Question stringlengths 2 3k | label int64 0 1 |
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84. Let $\vec{a}(x)=(\sin x) \hat{i}+(\cos x) \hat{j}$ and $\vec{b}(x)=(\cos 2 x) \hat{i}+(\sin 2 x) \hat{j}$ be two variable vectors $(x \in R)$. Then $\vec{a}(x)$ and $\vec{b}(x)$ are
a. collinear for unique value of $x$
b. perpendicular for infinite values of $x$
c. zero vectors for unique value of $x$
d. none of th... | 1 |
Why does the Ferranti effect increase the receiving end voltage when compared with the sending end voltage? | 0 |
34. The structure of which of the following chloro species can be explained on the basis of $d s p^{2}$ hybridisation?
[Main Online April 25, 2013]
(a) $\mathrm{PdCl}_{4}^{2-}$
(b) $\mathrm{FeCl}_{4}^{2-}$
(c) $\mathrm{CoCl}_{4}^{2-}$
(d) $\mathrm{NiCl}_{4}^{2-}$ | 1 |
9. $\int_{0}^{2} x \sqrt{2-x} d x$ | 1 |
11. The most unlikely representation of resonance structures of $p$ nitrophenoxide ion is
(a) 
(B) 
(c)  decrease in temperature
(b) increase in temperature
(c) decrease in pressure
(d) decrease in surface area | 1 |
What do rock stars do after a concert? | 0 |
14. Ammonia under a pressure of 15 atm at $27^{\circ} \mathrm{C}$ is heated to $347^{\circ} \mathrm{C}$ in a closed vessel in the presence of a catalyst. Under these conditions $\mathrm{NH}_3$ is partially decomposed according to the equation
$$
2 \mathrm{NH}_3 \rightleftharpoons \mathrm{~N}_2+3 \mathrm{H}_2 .
$$
T... | 1 |
22. Four harmonic waves of equal frequencies and equal intensities $I_{0}$ have phase angles $0, \frac{\pi}{3}, \frac{2 \pi}{3}$ and $\pi$. When they are superposed, the intensity of the resulting wave is $n I_{0}$. The value of $n$ is | 1 |
4. The displacement-time graph of a particle executing SHM is shown in figure. Which of the following statements is/are true?
(a) The velocity is maximum at $t=T / 2$
(b) The acceleration... | 1 |
10. In a stationary wave,
(a) all the particles of the medium vibrate in phase
(b) all the antinodes vibrate in phase
(c) the alternate antinodes vibrate in phase
(d) all the particles between consecutive nodes vibrate in phase. | 1 |
Why has pokemon GO suddenly stopped working in India? | 0 |
If you can describe life in one sentence, what it would be? | 0 |
Can I use two or more operating systems on a MacBook? | 0 |
2. Number of electrons involved in the electrodeposition of 63.5 g of Cu from a solution of $\mathrm{CuSO}_{4}$ is
(a) $6.022 \times 10^{23}$
(b) $3.011 \times 10^{23}$
(c) $12.044 \times 10^{23}$
(d) $6.022 \times 10^{22}$ | 1 |
17. The general solution of the trigonometric equation $\sin x+\cos x=1$ is given by
(1981, 2M)
(a) $x=2 n \pi ; n=0, \pm 1, \pm 2, .$.
(b) $x=2 n \pi+\pi / 2 ; n=0, \pm 1, \pm 2, \ldots$
(c) $x=n \pi+(-1)^{n} \frac{\pi}{4}-\frac{\pi}{4} ; n=0, \pm 1, \pm 2, \ldots$
(d) None of the above | 1 |
What diseases are transmitted through saliva? | 0 |
For controlling the fan, will we need to use a micro-processor or can we control it only using a micro-controller? | 0 |
I don't think I'm a smart person. Why do so many other people call me intelligent when really I'm not? Are they confused? Wishful thinking? | 0 |
7. For any $\theta \in \frac{\pi}{4}, \frac{\pi}{2}$, the expression $3(\sin \theta-\cos \theta)^{4}+6(\sin \theta+\cos \theta)^{2}+4 \sin ^{6} \theta$ equals (2019 Main, 9 Jan I) (a) $13-4 \cos ^{4} \theta+2 \sin ^{2} \theta \cos ^{2} \theta$
(b) $13-4 \cos ^{2} \theta+6 \cos ^{4} \theta$
(c) $13-4 \cos ^{2} \theta+... | 1 |
At what age did you first realize you were gay/bisexual and how did you realize it? | 0 |
Within the human body we observe multiple processes utilizing a liquid medium to transport data but when I look at a computer or robotic systems, I don't see a liquid medium like water being utilized for movement of data. Have we attempted to design a system which at its core uses a liquid medium to move data around? | 0 |
10. A radioactive element disintegrates for a time interval equal to its mean life. The fraction that has disintegrated is
(a) $\frac{1}{e}$
(b) $1-\frac{1}{e}$
(c) $\frac{0.693}{e}$
(d) $0.693\left(1-\frac{1}{e}\right)$ | 1 |
57. Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three points out of these lie on a rectangular hyperbola then the fourth point will lie on
a. the same hyperbola
b. conjugate hyperbola
c. one of the directrix
d. one of the asymptotes | 1 |
10. A diverging lens with magnitude of focal length $25 \mathrm{~cm}$ is placed at a distance of $15 \mathrm{~cm}$ from a converging lens of magnitude of focal length $20 \mathrm{~cm}$. A beam of parallel light falls on the diverging lens. The final image formed is (a) virtual and at a distance of $40 \mathrm{~cm}$ fro... | 1 |
1. Functional group not present in given compound is/are? | 1 |
17. The rate of a reaction decreased by 3.555 times when the temperature was changed from $40^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$. The activation energy (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) of the reaction is Take;
$\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ In $\overline{3.555=}=1.2... | 1 |
What are the most important tips on winter driving? | 0 |
I'm 14 and I just had sex for the first time, I feel so guilty and bad about myself, like I'm a failure. Why do I feel this? How do I feel better? | 0 |
What are reception statutes? | 0 |
In what id Jayapala see a danger to his dynasty? | 0 |
Is power a vector quantity? How is this determined? | 0 |
When did the British establish colonies in Australia? | 0 |
When did communism fall in allies of the Soviet Union? | 0 |
How many volts is an AA battery? | 0 |
21.
| Column I | | Column II | |
| :--- | :--- | :--- | :--- |
| (A) | If a circle passes through $A(1,0) B(0,-1)$ and $C\left(\frac{1}{\sqrt{3}}, \sqrt{\frac{2}{3}}\right)$ such that <br> the tangent at B makes an angle $\theta$ with line AB then $\tan \theta$ equals | ( p ) | -4 |
| (B) | From a point $(h, 0)$ co... | 1 |
3. The rate at which a substance cools in moving air is proportional to the difference between the temperatures of the substance and that of the air. If the temperature of the air is $290 \mathrm{~K}$ and the substance cools from $370 \mathrm{~K}$ to $330 \mathrm{~K}$ in $10 \mathrm{~min}$., when will the temperature b... | 1 |
5. Which of the vitamins given below is water soluble ?
[Main 2015]
(a) Vitamin E
(b) Vitamin K
(c) Vitamin C
(d) Vitamin D | 1 |
17. Geometrical isomerism is possible in :
 | 1 |
26. In the circuit shown in figure, the resistance of voltmeter is $6 \mathrm{k} \Omega$. The voltmeter reading will be
(a) $6 \mathrm{~V}$
(b) $5 \mathrm{~V}$
(c) $4 \mathrm{~V}$
(d) $... | 1 |
1. A circuit is connected as shown in the figure with the switch $S$ open. When the switch is closed, the total amount of charge that flows from $Y$ to $X$ is
(a) zero
(b) $54 \mu \mathrm... | 1 |
What is the name of the municipal government by which New Delhi is governed? | 0 |
What is digitisation? Why it has demand and why it is in India? | 0 |
When military pilots are flying a plane, what is the advantage of flight suits or coveralls compared to wearing traditional pants and a top? | 0 |
What resources are required to set up a soap manufacturing unit in India? | 0 |
139. If two of the lines represented by $x^{4}+x^{3} y+c x^{2} y^{2}-x y^{3}$ $+y^{4}=0$ bisect the angle between the other two, then the value of $c$ is
a. 0
b. -1
c. 1
d. -6 | 1 |
What company has a 40% stake in OTE? | 0 |
Which is the European country? | 0 |
41. When one drop of a concentrated HCl solution is added to one litre of pure water at $25^{\circ} \mathrm{C}$, the pH drops suddenly from 7 to about 4 . When the second drop of the same acid is added, the pH of the solution further drops to about
(a) 3.7
(b) 2.0
(c) 1.0
(d) 0 | 1 |
5. The minimum value of the expression $\sin \alpha+\sin \beta+\sin \gamma$, where $\alpha, \beta, \gamma$ are real numbers satisfying $\alpha$ $+\beta+\gamma=\pi$ is
a. positive
h zero
c. negative
d. -3
(IIT-JEE, 1995) | 1 |
6. Two solenoids have identical geometrical construction but one is made of thick wire and the other of thin wire.
Which of the following quantities are different for the two solenoids?
(a) self-inductance
(b) rate of Joule heating if the same current goes through them
(c) magnetic field energy if the same current g... | 1 |
How often should you wash your hair? | 0 |
24. A vertical spring is fixed to one of its end and a massless plank fitted to the other end. A block is released from a height $h$ as shown. Spring is in relaxed position. Then choose the correct statement.
(a) The maximum compression of the spring does not depend on $h$
(b) The maximum kinetic energy of the block ... | 1 |
-12 In Fig. 12-30, trying to get his car out of mud, a man ties one end of a rope around the front bumper and the other end tightly around a utility pole 18 m away. He then pushes sideways on the rope at its midpoint with a force of 550 N , displacing the center of the rope 0.30 m , but the car barely moves. What is th... | 1 |
What is the Deccan region known for culturally? | 0 |
What is true: the past, present or future? | 0 |
How do I find a good job? | 0 |
3. In given time $t=0$, Activity of two radioactive substances $A$ and $B$ are equal. After time $t$, the ratio of their activities $\frac{R_{B}}{R_{A}}$ decreases according to $e^{-3 t}$. If the half life of $A$ is $\operatorname{In} 2$, the half-life of $B$ will be
(a) $4 \ln 2$
(b) $\frac{\ln 2}{4}$
(c) $\frac{... | 1 |
Which exercise is effective to reduce tummy and belly fat? | 0 |
Emoticons: What does this mean? :^) | 0 |
14. If $\vec{a}$ satisfies $\vec{a} \times(\hat{i}+2 \hat{j}+\hat{k})=\hat{i}-\hat{k}$, then $\vec{a}$ is equal to
a. $\lambda \hat{i}+(2 \lambda-1) \hat{j}+\lambda \hat{k}, \lambda \in R$
b. $\lambda \hat{i}+(1-2 \lambda) \hat{j}+\lambda \hat{k}, \lambda \in R$
c. $\lambda \hat{i}+(2 \lambda+1) \hat{j}+\lambda \hat{k}... | 1 |
Why is ZEE News so anti-AAP? | 0 |
Some federal and state statutes remain on the books for how long after they are ruled unconstitutional? | 0 |
How does it feel to have your first salary? What did you do with it? What should I do with my salary? | 0 |
What is something you want to do, but would probably never do? | 0 |
How do I make her fall in love with me? | 0 |
What labels strove to support indie labels and music rightsholders? | 0 |
- Example 18.4 In interference, $\frac{I_{\max }}{I_{\min }}=\alpha$, find
$\left(a \frac{A_{\max }}{A_{\min }}\right.$
(b) $\frac{A_{1}}{A_{2}}$
(c) $\frac{I_{1}}{I_{2}}$ | 1 |
How much do I need to earn to live in New York City? | 0 |
What should I do re: new valuation and stock options? | 0 |
What type of system is American Federalism? | 0 |
If my dog bites me, should I kill it? | 0 |
If I open 2 bank accounts and one is with my husband, will he be able to know the activities in my other bank a/c or the presence of my 2nd bank a/c? | 0 |
21. Block $A$ of mass $m$ and block $B$ of mass $2 m$ are placed on a fixed triangular wedge by means of a massless, in extensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45^{\circ}$ to the horizontal on both sides. The coefficient of friction between block $A$ and the wedge is $2... | 1 |
76. The equation $\tan ^{4} x-2 \sec ^{2} x+a=0$ will have at least one solution if
a. $1<a \leq 4$
b $a \geq 2$
c. $a \leq 3$
d none of these | 1 |
Can somebody tell me a story of a successful long distance relationship that turned into a marriage? | 0 |
What was sometimes used or worn by early humans to form some type of culture visibly? | 0 |
Why is it black in outer space? | 0 |
What are some interview hacks? | 0 |
31. As shown in the figure, region $B C D E F$ and $A B F G$ are of refractive index 2.0 and 1.5 respectively. A particle $O$ is kept at the mid of $D H$. Image of the object as seen by the eye is at a distance
>\left(\frac{5}{2}-\frac{1}{x}\right)$ ?
a. $\left(\frac{2}{5}, \frac{1}{2}\right)$
b. $(1,2)$
c. $\left(\frac{2}{5}, \frac{3}{4}\right)$.
d. none of these | 1 |
I am not able to solve this physics question. Will somebody help me and solve it? | 0 |
Discuss the factors which influence the strength of timber and explain how the strength of timber is assessed in practice? | 0 |
7. The major product obtained from E2-elimination of 3-bromo-2fluoropentane is :
(a)
(b)
(c)
^2=x \log \frac{d^2 y}{d x^2}$
h. $\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^2=x \sin \left(\frac{d^2 y}{d x^2}\right)$
c. $x=\sin \left(\frac{d y}{d x}-2 y\right),|x|<1$... | 1 |
Why is YMCA so popular? | 0 |
17. Coordinates of vertex $B$ are
a. $(3 / 10,17 / 10)$
b. $(17 / 10,3 / 10)$
c. $(-5 / 2,9 / 2)$
d. $(1,1)$ | 1 |
10. Two friends $A$ and $B$ have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to the daughters of $A$ is $1 / 20$. Find the number of daughters each of them have. | 1 |
What philosophy formed at the time of the Gupta Empire? | 0 |
1. The determinant $\left|\begin{array}{ccc}a & b & a \alpha+b \\ b & c & b \alpha+c \\ a \alpha+b & b \alpha+c & 0\end{array}\right|=0$, if
a. $a, b ; c$ are in A.P.
b. $a, b, c$ are in G.P
c. $a, b, c$ are in H.P.
d. $\alpha$ is a root of the equation $a x^{2}+b x+c=0$
e. $(x-\alpha)$ is a factor of $a x^{2}+2 b x+c$... | 1 |
64. $A$ rectangle $A B C D$, where $A \equiv(0,0), B \equiv(4,0)$, $C \equiv(4,2), D \equiv(0,2)$, undergoes the following transformations successively:
(i) $f_{1}(x, y) \rightarrow(y, x)$,
(ii) $f_{2}(x, y) \rightarrow(x+3 y, y)$,
(iii) $f_{3}(x, y) \rightarrow((x-y) / 2,(x+y) / 2)$. The final figure will be
a. ... | 1 |
14. Equal weight of methane and oxygen are mixed in an empty container at $25^{\circ} \mathrm{C}$. The fraction of the total pressure exerted by oxygen is
(a) $1 / 3$
(b) $1 / 2$
(c) $2 / 3$
(d) $\frac{1}{3} \times \frac{273}{298}$ | 1 |
13. An object $A$ is kept fixed at the point $x=3 \mathrm{~m}$ and $y=1.25 \mathrm{~m}$ on a plank $P$ raised above the ground. At time $t=0$, the plank starts moving along the $+x$-direction with an acceleration $1.5 \mathrm{~m} / \mathrm{s}^{2}$. At
![](https://cdn.mathpix.com/cropped/2023_12_28_092f08a9ae3c385eb2cc... | 1 |
After I get a bachelor's degree in botany, should I get a job or continue my education? | 0 |
Why is memory associated with intelligence? | 0 |
What aspects of a building were considered part of the larger concept of function? | 0 |
What is your favorite place in the world? | 0 |
What can I do to be tall? | 0 |
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