degree of dissociation of water maximum?
(a) $\mathrm{NH}_4 \mathrm{Cl}$ solution
(b) $\mathrm{CH}_3 \mathrm{COONa}$ solution
(c) $\mathrm{CH}_3 \mathrm{COONH}_4$ solution
(d) NaCl solution
| 1
|
37. Consider an electrochemical cell:
$$
A(\mathrm{~s})\left|A^{\mathrm{nt}}(\mathrm{aq}, 2 \mathrm{M})\right| B^{2 \mathrm{n}+}(\mathrm{aq}, 1 \mathrm{M}) \mid B(\mathrm{~s})
$$
The value of $\Delta H^{\circ}$ for the cell reaction is twice that of $\Delta G^{\circ}$ at $300 \mathrm{~K}$. If the emf of the cell is zero, the $\Delta S^{\circ}$ (in $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ ) of the cell reaction per mole of $B$ formed at $300 \mathrm{~K}$ is
(Given: $\ln (2)=0.7, R$ (universal gas constant)
$=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} . H, S$ and $G$ are enthalpy, entropy and Gibbs energy, respectively.)
[Adv. 2018]
| 1
|
What was the significance of the battle of Somme, and how did this battle compare and contrast to the Battle of France?
| 0
|
Over what did Britain have direct control?
| 0
|
7. In the circuit shown in the figure, the switch $S$ is closed at the moment $t=0$. At the moment $t=R C \ln 2$, the currents through each of the two resistors were found to be equal (say $i$ ). Select the correct alternative
(a) $i=\frac{\varepsilon}{R}, R=\sqrt{\frac{L}{C}}$
(b) $i=\frac{\varepsilon}{2 R}, R=\sqrt{\frac{L}{C}}$
(c) $i=\frac{\varepsilon}{R}, R=\sqrt{\frac{L}{2 C}}$
(d) $i=\frac{\varepsilon}{2 R}, R=\sqrt{\frac{2 L}{C}}$
| 1
|
How much does it cost to build a warehouse?
| 0
|
93. If $\vec{a} \perp \vec{b}$, then vector $\vec{v}$ in terms of $\vec{a}$ and $\vec{b}$ satisfying the equations $\vec{v} \cdot \vec{a}=0$ and $\vec{v} \cdot \vec{b}=1$ and $[\vec{v} \vec{a} \vec{b}]=1$ is
a. $\frac{\vec{b}}{|\vec{b}|^{2}}+\frac{\vec{a} \times \vec{b}}{|\vec{a} \times \vec{b}|^{2}}$
b. $\frac{\vec{b}}{|\vec{b}|}+\frac{\vec{a} \times \vec{b}}{|\vec{a} \times \vec{b}|^{2}}$
c. $\frac{\vec{b}}{|\vec{b}|^{2}}+\frac{\vec{a} \times \vec{b}}{|\vec{a} \times \vec{b}|}$
d. none of these
| 1
|
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