Question stringlengths 2 3k | label int64 0 1 |
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75. If $\vec{r} \cdot \vec{a}=\vec{r} \cdot \vec{b}=\vec{r} \cdot \vec{c}=\frac{1}{2}$ for some non-zero vector $\vec{r}$, then the area of the triangle whose vertices are $A(\vec{a}), B(\vec{b})$ and $C(\vec{c})$ is $(\vec{a}, \vec{b}, \vec{c}$ are non-coplanar)
a. $|[\vec{a} \vec{b} \vec{c}]|$
b. $|\vec{r}|$
c. $|[\v... | 1 |
How did Robert Frost get involved with NASA? | 0 |
Will my daughter be adversely affected by having supervised visitation with her sociopathic narcissistic mother? | 0 |
What were credits given to European governments disguised as? | 0 |
Who guards the gates of hell? | 0 |
How is India fighting corruption by scrapping 500 and 1000 rupee notes? | 0 |
What's it like to work at Ply Gem Industries for your first job? | 0 |
What do you think about this poem? | 0 |
29. The given inequality has at least one positive solution for a $\in$
a. $(-\infty,-2)$
. $[3, \infty)$
c. $(2, \infty)$
d. $[-2, \infty)$ | 1 |
Did Neil Armstrong really travel to the moon? | 0 |
11. If $\left(1+x+x^{2}\right)^{n}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots .+a_{2 n} x^{2 n}$, then the value of $a_{0}+a_{3}+a_{6}+\ldots$. is [ $n$ is a multiple of 3 ]
(a) $a_{0}+a_{3}+a_{6}+\ldots=a_{1}+a_{4}+a_{7}+\ldots$
(b) $a_{0}+a_{3}+a_{6}+\ldots=a_{2}+a_{5}+a_{8}+\ldots$.
(c) $a_{1}+a_{4}+a_{7}+\ldots .=3^{n-1}$
(d... | 1 |
Do my brain have anything to do with my eyes? | 0 |
Ex. 21. Calculate the concentrations of all species of significant concentration present in $0.1 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}$ solution. $K_{1}=7.5 \times 10^{-3}, K_{2}=6.2 \times 10^{-8}, K_{3}=3.6 \times 10^{-13}$. | 1 |
How do I get a Android Junior developer job in America? I have experience but I'm not from the USA. | 0 |
How many Empires did the war cause destruction to? | 0 |
Who's the best Indian Comic ever? | 0 |
2. A ball is thrown vertically upwards from the ground. If $T_{1}$ and $T_{2}$ are the respective time taken in going up and coming down, and the air resistance is not ignored, then
(a) $T_{1}>T_{2}$
(b) $T_{1}=T_{2}$
(c) $T_{1}<T_{2}$
(d) nothing can be said | 1 |
What is the difference between a war and a battle? | 0 |
50. Distance of the point $P(\vec{p})$ from the line $\vec{r}=\vec{a}+\lambda \vec{b}$ is
a. $\left|(\vec{a}-\vec{p})+\frac{((\vec{p}-\vec{a}) \cdot \vec{b}) \vec{b}}{|\vec{b}|^{2}}\right|$
b. $\mid \vec{b}-\vec{p}) \left.+\frac{((\vec{p}-\vec{a}) \cdot \vec{b}) \vec{b}}{|\vec{b}|^{2}} \right\rvert\,$
c. $\mid \vec{a}-... | 1 |
What are some of the best ways to stretch jeans? | 0 |
8. For complete oxidation of 4 litres of CO at NTP, the required volume of $\mathrm{O}_{2}$ at NTP is
(a) 4 litres
(b) 8 litres
(c) 2 litres
(d) 1 litre | 1 |
4. The displacement of a particle in simple harmonic
motion in one time period is
(a) A (b) 2A (c) 4A (d) zero. | 1 |
7. $a^{2}+b^{2}+c^{2}$ is
a. $>2$
c. $>3$
d. $<3$.
d. $<2$ | 1 |
9. The lines $2 x-3 y=5$ and $3 x-4 y=7$ are diameters of a circle of area $154 \mathrm{sq}$ units. Then, the equation of this circle is
(a) $x^{2}+y^{2}+2 x-2 y=62$
(b) $x^{2}+y^{2}+2 x-2 y=47$
(c) $x^{2}+y^{2}-2 x+2 y=47$
(d) $x^{2}+y^{2}-2 x+2 y=62$ | 1 |
What is the mass of a neutron? How is this mass determined? | 0 |
8. Which of the following xenon-oxo compounds may not be obtained by hydrolysis of xenon fluorides?
(a) $\mathrm{XeO}_{2} \mathrm{~F}_{2}$
(b) $\mathrm{XeOF}_{4}$
(c) $\mathrm{XeO}_{3}$
(d) $\mathrm{XeO}_{4}$ | 1 |
Can spread spectrum be jammed? | 0 |
4. A piece of paper is in the shape of a square of side $1 \mathrm{~m}$ long. It is cut at the four comers to make a regular polygon of eight sides (octagon). The area of the polygon is
a. $2(\sqrt{2}-1) \mathrm{m}^{2}$
b. $(\sqrt{2}-1) m^{2}$
c. $\frac{1}{\sqrt{2}} \mathrm{~m}^{2}$
d. none of these | 1 |
13. The charge of an electron is $1.6 \times 10^{-19}$ coulomb. How many electrons per second pass through a cross section of a Cu wire carrying $10^{-16} \mathrm{amp}$ ?
(a) 300
(b) 1800
(c) 1200
(d) 600 | 1 |
3. $\lim _{x \rightarrow-\infty}\left\lceil\frac{x^{4} \sin \left(\frac{1}{x}\right)+x^{2}}{\left(1+|x|^{3}\right)}\right\rceil=$ | 1 |
What all mathematics do we need for competitive programming? | 0 |
Example 3 In the figure shown find relation between magnitudes of $\mathbf{a}_{A}$ and $\mathbf{a}_{B}$.
 | 1 |
20. Prove that $\left({ }^{2 n} C_{0}\right)^{2}-\left({ }^{2 n} C_{1}\right)^{2}+\left({ }^{2 n} C_{2}\right)^{2}-\ldots+\left({ }^{2 n} C_{2 n}\right)^{2}$ $=(-1)^{n} \cdot{ }^{2 n} C_{n}$.
$(1978,4$ M)
(a) $(-1)^{n / 2}(n+2)$
(b) $(-1)^{n}(n+1)$ | 1 |
Mr.Richard Muller, how can I get better at math in 8th grade? | 0 |
4.63. A small ball of mass $m=21 \mathrm{~g}$ suspended by an insulating thread at a height $h=12 \mathrm{~cm}$ from a large horizontal conducting plane performs small oscillations (Fig. 4.22). After a charge $q$ had been imparted to the ball, the oscillation period changed $\eta=2.0$ times. Find $q$.
 $\frac{1}{4}$
(b) $\frac{1}{7}$
(c) $\frac{1}{8}$
(d) $\frac{1}{49}$
$(1999,2 \mathrm{M})$ | 1 |
Do people see questions that are marked as needing improvement? | 0 |
Who followed Hitler to power? | 0 |
What are the chances of getting an Assistant Professor job back at the same Indian Institute of Technology (IIT) after declining the offer once? | 0 |
17. In the process of ice melting at $-15^{\circ} \mathrm{C}$
(a) $\Delta G<0$
(b) $\Delta G>0$
(c) $\Delta G=0$
(d) none of these | 1 |
Example 8.18 Evaluate $\int_{-\pi / 2}^{2 \pi} \sin ^{-1}(\sin x) d x$. | 1 |
(a) Cyclopropane, cyclobutane, cyclopentane | 1 |
Why many people hate USA ? | 0 |
6. If $I=\int \frac{\sin ^{3}\left(\frac{\theta}{2}\right)}{\cos \left(\frac{\theta}{2}\right) \sqrt{\cos ^{3} \theta+\cos ^{2} \theta+\cos \theta}} d \theta$, then $I$ equals
(a) $\cot ^{-1}(\tan \theta+\sec \theta)+c$
(b) $-\cot ^{-1} \sqrt{(\cos \theta+\sec \theta+1)}+c$
(c) $\tan ^{-1}\left(\tan \frac{\theta}{2}+\s... | 1 |
25. Let $A$ be a point on the line $\mathbf{r}=(1-3 \mu) \hat{\mathbf{i}}+(\mu-1) \hat{\mathbf{j}}+(2+5 \mu) \hat{\mathbf{k}}$ and $B(3,2,6)$ be a point in the space. Then, the value of $\mu$ for which the vector $\mathbf{A B}$ is parallel to the plane $x-4 y+3 z=1$ is
(a) $\frac{1}{4}$
(b) $-\frac{1}{4}$
(c) $\fr... | 1 |
(iv) Coupling reaction | 1 |
How can I improve a slow growing Youtube channel? | 0 |
How much time will I have to spend to be able to listen to English easily? | 0 |
Sample Problem 15.04 Angular simple harmonic oscillator, rotational inertia, period
Figure 15-10a shows a thin rod whose length $L$ is 12.4 cm and whose mass $m$ is 135 g , suspended at its midpoint from a long wire. Its period $T_{a}$ of angular SHM is measured to be 2.53 s . An irregularly shaped object, which we ca... | 1 |
13. If $|z|=1$ and $w=\frac{z-1}{z+1}$ (where, $z \neq-1$ ), then $\operatorname{Re}(w)$ is
(2003, 1M)
(a) 0
(b) $\frac{1}{|z+1|^{2}}$
(c) $\frac{1}{z+1} \cdot \frac{1}{|z+1|^{2}}$
(d) $\frac{\sqrt{2}}{|z+1|^{2}}$ | 1 |
How does the exit of Britain from European Union affect the Indian economy? | 0 |
- Compare the two protons identified below :
Identify which proton is more acidic, and explain why by comparing the stability of the conjugate bases. | 1 |
Do employees at Armor Minerals have a good work-life balance? Does this differ across positions and departments? | 0 |
What are some interesting puzzles to sharpen your brain? | 0 |
6. Let $a, b, c, d$ be positive integers such that $\log _{d} b=3 / 2$ and $\log _{c} d=5 / 4$. If $(a-c)=9$, then find the value of $(b-d)$. | 1 |
15. The least value of $\alpha \in R$ for which $4 \alpha x^{2}+\frac{1}{x} \geq 1$, for all $x>0$, is
(a) $\frac{1}{64}$
(b) $\frac{1}{32}$
(c) $\frac{1}{27}$
(d) $\frac{1}{25}$ | 1 |
24. Let $P$ be a point interior to the acute triangle $A B C$. If $\overrightarrow{P A}+\overrightarrow{P B}+\overrightarrow{P C}$ is a null vector, then w.r.t. triangle $A B C$, point $P$ is its
a. centroid
b. orthocentre
c. incentre
d. circumcentre | 1 |
They say that to be a good programmer you must think and dream like one | 0 |
Which country became Britain's main rival in the 18th century? | 0 |
Videos: What is the file size per hour of recording 720p of video? | 0 |
3. A rod of length $3 /$ is rotated with an angular velocity $\omega$ as shown in figure. The uniform magnetic field $B$ is into the paper. Find
(a) $V_{A}-V_{C}$
(b) $V_{A}-V_{D}$
Fig. 27... | 1 |
2.33 19 .5 g of $\mathrm{CH}_{2} \mathrm{FCOOH}$ is dissolved in 500 g of water. The depression in the freezing point of water observed is $1.0^{\circ} \mathrm{C}$. Calculate the van't Hoff factor and dissociation constant of fluoroacetic acid. | 1 |
15. In two separate bulbs containing ideal gases $A$ and $B$ respectively, the density of gas $A$ is twice that of gas $B$ while molecular weight of gas $A$ is half that of gas $B$ at the same temperature, pressure ratio $P_{A} / P_{B}$ will be
(a) $1 / 4$
(b) $1 / 2$
(c) 4
(d) 1 | 1 |
Corrupt people may manipulate what to receive more assistance? | 0 |
8. Consider the following reactions,
(i) $\mathrm{NaNO}_{2} / \mathrm{HCl}, 0-5^{\circ} \mathrm{C}$
The compound $[\mathrm{P}]$ is:
(a)
 $V$
(b)... | 1 |
50. Let $\alpha \in R$. Prove that a function $f: R \rightarrow R$ is differentiable at $\alpha$ if and only if there is a function $g: R \rightarrow R$ which is continuous at $\alpha$ and satisfies $f(x)-f(\alpha)=g(x)(x-\alpha), \forall x \in R$.
(2001, 5M) | 1 |
When did Australia achieve self-government? | 0 |
What are some of the books that are really worth reading that you can recommend? | 0 |
55. If $2 \tan ^{-1} x=\pi+\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)$, then
a. $x>1$
b $x<1$
c. $x>-1$
$d-1<x<1$ | 1 |
Which car should I buy: Maruti suzuki vitara brezza zdi+ or Renault duster RxE 85ps diesel? | 0 |
What was Jaipal action after his last defeat? | 0 |
35. In the alumino-thermite process, aluminium acts as
(a) an oxidizing agent
(b) a flux
(c) a reducing agent
(d) a solder | 1 |
18. The shown $p-V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is
(a)... | 1 |
11. A $2.0 \mathrm{~V}$ potentiometer is used to determine the internal resistance of a $1.5 \mathrm{~V}$ cell. The balance point of the cell in the open circuit is $75 \mathrm{~cm}$. When a resistor of $10 \Omega$ is connected across the cell, the balance point shifts to $60 \mathrm{~cm}$. The internal resistance of t... | 1 |
Which is a better FPS game between those: Warface, Special Force 2, and AVA? | 0 |
13. $\mathrm{HBr}$ reacts fastest with :
(a) 2-methylpropan-2-ol
(b) propan-1-ol
(c) propan-2-ol
(d) 2-methylpropan-1-ol | 1 |
What type of ink is often used in making comics? | 0 |
What are the most common types of eagles one might see in the Jaisalmer region? | 0 |
How do you unlock an iPad? | 0 |
6. The combustion of benzene (1) gives $\mathrm{CO}_{2}(\mathrm{~g})$ and $\mathrm{H}_{2} \mathrm{O}(l)$. Given that heat of combustion of benzene at constant volume is $-3263.9 \mathrm{~kJ} \mathrm{~mol}^{-}$ ${ }^{1}$ at $25^{\circ} \mathrm{C}$; heat of combustion (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) of benzene at c... | 1 |
What is the meaning of "mera rang de basanti chola"? | 0 |
17. When $\mathrm{O}_{2}$ is adsorbed on a metallic surface, electron transfer occurs from the metal to $\mathrm{O}_{2}$. The true statement(s) regarding this adsorption is(are)
(a) $\mathrm{O}_{2}$ is physisorbed
(b) Heat is released
(c) Occupancy of $\pi^{*} 2 \rho$ of $\mathrm{O}_{2}$ is increased
(d) Bond leng... | 1 |
What process is best used when only one manuscript is viable? | 0 |
4. The electronic configurations of bivalent europium and trivalent cerium are:
(atomic number : $\mathrm{Xe}=54, \mathrm{Ce}=58, \mathrm{Eu}=63$ )
(a) $[\mathrm{Xe}] 4 f^{2}$ and $[\mathrm{Xe}] 4 f^{7}$
(b) $[\mathrm{Xe}] 4 f^{7}$ and $[\mathrm{Xe}] 4 f^{1}$
(c) $[\mathrm{Xe}] 4 f^{7} 6 \mathrm{~s}^{2}$ and $[\m... | 1 |
What is th eofficial compilation of federal statutory law called? | 0 |
4. The image of an extended object, placed perpendicular to the principal axis of a mirror, will be erect if
(a) the object and the image are both real
(b) the object and the image are both virtual
(c) the object is real but the image is virtual
(d) the object is virtual but the image is real. | 1 |
What was Steve Jobs' hobby? | 0 |
9. An object is placed at a distance $u$ from a simple microscope of focal length $f$. The angular magnification obtained depends
(a) on $f$ but not on $u$
(b) on $u$ but not on $f$
(c) on $f$ as well as $u$
(d) neither on $f$ nor on $u$. | 1 |
29. The number of ways of arranging $m$ positive and $n(<m+1)$ negative signs in a row so that no two negative signs are together is
a. ${ }^{m+1} P_{n}$
b. ${ }^{n+1} P_{m}$
c. ${ }^{m+1}{ }^{1} C_{n}$
d. ${ }^{n+1} C_{m}$ | 1 |
At what location are the best known monuments in the south of India? | 0 |
- 47 A 75 g Frisbee is thrown from a point 1.1 m above the ground with a speed of $12 \mathrm{~m} / \mathrm{s}$. When it has reached a height of 2.1 m , its speed is $10.5 \mathrm{~m} / \mathrm{s}$. What was the reduction in $E_{\mathrm{mec}}$ of the Frisbee-Earth system because of air drag? | 1 |
$\bullet 38$ Figure 22-58a shows a circular disk that is uniformly charged. The central $z$ axis is perpendicular to the disk face, with the origin at the disk. Figure 22-58b gives the magnitude of the electric field along that axis in terms of the maximum magnitude $E_{m}$ at the disk surface. The $z$ axis scale is se... | 1 |
38. A certain physiologically important first-order reaction has an activation energy equal to $45.0 \mathrm{~kJ} / \mathrm{mol}$ at normal body temperature $\left(37^{\circ} \mathrm{C}\right)$. Without a catalyst, the rate constant for the reaction is $5.0 \times 10^{-4} \mathrm{~s}^{-1}$. To be effective in the human... | 1 |
What is the most ridiculous question you've been asked to answer on Quora? | 0 |
25. Two metallic rings $A$ and $B$, identical in shape and size but having different resistivities $\rho_{A}$ and $\rho_{B}$, are kept on top of two identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in identical manner, the rings $A$ and $B$ jump to heights $h_{A}$ and $h... | 1 |
15. Which one of the following reagents is not suitable for the elimination reaction
(a) $\mathrm{NaI}$
(b) $\mathrm{NaOEt} / \mathrm{EtOH}$
(c) $\mathrm{NaOH} / \mathrm{H}_{2} \mathrm{O}$
(d) $\mathrm{NaOH} / \ma... | 1 |
I got 11516 in neet2016 can I get less than 200 rank in 2017? | 0 |
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