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58. The average concentration of $\mathrm{SO}_{2}$ in the atmosphere over a city on a certain day is $10 \mathrm{ppm}$, when the average temperature is $298 \mathrm{~K}$. Given that the solubility of $\mathrm{SO}_{2}$ in water at $298 \mathrm{~K}$ is 1.3653 moles litre ${ }^{-1}$ and the $\mathrm{p} K_{a}$ of $\mathrm{... | 1 |
What field of communication has been investigated more thoroughly? | 0 |
Who was a notable student of Stanley Schachter? | 0 |
What are some of the world's greatest lies that most people believe in? | 0 |
What is the latin word for architecture? | 0 |
15. A massless $\operatorname{rod} B D$ is suspended by two identical massless strings $A B$ and $C D$ of equal lengths. A block of mass $m$ is suspended from point $P$ such that $B P$ is equal to $x$. If the fundamental frequency of the left wire is twice the fundamental frequency of right wire, then the value of $x$ ... | 1 |
50. Consider a pyramid $O P Q R S$ located in the first octant $(x \geq 0, y \geq 0, z \geq 0)$ with $O$ as origin, and $O P$ and $O R$ along the $X$-axis and the $Y$-axis, respectively. The base $O P Q R$ of the pyramid is a square with $O P=3$. The point $S$ is directly above the mid-point $T$ of diagonal $O Q$ such ... | 1 |
23. If the atomic weight of carbon were set at 24 amu , the value of the Avogadro constant would be
(a) $6.022 \times 10^{23}$
(b) $12.044 \times 10^{23}$
(c) $3.011 \times 10^{23}$
(d) none of these | 1 |
What affect on the Asian elephant in China will the communist party of chinas collapse have? | 0 |
57. Two teams are to play a series of five matches between them. A match ends in a win, loss or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the match... | 1 |
Is it true that English once used letters not included in the original latin alphabet? | 0 |
36. If ${ }^{n+1} C_{r+1}:{ }^{: n} C_{r}: n-1 C_{r-1}=11: 6: 3$, then $n r=$
a. 20
b. 30
c. 40
d. 50 | 1 |
How do I convince my friend's parents for an intercaste marriage of their daughter? | 0 |
What is God's role in the creation of the world? | 0 |
What cheeses are on a 4 cheese pizza? | 0 |
When did the Ottoman Empire conquer Constantinople? | 0 |
17. Let $f$.be a continuous function on $[a, b]$.
If $F(x)=\left(\int_{a}^{x} f(t) d t-\int_{x}^{b} f(t) d t\right)(2 x-(a+b))$; then prove that there exist some $c \in(a, b)$ such that $\int_{a}^{c} f(t) d t-\int_{c}^{b} f(t) d t$ $=f(c)(a+b-2 c)$. | 1 |
21. The integral $\int_{0}^{\pi} \sqrt{1+4 \sin ^{2} \frac{x}{2}-4 \sin \frac{x}{2}} d x$ is equal to
(a) $\pi-4$
(b) $\frac{2 \pi}{3}-4-4 \sqrt{3}$
(c) $4 \sqrt{3}-4$
(d) $4 \sqrt{3}-4-\pi / 3$ | 1 |
28. The equation ||$x-2|+a|=4$ can have four distinct real solutions for $x$ if $a$ belongs to the interval
a. $(-\infty,-4)$
b. $(-\infty, 0]$
c. $[4, \infty)$
d. None of these | 1 |
8. A non-uniform ball of radius $R$ and radius of gyration about geometric centre $=R / 2$, is kept on a frictionless surface. The geometric centre coincides with the centre of mass. The ball is struck horizontally with a sharp impulse $=J$. The point of application of the impulse is at a height $h$ above the surface. ... | 1 |
21. In the hydroboration - oxidation reaction of propene with diborane, $\mathrm{H}_{2} \mathrm{O}_{2}$ and $\mathrm{NaOH}$, the organic compound formed is:
[Main Online April 9, 2014]
(a) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$
(b) $\mathrm{CH}_{3} \mathrm{CHOHCH}_{3}$
(c) $\mathrm{CH}_{3} \mathrm{CH}_{2} \m... | 1 |
6. A beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the liquid will
(a) increase
(b) decrease
(c) remain constant
(d) first decrease and then increase. | 1 |
8. Total number of lone pair of electrons in $\mathrm{I}^{-}_{3}$ ion is :
(a) 3
(a) 6
(c) 9
(d) 12 | 1 |
What are the best sad songs? | 0 |
40. An intimate mixture of ferric oxide, $\mathrm{Fe}_{2} \mathrm{O}_{3}$, and aluminium, $\mathrm{Al}$, is used in solid fuel rockets. Calculate the fuel value per gram and fuel value per $\mathrm{cc}$ of the mixture. Heats of formation and densities are as follows :
$\mathrm{H}_{j}\left(\mathrm{Al}_{2} \mathrm{O}_{... | 1 |
Along with Bari, what was a notable new pilgrimage site in this era? | 0 |
How many soldiers died? in World War I? | 0 |
What are some reasons a Samsung TV might be turning off and on? | 0 |
Why do people say bad things about other people? | 0 |
8. If $\left(1+2 x+x^{2}\right)^{n}=\sum_{r=0}^{2 n} a_{r} x^{r}$, then $a_{r}=$
a. $\left({ }^{n} C_{r}\right)^{2}$
b. ${ }^{n} C_{r} \cdot{ }^{n} C_{r+1}$
c. ${ }^{2 n} C_{r}$
d. ${ }^{2 n} C_{r+1}$ | 1 |
How do I increase body height? | 0 |
1. Light of wavelength $2000 \AA$ is incident on a metal surface of work-function $3.0 \mathrm{eV}$. Find the minimum and maximum kinetic energy of the photoelectrons. | 1 |
29. With respect to the compounds I-V, choose the correct statement(s).
I
=\int_{0}^{1} x^{m-1}(1-x)^{n-1} d x$, then $(m, n \in I, m ; n \geq 0)$
a. $Y(m, n)=\int_{0}^{\infty} \frac{x^{m-1}}{(1+x)^{m-n}} d x$
b. $I(m, n)=\int_{0}^{\infty} \frac{x^{m}}{(1+x)^{m+n}} d x$
c. $I(m, n)=\int_{0}^{\infty} \frac{x^{n-1}}{(1+x)^{m+n}} d x$
d. $I(m, n)=\int_{0}^{\infty} \frac{x^{n}}{(1... | 1 |
During what era was The Defence Research and Development Organisation founded? | 0 |
Example 3.38 Fifth term of a G.P. is 2. Find the product of its first nine terms. | 1 |
(iii) 1-Chloro-4-ethylcyclohexane | 1 |
16. The equivalent conductance of $\mathrm{NaCl}$ at concentration $\mathrm{C}$ and at infinite dilution are $\lambda_{C}$ and $\lambda_{\infty}$, respectively. The correct relationship between $\lambda_{C}$ and $\lambda_{\infty}$ is given as:
(Where the constant B is positive)
(a) $\lambda_{C}=\lambda_{\infty}+(B) ... | 1 |
Why are graduates in Mathematics hired for software engineering job? | 0 |
How can one be curious about almost everything? | 0 |
12. The ends of a copper rod of length $1 \mathrm{~m}$ and area of cross-section $1 \mathrm{~cm}^{2}$ are maintained at $0^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$. At the centre of the rod there is a source of heat of power $25 \mathrm{~W}$. Calculate the temperature gradient in the two halves of the rod in st... | 1 |
What does secondary education comprise of? | 0 |
I am 23, and I've changed my job 3 times this year. Is it normal to keep changing job? | 0 |
5.228. The Doppler effect has made it possible to discover the double stars which are so distant that their resolution by means of a telescope is impossible. The spectral lines of such stars periodically become doublets indicating that the radiation does come from two stars revolving about their centre of mass. Assumin... | 1 |
Example 1.67. If $f: R \rightarrow R$ be a function such that $f(x)=x^{3}$. $+x^{2}+3 x+\sin x$. Then identify the type of function. | 1 |
12. The factor $\Delta T_{f} / K_{f}$ represents
(a) molarity
(b) formality
(c) normality
(d) molality | 1 |
30. Which of the following molecular species has unpaired electron(s) ?
(a) $\mathrm{N}_{2}$
(b) $\mathrm{F}_{2}$
(c) $\mathrm{O}_{2}^{-}$
(d) $\mathrm{O}_{2}^{2-}$ | 1 |
71. If $\left[\cos ^{-1} x\right]+\left[\cot ^{-1} x\right]=0$, where $[$.] denotes the greatest integer function, then the complete set of values of $x$ is
a. $(\cos 1,1]$
c. $(\cot 1,1]$
d. $[0, \cot 1)$
h. $(\cos 1, \cot 1)$ | 1 |
What would happen if a lower court tried to enforce an unconstitutional statute? | 0 |
5. If $E$ and $F$ are independent events such that $0<P(E)<1$ and $0<P(F)<1$, then
a. $B$ and $F$ are mutually exclusive
b. $E$ and $F^{C}$ (the complement of the event $F$ ) are independent
c. $E^{\complement}$ and $F^{C}$ are independent
d. $P(E \mid F)+P\left(E^{C} \mid F\right)=1$ | 1 |
What were the major effects of the cambodia earthquake, and how do these effects compare to the Peru earthquake in 1687? | 0 |
Which is the best book for learning c for novice? | 0 |
2. A ball is dropped from a height of $49 \mathrm{~m}$. The wind is blowing horizontally. Due to wind a constant horizontal acceleration is provided to the ball. Choose the correct statement (s).
[Take $g=9.8 \mathrm{~ms}^{-2}$ ]
(a) Path of the ball is a straight line
(b) Path of the ball is a curved one
(c) The t... | 1 |
Example 2.56 Find the maximum value of $\sqrt{3} \sin x+\cos x$ and $x$ for which a maximum value occurs. | 1 |
7. The number of roots of the equation $\sqrt{x-2}\left(x^{2}-4 x+3\right)=0$ is
a. three
b. four
c. one
d. two | 1 |
7. Find the energy liberated in the reaction
$$
{ }^{223} \mathrm{Ra} \rightarrow{ }^{209} \mathrm{~Pb}+{ }^{14} \mathrm{C} .
$$
The atomic masses needed are as follows.
\begin{tabular}{lll}
${ }^{223} \mathrm{Ra}$ & ${ }^{209} \mathrm{~Pb}$ & ${ }^{14} \mathrm{C}$ \\
$223 \cdot 018 \mathrm{u}$ & $208 \cdot 981 \mat... | 1 |
16. $|\mathrm{OX} \times \mathrm{OY}|=$
(a) $\sin (P+Q)$
(b) $\sin (P+R)$
(c) $\sin (Q+R)$
(d) $\sin 2 R$ | 1 |
After what event did the last citta irredente join Italy? | 0 |
Is there any accounting software that I can use to manage a startup finance? | 0 |
What is the difference between Hysteresis loss & Eddy current loss? | 0 |
Where can I watch Dragon Ball Z episodes english dubbed? | 0 |
Example 10.1 Draw the structures of all the eight structural isomers that have the molecular formula $\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{Br}$. Name each isomer according to IUPAC system and classify them as primary, secondary or tertiary bromide. | 1 |
Why is it important to document variations in witness texts when compiling a critical text? | 0 |
34. On heating ammonium dichromate, the gas evolved is
(a) oxygen
(b) ammonia
(c) nitrous oxide
(d) nitrogen | 1 |
How is the average case running time of the quick sort algorithm closer to the best case : O(n log n) than the worst case : O(n^2)? | 0 |
When did Le Corbusier live and write? | 0 |
Example 2.4
$$
\begin{aligned}
\operatorname{Let} f(x) & =\left\{\begin{array}{ll}
x+1, & x>0 \\
2-x, & x \leq 0
\end{array}\right. \text { and } \\
g(x) & = \begin{cases}x+3, & x<1 \\
x^{2}-2 x-2, & 1 \leq x<2 \\
x-5, & x \geq 2\end{cases}
\end{aligned}
$$
find L.H.L. and R.H.L. of $g(f(x))$ at $x=0$ and hence find $... | 1 |
4. If $x^{3}-2 x^{2} y^{2}+5 x+y-5=0$ and $y(1)=1$, then
a. $y^{\prime}(1)=4 / 3$
b. $y^{\prime \prime}(1)=-4 / 3$
c. $y^{\prime \prime}(1)=-8 \frac{22}{27}$
d. $y^{\prime}(1)=2 / 3$ | 1 |
Which type of people might have migrated from Taiwan into Southeast Asia? | 0 |
Example 7.9 Prove that the value of the determinant
$\left|\begin{array}{ccc}-7 & 5+3 i & \frac{2}{3}-4 i \\ 5-3 i & 8 & 4+5 i \\ \frac{2}{3}+4 i & 4-5 i & 9\end{array}\right|$ is real. | 1 |
5. Statement 1: If $a^{2}+b^{2}+c^{2}<0$, then if roots of the equation $a x^{2}+b x+c=0$ are imaginary. then they are not complex conjugates.
Statement 2: Equation $a x^{2}+b x+c=0$ has complex conjugate roots when $a, b, c$ are real. | 1 |
50. Calculate the heat of the following homogeneous gaseous reaction
$$
\mathrm{CH}_{3} \mathrm{COCH}_{3}+2 \mathrm{O}_{2} \rightarrow \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}
$$
from the following data:
Bond energies ( kJ ):
| $\mathrm{C}-\mathrm{H}=414 \cdot 49$ | $\mathrm{C}-\mathrm... | 1 |
Where can I find a cool black/brown leather jacket in Mumbai? | 0 |
2. Boron and silicon of very high purity can be obtained through :
(a) liquation
(b) zone refining
(c) vapour phase refining
(d) electrolytic refining | 1 |
2. If $\tan \theta=-\frac{4}{3}$, then $\sin \theta$ is
(IIT-JEE, 1979)
a. $-\frac{4}{5}$ but not $\frac{4}{5}$
h $-\frac{4}{5}$ or $\frac{4}{5}$
c. $\frac{4}{5}$ but not $-\frac{4}{5}$
d. none of these | 1 |
A group of neuron-clusters scattered in the core of the lower brain is called what? | 0 |
5. The reagent needed for the given conversion is
$$
\mathrm{Ph}-\mathrm{C} \equiv \mathrm{C}-\mathrm{Ph} \longrightarrow \stackrel{\mathrm{Ph}}{\mathrm{H}} \mathrm{C}=\mathrm{C}_{\mathrm{Ph}}^{\mathrm{H}}
$$
[Main Online April 11, 2014]
(a) Cat. hydrogenation
(b) $\mathrm{H}_{2}$ / Lindlar Cat.
(c) $\mathrm{Li} /... | 1 |
3. A source of sound $S$ is moving with a velocity of $50 \mathrm{~m} / \mathrm{s}$ towards a stationary observer. The observer measures the frequency of the source as $1000 \mathrm{~Hz}$. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take, velocity of s... | 1 |
Who discovered the process of refining kerosene from coal? | 0 |
What is the best demat account service provider in India? | 0 |
45. If $f(x)=\cos \pi(|x|+[x])$, (where [.] denotes the greatest integral function), then which is not true?
a. continuous at $x=1 / 2$
h continuous at $x=0$
c. differentiable in $(-1,0)$
d differentiable in $(0,1)$ | 1 |
What is the power consumption of a 2000 kVA transformer? | 0 |
Through what period did European powers expand control in Africa? | 0 |
3. Number of Resonating structures of the given compound are :
(A) 7
(B) 8
(C) 9
(D) 10 | 1 |
Where can I find a good Bible study in Kew Gardens? | 0 |
When people convert there religion why do they first try to convert others instead of learning about the religion themselves? | 0 |
Why did the Pan American Health Organization release this statement? | 0 |
8. If the system is released from rest, then match the following two columns.
\begin{tabular}{ll|l}
\hline & \multicolumn{1}{c|}{ Column I } & \multicolumn{1}{c}{ Column II } \\
\hline (a)... | 1 |
How will demonetization of 500 and 1000 rupee notes stop corruption? | 0 |
11. $[\mathrm{Pd}(\mathrm{F})(\mathrm{Cl})(\mathrm{Br})(\mathrm{I})]^{2-}$ has $n$ number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy $[\mathrm{CFSE}]$ of $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{n-6}$, respectively, are:
[Note : Ignore the pairing energy]
[Ma... | 1 |
What are some good websites to download free music? | 0 |
5. Let the algebraic sum of the perpendicular distance from the points $(2,0),(0,2)$ and $(1,1)$ to a variable straight line be zero. Then the line passes through a fixed point whose coordinates are $\qquad$ | 1 |
Is it true that ₹ 2000 currency notes in India are embedded with GPS chips? Can it be done at all? | 0 |
- Example 1 In the figure shown, $u=\sqrt{6 g R}(>\sqrt{5 g R})$
Find $h, v, a_{r}, a_{t}, T$ and $F_{\text {net }}$ when
(a) $\theta=60^{\circ}$
(b) $\theta=90^{\circ}$
(c) $\theta=180^{\circ}$
 Kinetic
(b) Total
(c) Mechanical
(d) Internal | 1 |
4. Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit. | 1 |
- Example 9.19 A body is displaced from position A to position B. Kinetic and potential energies of the body at positions $A$ and $B$ are
$$
K_{A}=50 \mathrm{~J}, U_{A}=-30 \mathrm{~J}, K_{B}=10 \mathrm{~J} \text { and } U_{B}=20 \mathrm{~J}
$$
Find work done by
(a) conservative forces (b) all forces (c) forces othe... | 1 |
How can I learn PHP in a week? | 0 |
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