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15. An element having an atomic radius of $0.14 \mathrm{~nm}$ crystallizes in an fcc unit cell. What is the length of a side of the cell?
[Main Online April 9, 2013]
(a) $0.56 \mathrm{~nm}$
(b) $0.24 \mathrm{~nm}$
(c) $0.96 \mathrm{~nm}$
(d) $0.4 \mathrm{~nm}$ | 1 |
What famous dish is also known as hot garlic paste? | 0 |
(b) Calculate the energy to be supplied to ${ }^{238} \mathrm{U}$ if two protons and two neutrons are to be emitted one by one. | 1 |
What are the best gadgets of 2016? | 0 |
When did the Romans make Christianity their official religion? | 0 |
6. Two thin long parallel wires separated by a distance $b$ are carrying a current $i$ ampere each. The magnitude of the force per unit length exerted by one wire on the other is
(a) $\frac{\mu_{0} i^{2}}{b^{2}}$
(b) $\frac{\mu_{0} i^{2}}{2 \pi b}$
(c) $\frac{\mu_{0} i}{2 \pi b}$
(d) $\frac{\mu_{0} i}{2 \pi b^{2}}$ | 1 |
15. The value of the expression
$1(2-\omega)\left(2-\omega^{2}\right)+2(3-\omega)\left(3-\omega^{2}\right)+\ldots$
$+(n-1) \cdot(n-\omega)\left(n-\omega^{2}\right)$,
where, $\omega$ is an imaginary cube root of unity, is....
$(1996,2 \mathrm{M})$ | 1 |
66. If $f: R \rightarrow R$ and $g: R \rightarrow R$ are two functions such that $f(x)+f^{\prime \prime}(x)=-x g(x) f^{\prime}(x)$ and $g(x)>0 \forall x \in R$, then the functions $f^{2}(x)+\left(f^{\prime}(x)\right)^{2}$ has
a. a maxima at $x=0$
h. a minima at $x=0$
c. a point of inflexion at $x=0$
d None of these | 1 |
1.349. A rod moves along a ruler with a constant velocity. When the positions of both ends of the rod are marked simultaneously in the reference frame fixed to the ruler, the difference of readings on the ruler is equal to $\Delta x_{1}=4.0 \mathrm{~m}$. But when the positions of the rod's ends are marked simultaneousl... | 1 |
23. Photochemical smog consists of excessive amount of $X$, in addition to aldehydes, ketones, peroxyacetyl nitrate (PAN), and so forth $\mathrm{X}$ is :
(a) $\mathrm{CO}$
(b) $\mathrm{CH}_{4}$ (c) $\mathrm{O}_{3}$
(d) $\mathrm{CO}_{2}$ | 1 |
Did mens arousal relate to the sexual interests? | 0 |
Which religion came first, Jainism or Hinduism? | 0 |
17. Which of the following curves represents a zero order reaction? [ $(a-x)=$ reactant concn.]
(a)
(b)
 zero
(b) $\frac{q\left(Q_{1}-Q_{2}\right)(\... | 1 |
What sort of quest lacks purpose? | 0 |
What is the study of human communication called? | 0 |
25. If the magnetic field of a plane electromagnetic wave is given by
$B=100 \times 10^{-6} \sin [2 \pi \times 2 \times 10^{15} t-\frac{x}{c}]$,
then the maximum electric field associated with it is (Take, the speed of light $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ )
(a) $6 \times 10^{4} \mathrm{~N} / \mathrm{C... | 1 |
7. In a collage of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is
(1998, 2M)
(a) atleast 30
(b) atmost 20
(c) exactly 25
(d) None of the above | 1 |
What two democratic values are soiled due to corruption? | 0 |
14. The bond between two identical non-metal atoms has a pair of electrons :
(a) unequally shared between the two
(b) transferred fully from one atom to another
(c) with identical spins
(d) equally shared between them | 1 |
How do you celebrate Christmas this year? | 0 |
What is the best gaming PC? | 0 |
What are the main imports and exports of Venezuela, and how does Venezuela's industry compare to Honduras'? | 0 |
From whom did Balkan states start retaking their independence? | 0 |
What is the best mattress for people with lower back pain? | 0 |
What are alternatives to healthprofs.com? | 0 |
Example 5.75 Six persons $A, B, C, D, E, F$ are to be seated at a circular table. In how many ways can this be done if $A$ should have either $B$ or $C$ on his right and $B$ must always have either $C$ or $D$ on his right. | 1 |
When is the modern period dated in England? | 0 |
What kind of religion is Hinduism considered? | 0 |
3. Regarding stationary waves, choose the correct options.
(a) This is an example of interference
(b) Amplitudes of waves may be different
(c) Particles at nodes are always at rest
(d) Energy is conserved | 1 |
32. Which of the following is the unit of eq. conductance?
(a) mho
(b) mho $\mathrm{cm}^{2}$
(c) $\mathrm{mho} \mathrm{cm}^{-1}$
(d) $\mathrm{mho} \mathrm{cm}^{-2}$ | 1 |
What percent of the worlds population did Africa posses at the Berlin Conference? | 0 |
40. White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is $b$ and the screen is at a distance $d(\gg>b)$ from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths a... | 1 |
45. The Cannizzaro reaction is not given by
(a) trimethylacetaldehye
(b) acetaldehyde
(c) benzaldehyde
(d) formaldehyde | 1 |
What are the strangest and most unusual dreams you have ever experienced? | 0 |
What is the deeper meaning of the song "Starboy"? | 0 |
Who is your favorite character you have ever written? | 0 |
15. The dynamic plate resistance of a triode valve is $10 \mathrm{k} \Omega$. Find the change in the plate current if the plate voltage is changed from $200 \mathrm{~V}$ to $220 \mathrm{~V}$. | 1 |
19. A circle is given by $x^{2}+(y-1)^{2}=1$, another circle $C$ touches it externally and also the $x$-axis, then the locus of its centre is
a. $\left\{(x, y): x^{2}=4 y\right\} \cup\{(x, y): y \leq 0\}$
b. $\left\{(x, y): x^{2}+(y-1)^{2}=4\right\} \cup\{(x, y): y \leq 0\}$
c. $\left\{(x, y): x^{2}=y\right\} \cup\{(0,... | 1 |
5. A flat steel plate is of trapezoidal form of uniform thickness of $t$ and tapers uniformly from a width $b_{1}$ to $b_{2}$ in a length of $l$. Determine the elongation of the plate under an axial force of $F$ at each end. Young's modulus of steel plate is $Y$.
(a) $\Delta l=\frac{F l \ln \left(\frac{b_{2}}{b_{1}}\ri... | 1 |
66. The value of $\lim _{x \rightarrow 1^{-}} \frac{1-\sqrt{x}}{\left(\cos ^{-1} x\right)^{2}}$ is
a. 4
b. $1 / 2$
c. 2
d. $1 / 4$ | 1 |
3. Calculate the limit of resolution of a telescope objective having a diameter of $200 \mathrm{~cm}$, if it has to detect light of wavelength $500 \mathrm{~nm}$ coming from a star.
(a) $610 \times 10^{-9} \mathrm{rad}$
(b) $305 \times 10^{-9} \mathrm{rad}$
(c) $457.5 \times 10^{-9} \mathrm{rad}$
(d) $152.5 \times 10^{... | 1 |
Who developed the spice trade initially? | 0 |
9. A particle moves in a region having a uniform magnetic
field and a parallel, uniform electric field. At some
instant, the velocity of the particle is perpendicular to
the field direction. The path of the particle will be
(a) a straight line (b) a circle
(c) a helix with uniform pitch
(d) a helix with nonuniform pitc... | 1 |
What portion of Rajasthan is east and south of the Aravalli Range? | 0 |
What is the difference of Qualcomm Quick Charge 3.0 vs 2.0 vs 1.0 solution? | 0 |
How often should I brush my teeth? | 0 |
What do Pakistani citizens think about Uri Attack? | 0 |
4. A metal sheet is placed in front of a strong magnetic pole. A force is needed to
(a) hold the sheet there if the metal is magnetic
(b) hold the sheet there if the metal is nonmagnetic
(c) move the sheet away from the pole with uniform velocity if the metal is magnetic
(d) move the sheet away from the pole with u... | 1 |
Who gave followers of Humanism the ability to think out of bounds? | 0 |
How does anything exist? | 0 |
What is the best laptop under 30000 INR? | 0 |
Who do you think is going to win the presidential elections and why? | 0 |
1.65. A plank of mass $m_{1}$ with a bar of mass $m_{2}$ placed on it lies on a smooth horizontal plane. A horizontal force growing with time $t$ as $F=a t$ ( $a$ is constant) is applied to the bar. Find how the accelerations of the plank $w_{1}$ and of the bar $w_{2}$ depend on $t$, if the coefficient of friction betw... | 1 |
Who argued that colonies were redundant? | 0 |
What became cheap enough for the middle class to buy? | 0 |
Have you had a paranormal experience? What happened? | 0 |
How do people earn money from YouTube? | 0 |
Is Sony Xperia C waterproof? | 0 |
How is demonetization helping India? | 0 |
Why do people ask such stupid questions on Quora? | 0 |
- Example 2 A raft of wood (density $=600 \mathrm{~kg} / \mathrm{m}^{3}$ ) of mass $120 \mathrm{~kg}$ floats in water. How much weight can be put on the raft to make it just sink? | 1 |
When these laws are broken, corrupt countries gain what in the international market? | 0 |
Which evolved first music or language? | 0 |
What was the federal Government responsible for? | 0 |
2.66 Indicate the number of unpaired electrons in : (a) P , (b) Si , (c) Cr , (d) Fe and (e) Kr . | 1 |
How much money do I need to start a TV channel? | 0 |
3. There are 5 historical monuments, 6 gardens and 7 shopping malls in a city. In how many ways a tourist can visit the city if he visits at least one shopping mall. | 1 |
11. A transverse sinusoidal wave of amplitude $a$, wavelength $\lambda$ and frequency $f$ is travelling on a stretched string. The maximum speed of any point on the string is $v / 10$, where $v$ is the speed of propagation of the wave. If $a=10^{-3} \mathrm{~m}$ and $v=10 \mathrm{~m} / \mathrm{s}$, then $\lambda$ and $... | 1 |
7. Identify the correct statement related to the direction of magnetic moment of a planar loop.
(a) It is always perpendicular to the plane of the loop
(b) It depends on the direction of current
(c) It is obtained by right hand screw rule
(d) All of the above | 1 |
3. $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors of equal magnitude. The angle between each pair of vectors is $\pi / 3$ such that $|\vec{a}+\vec{b}+\vec{c}|=\sqrt{6}$. Then $|\vec{a}|$ is equal to
a. 2
b. -1
c. 1
d. $\sqrt{6} / 3$ | 1 |
4.13 Write the resonance structures for $\mathrm{SO}_{3}, \mathrm{NO}_{2}$ and $\mathrm{NO}_{3}^{-}$ | 1 |
(a) During the fall through a distance $d=12 \mathrm{~m}$, what is the work $W_{g}$ done on the cab by the gravitational force $\vec{F}_{g}$ ? | 1 |
What is it like to be Batman? | 0 |
11. Statement 1: There are no common tangents between circle $x^{2}+y^{2}-4 x+3=0$ and parabola $y^{2}=2 x$.
Statement 2: Given circle and parabola do not intersect. | 1 |
7. The maximum values of the alternating voltages and current are $400 \mathrm{~V}$ and $20 \mathrm{~A}$ respectively in a circuit connected to $50 \mathrm{~Hz}$ supply and these quantities are sinusoidal. The instantaneous values of the voltage and current are $200 \sqrt{2} \mathrm{~V}$ and $10 \mathrm{~A}$, respectiv... | 1 |
How many measures does Transparency International publish right now? | 0 |
Example 7.65 Evaluate $\int \frac{\sec ^{2} x}{\sqrt{16+\tan ^{2} x}} d x$. | 1 |
Is it a good idea to write a book using my blog? | 0 |
Why was secondary school introduced in the U.S? | 0 |
16. Carbon tetrachloride has no net dipole moment because of
(a) its planar structure
(b) its regular tetrahedral structure
(c) similar sizes of carbon and chlorine
(d) similar electron affinities of carbon and chlorine | 1 |
18. An ellipse having foci at $(3,3)$ and $(-4,4)$ and passing through the origin has eccentricity equal to | 1 |
Who would've ran for President if FDR had not been allowed to campaign for a third term in 1940? | 0 |
1.1 What is the force between two small charged spheres having charges of $2 \times 10^{-7} \mathrm{C}$ and $3 \times 10^{-7} \mathrm{C}$ placed 30 cm apart in air? | 1 |
18. In a body-centred cubic cell, an atom at the body centre is shared by
(a) 1 unit cell
(b) 4 unit cells
(c) 2 unit cells
(d) 8 unit cells | 1 |
What are the disadvantages of reading? | 0 |
I forgot my hdfc bank password and do not have the mobile number registered with the account. What shall I do now? | 0 |
10. A source of emf $E=10 \mathrm{~V}$ and having negligible internal resistance is connected to a variable resistance. The resistance varies as shown in figure. The total charge that has passed through the resistor $R$ during the time interval from $t_{1}$ to $t_{2}$ is
 $1.2 \mathrm{~cm}$
(b) $1.2 \mathrm{~mm}$
(c) $2.4 \mathrm{~cm}$
(d) $2.4 \mathrm{~mm}$ | 1 |
29. The major product $H$ of the given reaction sequence is
$\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CO}-\mathrm{CH}_{3}$ $\xrightarrow{\mathrm{CN}^{-}} G \xrightarrow[\text { Heat }]{95 \% \mathrm{H}_{2} \mathrm{SO}_{4}} H$
=\frac{2 F(n)+1}{2} n=1,2, \ldots$ and $F(1)=2$, then $F(101)$ equals
a. 52
b. 49
c. 48
d. 51 | 1 |
14.9 What are the reactions involved for ozone layer depletion in the stratosphere? | 1 |
5. Which of the following is true?
a. $f(x)$ is discontinuous function for any value of $a$ and $b$
b. $f(x)$ is continuous for finite number of values of $a$ and $b$
c. $f(x)$ cannot be differentiable for any value of $a$ and $b$.
d. $f(x)$ is continuous for infinite values of $a$ and $b$ | 1 |
In which period did Gellius gain fame? | 0 |
29. Which of the following statement(s) is (are) true?
[Adv. 2019]
(a) Oxidation of glucose with bromine water gives glutamic acid.
(b) Hydrolysis of sucrose gives dextrorotatory glucose and laevorotatory fructose.
(c) The two six-membered cyclic hemiacetal forms of D-(+)- glucose are called anomers.
(d) Monosacch... | 1 |
How do I send 10kgs of food (packaged and vacuum sealed) from India to Australia? Which courier company's are the most reliable and reasonable? | 0 |
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