List of practice Questions

Given below are two statements.
Statement I: The presence of weaker π-bonds make alkenes less stable than alkanes.
Statement II: The strength of the double bond is greater than that of carbon-carbon single bond.
In the light of the above statements, choose the correct answer from the options given below.

If \(a = \lim_{{n \to \infty}} \sum_{{k=1}}^{n} \frac{2n}{{n^2 + k^2}}\)and
\(f(x) = \sqrt{\frac{1 - \cos x}{1 + \cos x}}, \quad x \in (0, 1)\) then

Match List-I with List-II.

List-I (Metal) 

 

 

List-II (Emitted light

 

wavelength (nm))

(A) Li (I) 670.8
(B) Na (II) 589.2
(C) Rb (III) 780.0
(D) Cs (IV) 455.5

Choose the most appropriate answer from the options given below:

A granite block starts sliding on a slope (inclination of 30° with the horizontal) under the effect of gravity only, along the true direction of inclination of the slope and hits the ground in 4 seconds. Considering zero friction and zero cohesion during sliding, the vertical height of the point (with respect to the ground) from where the block was dislodged is _____m. (g = 10 m/s2) (In integer)
The number of $\beta$ particles emitted in the nuclear reaction $^{238}U_{92} → ^{206}Pb_{82}$ is _______.
The number of significant figures in $5.0820 x 10^2$ is _________.
The pH of an aqueous buffer prepared using CH3COOH and CH3COO Na+ is 4.80.
The quantity \(\frac{[CH_3COO^-]-[CH_3COOH]}{[CH_3COOH]}\) is _____. (round off to three decimal places)
[Given: pKa of CH3COOH in water is 4.75]
2 L of 0.2 M \(H_2SO_4\) is reacted with 2 L of 0.1 M NaOH solution, the molarity of the resulting product \(Na_2SO_4\) in the solution is _______ millimolar. (Nearest integer)
16 sin(20°) sin(40°) sin(80°) is equal to :

The area bounded by the curves y = |x2 – 1| and y = 1 is

Suppose that four persons enter a lift on the ground floor of a building. There are seven floors above the ground floor and each person independently chooses her exit floor as one of these seven floors. If each of them chooses the topmost floor with probability \(\frac{1}{3}\) and each of the remaining floors with an equal probability, then the probability that no two of them exit at the same floor equals
The integral \(\iint(x^2+y^2)dxdy\) over the area of a disk of radius 2 in the xy plane is ___π.
An act to discourage or dissuade an intending bidder from bidding at an auction sale is known as
\(\lim\limits_{n \rightarrow \infin}\frac{6}{n+2}\left\{(2+\frac{1}{n})^2+(2+\frac{2}{n})^2+...+(2+\frac{n-1}{2})^2\right\}\) equals
A solid sphere of mass $1 \,kg$ and radius $1 \,m$ rolls without slipping on a fixed inclined plane with an angle of inclination $\theta=30^{\circ}$ from the horizontal .Two forces of magnitude $1 \,N$ each, parallel to the incline, act on the sphere, both at distance $r=05 \,m$ from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ____ $ms ^{-2}$ (Take $g=10 \,m s ^{-2}$)
A solid sphere
If $y = y ( x ), x \in\left(0, \frac{\pi}{2}\right)$ be the solution curve of the differential equation$ \left(\sin ^2 2 x\right) \frac{d y}{d x}+\left(8 \sin ^2 2 x+2 \sin 4 x\right) y$ $ =2 e^{-4 x}(2 \sin 2 x+\cos 2 x), \text { with } y\left(\frac{\pi}{4}\right)=e^{-\pi},$ then $y\left(\frac{\pi}{6}\right)$ is equal to:
In the process of extraction, if maceration is accomplished by heating the drug and solvent in a close vessel, then this modification is known as _____
Consider a particle of mass m moving in a plane with a constant radial speed \(\dot{r}\) and a constant angular speed \(\dot{\theta}\). The acceleration of the particle in (r,\(\theta\)) coordinates is

If 
\(n(2n+1)\int_{0}^{1}(1−xn)^{2n}dx=1177\int_{0}^{1}(1−x^n)^{2n+1}dx\)
,then n ∈ N is equal to ______.

A 500 nm light is used for imaging in a confocal microscope. What will be the best resolution (in nm) of this microscope?
Total number of isomers (including stereoisomers) obtained on monochlorination of methylcyclohexane is____.

Let A, B, C be three points whose position vectors respectively are
\(\vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}\)
\(\vec{b} = 2\hat{i} + α\hat{j} + 4\hat{k}, α ∈ R\)
\(\vec{c} = 3\hat{i} - 2\hat{j} + 5\hat{k}\)
If α is the smallest positive integer for which\(\vec{a},\vec{b},\vec{c}\)
are non collinear, then the length of the median, in ΔABC, through A is:

In an actively growing population from a single bacterium, 1,048,576 cells are present after 20th generation. How many cells were there in 5th generation?
Let a vector $\vec{a}$ has a magnitude 9. Let a vector $\vec{b}$ be such that for every $(x, y) \in R \times R-\{(0,0)\}$, the vector $(x \vec{a}+y \vec{b})$ is perpendicular to the vector $(6 y \vec{a}-18 x \vec{b})$. Then the value of $|\vec{a} \times \vec{b}|$ is equal to:
The average unit weight of the uppermost part of the crust is 25000 N/m³. The vertical stress at a depth of 1 km would be MPa. (In integer)