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35. In a group of data, there are $n$ observations, $x, x_{2}, \ldots, x_{n}$. If $\sum_{i=1}^{n}\left(x_{i}+1\right)^{2}=9 n$ and $\sum_{i=1}^{n}\left(x_{i}-1\right)^{2}=5 n$, the standard deviation of the data is
(a) 2
(b) $\sqrt{7}$
(c) 5
(d) $\sqrt{5}$ | 1 |
43. Of the given anions, the strongest Bronsted base is
(a) $\mathrm{ClO}^{-}$
(b) $\mathrm{ClO}_{2}^{-}$
(c) $\mathrm{Cl} \mathrm{O}_{3}^{-}$
(d) $\mathrm{ClO}_{4}^{-}$ | 1 |
7. Let the moment of inertia of a hollow cylinder of length 30 $\mathrm{cm}$ (inner radius $10 \mathrm{~cm}$ and outer radius $20 \mathrm{~cm}$ ) about its axis be $I$. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also $I$, is
(a) $16 \mathrm{~cm}$
(b) $14 \mathrm{~... | 1 |
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6. The rate of the simple reaction $2 \mathrm{NO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}$, when the volume of the reaction vessel is doubled,
(a) will grow eight times of its initial rate
(b) reduce to one-eighth of its initial rate
(c) will grow four times of its initial rate
(d) reduce to one-fourth of its init... | 1 |
How long and how many failures made you start accepting failures as a part of life? What was your most dreaded and horrible failure? How did you manage to get back on your feet? | 0 |
26. The 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) $5 x+2 y-4 z=0$
(b) $x+2 y-2 z=0$
(c) $3 x+2 y-3 z=0$
(d) $x-2 y+z=0$ | 1 |
Which are the most important questions of IE Irodov for JEE Advanced? | 0 |
Who was the last Western Roman Emperor? | 0 |
12. A bag contains 10 different balls. Five balls are drawn simultaneously and then replaced and then seven balls are drawn. The probability that exactly three balls are common to the two drawn is $p$, then the value of $12 p$ is. | 1 |
8. The major product of the following reaction is -
$\xrightarrow[\text { dimethylformamide }]{\mathrm{Ph} \stackrel{\ominus}{\mathrm{S}} \stackrel{\oplus}{\mathrm{Na}}}$
(a)
 x+b y+c z=0 \\
& a x+(q+b) y+c z=0 \\
& a x+b y+(r+c) z=0
\end{aligned}
$$
has a non-trivial solution, then value of $\frac{a}{p}+\frac{b}{q}+\frac{c}{r}$ is
a. -1
b. 0
c. 1
d. 2 | 1 |
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4. A turn of radius $20 \mathrm{~m}$ is banked for the vehicles going at a speed of $36 \mathrm{~km} / \mathrm{h}$. If the coefficient of static friction between the road and the tyre is 0.4 . What are the possible speeds of a vehicle so that it neither slips down nor skids up $?\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}... | 1 |
6. Let $f=\left\{\left(x, \frac{x^{2}}{1+x^{2}}\right): x \in \mathbf{R}\right\}$ be a function from $\mathbf{R}$ into $\mathbf{R}$. Determine the range of $f$. | 1 |
86. There are three copies each of four different books. The number of ways in which they can be arranged in a shelf is
a. $\frac{12!}{(3!)^{4}}$
b. $\frac{12!}{(4!)^{3}}$
c. $\frac{21!}{(3!)^{+} 4!}$
d. $\frac{12!}{(4!)^{3} 3!}$ | 1 |
What is monotheism? | 0 |
26. Figure (27-E4) shows a cylindrical tube with adiabatic walls and fitted with an adiabatic separator. The separator can be slid into the tube by an external mechanism. An ideal gas $(\gamma=1 \cdot 5)$ is injected in the two sides at equal pressures and temperatures. The separator remains in equilibrium at the middl... | 1 |
11. The major product of the following addition reaction is
$\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2} \xrightarrow{\mathrm{Cl}_{2} / \mathrm{H}_{2} \mathrm{O}}$
[Main April 12, 2019 (I)]
(a)
(d)
 $\frac{1}{3}$
(b) $\frac{1}{6}$
(c) $\frac{1}{2}$
(d) $\frac{1}{4}$
(1998, 2M) | 1 |
A wire of resistance 36 ohms is bent into an equilateral triangle. What is the resistance between its vertices? | 0 |
15. In the above question, the amount of salt in the tank at the moment of overflow is
a. $20 \mathrm{lb}$
b. $50 \mathrm{lb}$
c. $30 \mathrm{lb}$
d. None of these | 1 |
What would one do in the last 24 hours of one's life? | 0 |
What is the meaning of intragency? | 0 |
4. Refer to figure (26-Q1). Let $\Delta U_{1}$ and $\Delta U_{2}$ be the changes in internal energy of the system in the processes $A$ and B. Then
(a) $\Delta U_{1}>\Delta U_{2}$
(b) $\Delta U_{1}=\Delta U_{2}$
(c) $\Delta U_{1}<\Delta U_{2}$
(d) $\Delta U_{1} \neq \Delta U_{2}$. | 1 |
As products came within their financial reach what concept began to interest the middle class? | 0 |
43. A person on a diet might lose 2.3 kg per week. Express the mass loss rate in milligrams per second, as if the dieter could sense the second-by-second loss. | 1 |
51. With reference to the scheme given below, which of the given statement(s) about $T, U, V$ and $W$ is (are) correct?
(a) $T$ is soluble in hot aqueous $\mathrm{NaOH}$
(b) $U$ is opti... | 1 |
(b) $t=10 \mathrm{~ms}$ and | 1 |
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21. $\cot x \cot 2 x-\cot 2 x \cot 3 x-\cot 3 x \cot x=1$ | 1 |
6. Which one of the following molecules is polar ?
(a) $\mathrm{XeF}_{4}$
(b) $\mathrm{IF}_{5}$
(c) $\mathrm{SbF}_{5}$
(d) $\mathrm{CF}_{4}$ | 1 |
2.5 Yellow light emitted from a sodium lamp has a wavelength $(\lambda)$ of 580 nm . Calculate the frequency $(v)$ and wavenumber $(\bar{v})$ of the yellow light. | 1 |
What is the best place to buy Bitcoins in Israel? | 0 |
Example 7.10 If $a_{r}=(\cos 2 r \pi+i \sin 2 r \pi)^{\frac{1}{9}}$, then prove that $\left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right|=0$ | 1 |
From a candidate's point of view, what are the qualities of a great recruiter? | 0 |
2. The resistive network shown below is connected to a DC source of $16 \mathrm{~V}$. The power consumed by the network is $4 \mathrm{~W}$. The value of $R$ is
(2019 Main, 12 April I)
(a) $... | 1 |
57. Which of the following options has correct combination considering List - I and List - II?
(a) (IV), (Q), (R)
(b) (IV), (Q), (U)
(c) (III), (S), (R)
(d) (III), (T), (U)
Directions [Qs. 58-60] : By appropriately matching the information given in the three columns of the following table. Columns 1, 2 and 3 conta... | 1 |
I forgot my email Id and password on Facebook. How can I log into Facebook? | 0 |
New Delhi's Per Capita income grew by what percentage in 2009-10? | 0 |
19. If $z=x+i y$ and $w=(1-i z) /(z-i)$, then $|w|=1$ implies that, in the complex plane
(1983, 1M)
(a) $z$ lies on the imaginary axis
(b) $z$ lies on the real axis
(c) $z$ lies on the unit circle
(d) None of these | 1 |
42. What mass of NaCl would contain the same total number of ions as 245 g of $\mathrm{MgCl}_2$ ? | 1 |
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What is the thalamus a part of? | 0 |
When will Apple release the next generation of MacBook Pros with redesigned hardware? | 0 |
71. A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three.digits same is
a. $1 / 9$
b. $1 / 10$
c. $1 / 50$
d. $1 / 100$ | 1 |
41. In the above question, the velocity of end $A$ at the instant it hits the ground is
(a) $\sqrt{3 g l}$
(b) $\sqrt{12 g l}$
(c) $\sqrt{6 g l}$
(d) None of these | 1 |
51. Match the transformations in column I with appropriate options in column II
## Column-I
(A) $\mathrm{CO}_{2}(\mathrm{~s}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})$
(B) $\mathrm{CaCO}_{3}(\mathrm{~s}) \rightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})$
(C) $2 \mathrm{H}^{\circ} \rightarrow \mathr... | 1 |
Example 2.94. The product of the sines of the angles of a triangle is $p$ and the product of their cosines is $q$. Show that the tangents of the angles are the roots of the equation $q x^{2}-p x^{2}+(1+q)$ $x-p=0$. | 1 |
How can I be more approachable? | 0 |
5. In a room, there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amount of illumination is
a. $12^{2}-1$
b. $2^{12}$
c. $2^{12} \cdots 1$
d. $12^{2}$ | 1 |
9. In the given circuit, the internal resistance of the $18 \mathrm{~V}$ cell is negligible. If $R_{1}=400 \Omega, R_{3}=100 \Omega$ and $R_{4}=500 \Omega$ and the reading of an ideal voltmeter across $R_{4}$ is $5 \mathrm{~V}$, then the value of $R_{2}$ will be
(2019 Main, 9 Jan II)
 $R=\frac{1}{2} b \operatorname{cosec} \alpha$
(b) $R=\frac{2}{3} b \cos \alpha$
(c) $r=\frac{b \sin 2 \alpha}{2(1+\cos \alpha)}$
(... | 1 |
Poetry was considered to need lines and meter until when? | 0 |
Are all Roman gods borrowed from Greek mythology? | 0 |
The Chowmahalla Palace represents what type of architecture? | 0 |
How do I manage school studies (PCM), tuitions (PCM) and law coaching (preparing for CLAT- aiming for NLSIU Banglore)? How do I devote time to each? | 0 |
Why does psychiatrist Anil Aggrawal say androphilia and gynephilia are needed terms? | 0 |
The question is bearing in mind their hasn't been a new years attack intensifies the need for absolutely security lock down? | 0 |
12. For an ideal solution of two components $\mathrm{A}$ and $\mathrm{B}$, which of the following is true?
(a) $\Delta \mathrm{H}_{\text {mixing }}<0$ (zero)
(b) $\Delta \mathrm{H}_{\text {mixing }}>0$ (zero)
(c) $\mathrm{A}-\mathrm{B}$ interaction is stronger than $\mathrm{A}-\mathrm{A}$ and $\mathrm{B}-\mathrm{B}$... | 1 |
- Example 12.1 Three particles of masses $1 \mathrm{~g}, 2 \mathrm{~g}$ and $3 \mathrm{~g}$ are kept at points $(2 \mathrm{~cm}, 0),(0,6 \mathrm{~cm}),(4 \mathrm{~cm}, 3 \mathrm{~cm})$. Find moment of inertia of all three particles (in gm-cm ${ }^{2}$ ) about, (a) $x$-axis $\quad$ (b) $y$-axis $\quad$ (c) $z$-axis | 1 |
4. The smallest natural number $n$, such that the coefficient of $x$ in the expansion of $x^{2}+\frac{1}{x^{3}} \quad$ is ${ }^{n} C_{23}$, is
(2019 Main, 10 April II)
(a) 35
(b) 23
(c) 58
(d) 38 | 1 |
23. In the given potentiometer arrangement, the null point
(a) can be obtained for any value of $V$
(b) can be obtained only if $V<V_{0}$
(c) can be obtained only if $V>V_{0}$
(d) can never be obtained
 | 1 |
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6. The value of $\int_{0}^{\pi / 2} \frac{d x}{1+\tan ^{3} x}$ is
a. 0
b. 1
c. $\pi / 2$
d. $\pi / 4$ | 1 |
13. Which of the following is the condensed formula for 3-oxopentanal?
(A) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{2} \mathrm{COH}$
(B) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{2} \mathrm{CHO}$
(C) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COCHO}$
(D) $\mathrm{CH}_{3} \mathrm{CH}_{2} \math... | 1 |
6. Radiation coming from transitions $n=2$ to $n=1$ of hydrogen atoms fall on $\mathrm{He}^{+}$ions in $n=1$ and $n=2$ states. The possible transition of helium ions as they absorb energy from the radiation is
(a) $n=2 \rightarrow n=3$
(b) $n=1 \rightarrow n=4$
(c) $n=2 \rightarrow n=5$
(d) $n=2 \rightarrow n=4$ | 1 |
5.196. A certain substance is placed in a longitudinal magnetic field of a solenoid located between two Polaroids. The length of the tube with substance is equal to $l=30 \mathrm{~cm}$. Find the Verdet constant if at a field strength $H=56.5 \mathrm{kA} / \mathrm{m}$ the angle of rotation of polarization plane is equal... | 1 |
7. Write the following statement in five different ways, conveying the same meaning. p: If a triangle is equiangular, then it is an obtuse angled triangle. | 1 |
5. Which of the following is a mechanical wave?
(a) Radio waves
(b) $X$-rays
(c) Light waves
(d) Sound waves. | 1 |
Ex. 3. The degree of dissociation of pure water at $18^{\circ} \mathrm{C}$ is found to be $1.8 \times 10^{-9}$. Find ionic product of water and its dissociation constant at $18^{\circ} \mathrm{C}$. | 1 |
How to determine whether the reaction is endothermic or exothermic if the value delta energy is not given? | 0 |
80 A thin film with index of refraction $n=1.40$ is placed in one arm of a Michelson interferometer, perpendicular to the optical path. If this causes a shift of 7.0 bright fringes of the pattern produced by light of wavelength 589 nm , what is the film thickness? | 1 |
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(a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system. | 1 |
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3. A ball is projected from point $A$ with velocity $10 \mathrm{~ms}^{-1}$ perpendicular to the inclined plane as shown in figure. Range of the ball on the inclined plane is
(a) $\frac{40}{3} \mathrm{~m}$
(b) $\frac{20}{3} \mathrm{~m}$
(c) $\frac{12}{3} \mathrm{~m}$
(d) $\frac{60}{3} \mathrm{~m}$
![](https://cdn.mathp... | 1 |
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Are we on track for world war 3? | 0 |
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