List of practice Questions

Let $ P(x,y) $ be a point on the curve $ {{y}^{2}}=4x $ at which the tangent is perpendicular to the line $ 2x+y=-2. $ Then, the coordinates of the point $P$ are

If the points $ (2a,\,a),\,(a,\,2a) $ and $ (a,\,\,a) $ form a triangle of area $ 32\text{ }sq $ units, then the centroid of the triangle is

Let \(f:R\to R\) be a function such that the third derivative of \(f(x)\) vanishes for all \(x\). If \(f(0)=1,\,f'(2)=4\) and \(f''(1)=2,\) then \(f(x)\) equals to

In the binomial expansion of $ {{(a-b)}^{n}},\,\,n\,\,\ge \,5, $ the sum of $5^{th}$ and $6^{th}$ term is zero. Then, $ \frac{a}{b} $ is equal to

The angle between the two lines $ \frac{2-x}{1}=\frac{y}{2}=\frac{z+3}{1} $ and $ \frac{x-4}{4}=\frac{y-1}{1}=\frac{z-5}{2} $ is

If $ f(x)={{\log }_{e}}\,(1+x)-{{\log }_{e}}(1-x), $ then the value of $ \int_{-1/2}^{1/2}{f(x)\,\,\,dx} $ equals to

Consider two half-cells based on the reaction $A g^{+}(a q)+e^{-} \rightarrow A g(s)$ The left half-cell contains $A g^{+}$ions at unit concentration, and the right half-cell initially had the same concentration of $A g^{+}$ions, but just enough $NaCl_{(a q)}$ had been added to completely precipitate the $A g_{(a q)}^{+}$as $AgCl$. If the emf of the cell is $0.29\, V$, the $\log _{10} K_{s p}$ would have been

When $Cl_2$ gas reacts with hot and concentrated sodium hydroxide solution, the oxidation number of chlorine changes from

Aluminium is extracted from alumina $(Al_2O_3)$ by electrolysis of a molten mixture of

Two spheres $A$ and $B$ of masses $m_1$ and $m_2$ respectively collide. $A$ is at rest initially and $B$ is moving with velocity $v/2$ along x-axis. After collision $B$ has a velocity in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction

The magnetic flux linked with a coil satisfies the relation $\phi= (4t^2 + 6t + 9) Wb$, where $t$ is the time in second. The e.m.f. induced in the coil at $t\, =\, 2$ second is

The site of Krebs cycle is

The Lac Operon is turned on when allolactose molecules bind to :

Which of the statements is not true?

A metal crystallizes with a face-centered cubic lattice. The edge of the unit cell is $408\, pm$. The diameter of the metal atom is

A certain gas takes three times as long to effuse out as helium. Its molecular mass will be:

A nucleophilic substitution reaction proceeds through $S _{ N } 1$ mechanism. So, the reaction is

The molecules in an ideal gas at $27^{\circ} C$ have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?

Dimension of universal gas constant $(R)$ is

A uniform rod of length $L$ and mass $M$ is held vertical, with its bottom end pivoted to the floor. The rod falls under gravity, freely turning about the pivot. If acceleration due to gravity is $g$, what is the instantaneous angular speed of the rod when it makes an angle $60^{\circ}$ with the vertical?

A travelling harmonic wave on a string is described by $y$ = 7.5 sin (0.005$x$ + 12$t$) in metre. Its time period in second is

The product of reaction between aniline and acetic anhydride is

What are the dimensions of electrical conductivity?

The $ C-H $ bond distance is the longest in

The correct order of electron gain enthalpy $ (\Delta _{eg}H) $ of the halogen atoms is