Question stringlengths 2 3k | label int64 0 1 |
|---|---|
20. The moment of inertia of hollow sphere (mass $M$ ) of inner radius $R$ and outer radius
$2 R$, having material of uniform density, about a diametric axis is
(a) $31 M R^{2} / 70$
(b) $4... | 1 |
8. If the slope of line through the origin which is tangent to the curve $y=x^{3}+x+16$ is $m$, then the value of $m-4$ is | 1 |
12. Let $z$ and $z_{0}$ be two complex numbers. It is given that $|z|=1$ and the numbers $z, z_{0}, z \bar{z}_{0}, 1$ and 0 are represented in an Argand diagram by the points $P, P_{0}, Q, A$ and the origin, respectively Show that the triangles $P O P_{0}$ and $A O Q$ are congruent. Hence, or otherwise, prove that $\le... | 1 |
5 A slab is subjected to two forces $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ of same magnitude $F$ as shown in the figure. Force $\mathbf{F}_{2}$ is in $x y$-plane while force $\mathbf{F}_{1}$ acts along $Z$-axis at the point $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}})$. The moment of these forces about point $O$ will be
!... | 1 |
On what date was it announced that the capital of India would be moved to Delhi? | 0 |
How can I stop wasting time on unproductive websites? | 0 |
56. If $I_{m, n}=\int \cos ^{m} x \sin n x d x$, then $7 I_{4,3}-4 I_{3,2}$ is equal to
a. constant
b. $-\cos ^{2} x+C$
c. $-\cos ^{4} x \cos 3 x+C$
d. $\cos 7 x-\cos 4 x+C$ | 1 |
Can you sue a judge if they denied a constitutional right? | 0 |
Is there a relationship between multiple personality disorder and borderline personality disorder? | 0 |
6. Equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ is
a. $x+2 y-2 z=0$
b. $3 x+2 y-2 z=0$
c. $x-2 y+z=0$
d. $5 x+2 y-4 z=0$ | 1 |
Example 3.38 Discuss the differentiability of
$$
f(x)= \begin{cases}(x-e) 2^{-2\left(\frac{1}{1(a-x)}\right)}, & x \neq e \text { at } x=e . \\ 0, & x=e\end{cases}
$$ | 1 |
20. In the $L$ - $C$ circuit shown, $C=1 \mu \mathrm{F}$. With capacitor charged to $100 \mathrm{~V}$, switch $S$ is suddenly closed at time $t=0$. The circuit then oscillates at $10^{3} \mathrm{~Hz}$.
(a) Calculate $\omega$ and $T$
(b) Express $q$ as a function of time
(c) Calculate $L$
 $2 \sqrt{5}$
(b) $\frac{\sqrt{5}}{4}$
(c) $4 \sqrt{5}$
(d) $\frac{\sqrt{5}}{2}$ | 1 |
What are techniques for avoiding pregnancy? | 0 |
27. The compound having both $s p$ and $s p^{2}$ hybridized carbon atoms is \$ \qquad \$
(propene, propane, propadiene) | 1 |
39. The normal at a variable point $P$ on the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ of eccentricity $e$ meets the axes of the ellipse at $Q$ and $R$, then the locus of the midpoint of $Q R$ is a conic with an eccentricity $e^{\prime}$ such that
a. $e^{\prime}$ is independent of $e$
b. $e^{\prime}=1$
c. $e... | 1 |
Which English words are now disappearing? | 0 |
What are the real world application of Depth first search for graph? | 0 |
Phone with removable battery or non-removable battery, which one is better and why? | 0 |
129. All the jacks, queens, kings and aces of a regular 52 cards deck are taken out. The 16 cards are thoroughly shuffled and my
opponent, a person who always tells the truth, simultaneously draws two cards at random and says, 'I hold at least one ace'. The probability that he holds two aces is
a. $2 / 8$
b. $4 / 9$
c.... | 1 |
What do European powers that exibit their control ovet an area accept? | 0 |
67. The coefficient of $x^{4}$ in the expansion of $\left\{\sqrt{1+x^{2}}-x\right\}^{-}$ in ascending powers of $x$, when $|x|<1$, is
a. 0
b. $\frac{1}{2}$
c. $-\frac{1}{2}$
d. $-\frac{1}{8}$ | 1 |
Can Donald Trump become the next Hitler? | 0 |
5. Let $C_{1}$ and $C_{2}$ be two circles whose equations are $x^{2}+y^{2}$ $-2 x=0$ and $x^{2}+y^{2}+2 x=0 . P(\lambda, \lambda)$ is a variable point. Then match the following.
| Column I | Column II |
| :--- | :--- |
| a. $\quad P$ lies inside $C_{1}$ but outside $C_{2}$ | p. $\lambda \in(-\infty,-1) \cup(0, \infty)... | 1 |
In the example given, what seemed exotic when introduced into China but is common in the United States? | 0 |
7. When YDSE is conducted with white light, a white fringe is observed at the centre of the screen. When the screen is moved towards the slits by $5 \mathrm{~mm}$, then this white fringe
(a) does not move
(b) becomes red
(c) disappears
(d) Nothing can be said | 1 |
How many stations are there on the Delhi Metro? | 0 |
Should I quit medical school if it is making me miserable? | 0 |
New restrictions on New Delhi's transportation system were enacted by the Supreme Court to accomplish what goal? | 0 |
12.26 Explain the reason for the fusion of an organic compound with metallic sodium for testing nitrogen, sulphur and halogens. | 1 |
What is Kalamkari? | 0 |
Is it safe to travel/visit Pakistan? | 0 |
What did Peter I found on the Baltic Sea? | 0 |
What is scope of data science in coming years? | 0 |
Is there any easy way to get job in Chicago? | 0 |
14. Dissolving $120 \mathrm{~g}$ of a compound of (mol. wt. 60 ) in $1000 \mathrm{~g}$ of water gave a solution of density $1.12 \mathrm{~g} / \mathrm{mL}$. The molarity of the solution is:
(a) $1.00 \mathrm{M}$
(b) $2.00 \mathrm{M}$
(c) $2.50 \mathrm{M}$
(d) $4.00 \mathrm{M}$ | 1 |
25. If $4 \hat{i}+7 \hat{j}+8 \hat{k}, 2 \hat{i}+3 \hat{j}+4 \hat{k}$ and $2 \hat{i}+5 \hat{j}+7 \hat{k}$ are the position vectors of the vertices $A, B$ and $C$, respectively, of triangle $A B C$, then the position vector of the point where the bisector of angle $A$ meets $B C$ is
a. $\frac{2}{3}\left(-6 \hat{i}^{\pri... | 1 |
What is the possibility of building elevated roads above railway line? | 0 |
103. Let these base $A B$ of a triangle $A B C$ be fixed and the vertex $C$ lie on a fixed circle of radius $r$. Lines through $A$ and $B$ are drawn to intersect $C B$ and $C A$, respectively, at $E$ and $F$ such that $C E: E B=1: 2$ and $C F: F A=$ $1: 2$. If the point of intersection $P$ of these lines lies on the me... | 1 |
(ii) $\left[\mathrm{CoBr}_2(\text { en })_2\right]^{+}$ | 1 |
What are the pros and cons of studying in Canada vs studying in US? | 0 |
29. Vapour density of $\mathrm{N}_2 \mathrm{O}_4$ which dissociated according to the equation $\mathrm{N}_2 \mathrm{O}_4(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_2(\mathrm{~g})$ is 25.67 at $100^{\circ} \mathrm{C}$ and a pressure of 1 atm . Calculate the degree of dissociation and $K_p$ for the reaction. | 1 |
19. The order of reactivity of the given haloalkanes towards nucleophile is
(a) $\mathrm{RI}>\mathrm{RBr}>\mathrm{KCl}$
(b) $\mathrm{RCl}>\mathrm{RBr}>\mathrm{RI}$
(c) $\mathrm{RBr}>\mathrm{RCl}>\mathrm{RI}$
(d) $\mathrm{RBr}>\mathrm{RI}>\mathrm{RCl}$ | 1 |
Question 15:
Solve $\sin \left(\tan ^{-1} x\right),|x|<1$ is equal to
(A) $\frac{x}{\sqrt{1-x^2}}$
(B) $\frac{1}{\sqrt{1-x^2}}$
(C) $\frac{1}{\sqrt{1+x^2}}$
(D) $\frac{x}{\sqrt{1+x^2}}$ | 1 |
18. The minimum number of times a fair coin needs to be tossed, so that the probability of getting atleast two heads is atleast 0.96 , is
(2015 Adv.) | 1 |
5. Assertion : A normal body can radiate energy more than a perfectly black body.
Reason: A perfectly black body is always black in colour. | 1 |
15. If $f:[0,4 \pi] \rightarrow[0, \pi]$ be defined by $f(x)=\cos ^{-1}(\cos x)$. Then, the number of points $x \in[0,4 \pi]$ satisfying the equation $f(x)=\frac{10-x}{10}$, is | 1 |
What is the GDS of Traveloka? | 0 |
Where is the Golgi apparatus located? | 0 |
Ex 2.50
Find The nuber of common circles
circles $x^{2}+y^{2}+2 x+8 y-23=0$ and $x^{2}+y^{2}-4 x-10 y+9$ $=0$ | 1 |
3. Among the following, the set of parameters that represents path functions, is:
(A) $q+w$
(B) $q$
(C) $w$
(D) $H-T S$
(a) (B) and (C)
(b) (B), (C) and (D)
(c) $(\mathrm{A})$ and (D)
(d) $(\mathrm{A}),(\mathrm{B})$ and $(\mathrm{C})$ | 1 |
Name one of the tribes Native Americans formed in the Americas? | 0 |
30. In the following reaction,
the structure of the major product ' $X$ ' is
(a)
: How do I add topics to my blog post on Quora? | 0 |
In what year did Sony and BMG Germany merge? | 0 |
7. An infinite GP has first term $x$ and sum 5 , then $x$ belongs to
(2004, 1M)
(a) $x<-10$
(b) $-10<x<0$
(c) $0<x<10$
(d) $x>10$ | 1 |
How did Christopher columbus treat or encounter with native Americans? | 0 |
(a) Find the time when they collide. | 1 |
What are the names for a traditional female short-top piece of clothing? | 0 |
How do I save money while online shopping? | 0 |
Was there slavery in vedic era? | 0 |
In what year what New Delhi inaugurated as the capital of India? | 0 |
Where is Basque Country located? | 0 |
2.31. As a result of the isobaric heating by $\Delta T=72 \mathrm{~K}$ one mole of a certain ideal gas obtains an amount of heat $Q=1.60 \mathrm{~kJ}$. Find the work performed by the gas, the increment of its internal energy, and the value of $\gamma=C_{p} / C_{V}$. | 1 |
7. $S_{1}$ and $S_{2}$ are two coherent sources of sound having no initial phase difference. The velocity of sound is $330 \mathrm{~m} / \mathrm{s}$. No maxima will be formed on the line passing through $S_{2}$ and perpendicular to the line joining $S_{1}$ and $S_{2}$. If the frequency of both the sources is
 electric field (b) magnetic field (c) electric energy (d) magnetic energy | 1 |
17. Complete hydrolysis of starch gives :
(a) glucose only
[Main Online April 10, 2015]
(b) galactose and fructose in equimolar amounts
(c) glucose and galactose in equimolar amounts
(d) glucose and fructose in equimolar amounts | 1 |
1. For the $x$-t equation of a particle in SHM along $x$-axis, match the following two columns.
$$
x=2+2 \cos \omega t
$$
| Column I | Column II |
| :--- | :--- |
| (a) Mean position | (p) $x=0$ |
| (b) Extreme position | (q) $x=2$ |
| (c) Maximum potential energy at | (r) $x=4$ |
| (d) Zero potential energy at | (s)... | 1 |
Which is the least corrupt country? | 0 |
What are the best ways to start investing in real estate? | 0 |
How does Reliance Jio provides free voice calling? | 0 |
How can I stop my zipper from falling down? | 0 |
12.
(I) (II)
$\mathrm{H}-\mathrm{N}---\mathrm{N}---\mathrm{N}$
In hydrogen azide, the bond orders of bonds (I) and (II) are
(a) I $<2$, II $>2$
(b) I $>2$, II $>2$
(c) I $>2$, II $<2$
(d) I $<2$, II $<2$ | 1 |
What is the Sahara, and how do the average temperatures there compare to other deserts? | 0 |
2.  | 1 |
29. If $(1+a x)^{n}=1+8 x+24 x^{2}+\ldots$, then $a=\ldots$ and $n=\ldots$.
(1983, 2M) | 1 |
Who is the fastest woman athlete in the world? | 0 |
**Example 4.1** A straight wire of mass 200 g and length 1.5 m carries a current of 2 A . It is suspended in mid-air by a uniform horizontal magnetic field B (Fig. 4.3). What is the magnitude of the magnetic field?
 6
(b) 10
(c) 4
(d) 8 | 1 |
When was the Government of India Act passed? | 0 |
Which one is easier, IELTS or TOEFL? How much time is required for the preparation if I have good English? | 0 |
13. On which of the following intervals is the function $f$ given by $f(x)=x^{100}+\sin x-1$ decreasing ?
(A) $(0,1)$
(B) $\frac{\pi}{2}, \pi$
(C) $0, \frac{\pi}{2}$
(D) None of these | 1 |
Example 3.89 Find the sum to $n$ terms of the series $1 /(1 \times 3)+1 /(3 \times 5)+1 /(5 \times 7)+\cdots$. | 1 |
What was Le Corbusier 's profession? | 0 |
15. The positive value of $k$ for which $k e^x-x=0$ has only one root is
(a) $\frac{1}{2}$
(b) 1
(c) $e$
(d) $\log _e 2$ | 1 |
What exactly does the 7th Amendment of the U.S. Constitution mean? | 0 |
16. The length of vector $\overrightarrow{A G}$ is
a. $\sqrt{17}$
b. $\sqrt{51} / 3$
c. $3 / \sqrt{6}$
d. $\sqrt{59} / 4$ | 1 |
2. Find the values of
(a) $(4 \hat{\mathbf{i}}) \times(-6 \hat{\mathbf{k}})$
(b) $(3 \hat{\mathbf{j}}) \cdot(-4 \hat{\mathbf{j}})$
(c) $(2 \hat{\mathbf{i}}) \cdot(-4 \hat{\mathbf{k}})$ | 1 |
What are the best things to learn in Pune? | 0 |
2. If the boiling point of $\mathrm{H}_{2} \mathrm{O}$ is $373 \mathrm{~K}$, the boiling point of $\mathrm{H}_{2} \mathrm{~S}$ will be :
(a) less than $300 \mathrm{~K}$
(b) equal to $373 \mathrm{~K}$
(c) more than $373 \mathrm{~K}$
(d) greater than $300 \mathrm{~K}$ but less than $373 \mathrm{~K}$ | 1 |
51. Which of the following have identical bond order?
(a) $\mathrm{CN}^{-}$
(b) $\mathrm{O}_{2}^{-}$
(c) $\mathrm{NO}^{+}$
(d) $\mathrm{CN}^{+}$ | 1 |
Why did the USA leave the Republic of China after WWII and instead assisted in rebuilding Japan? | 0 |
18. Bakelite is obtained from phenol by reacting with:
(a) Acetal
(b) $\mathrm{CH}_{3} \mathrm{CHO}$
(c) $\mathrm{HCHO}$
(d) Chlorobenzene | 1 |
How do we prevent acne? | 0 |
How did the Chinese and Japanese type their native language before computers? | 0 |
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