List of practice Questions

The isoelectric point of glutamic acid is ______.

(round off to two decimal places)

The standard reduction potential (E⁰ ) of Fe³⁺→Fe is____V.
[Given: Fe³⁺→Fe2+ E ⁰ = 0.77 V and 
Fe²⁺→Fe E ⁰=−0.44 V] 
(round off to three decimal places)

The spin-only magnetic moment of B₂ molecule is_____ μ_𝐵 .
(round off to two decimal places)

The sum of the total number of stereoisomers (including enantiomers) present in the following molecules is _____.

The number of singlets observed in the 1H NMR spectrum of P is ____.

When a glass capillary tube is dipped in water, a 1.0 cm rise in the water level is observed at 18 °C. The internal radius of the capillary is ______ cm.
[Given: Surface tension of water at 18 °C = 73.2 dyne cm⁻¹ ; difference in the densities of water and air at 18 °C = 0.996 g cm⁻³ ; gravitational acceleration constant, g = 980 cm s⁻² .
Assume that water completely wets the glass capillary and the interface between the water and the air phase inside the capillary is a hemisphere.] (round off to two decimal places)

The volume of 2.0 mol of an ideal gas is reduced to half isothermally at 300 K in a closed system. The value of ΔG is_____ kJ.
[Given: R=8.314 J mol^-1 K^-1 ] 
(round off to two decimal places)

The spin-only magnetic moment of [Fe(acac)₃] is____μ𝐵 .
(round off to two decimal places)

Which one of the following groups has elements of order 1, 2, 3, 4, 5 but does not have an element of order greater than or equal to 6 ?

The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0,2π] is

The total number of acidic oxides from the following list is: $NO , N _2 O , B _2 O _3, N _2 O _5$, $CO , SO _3, P _4 O _{10}$

In a moving coil galvanometer if the number of turns increases by 25%, then change in voltage sensitivity is?

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion If the ratio of radii of their circular paths is $6: 5$ and their respective masses ratio is $9: 4$ Then, the ratio of their charges will be :

The points of intersection of the line $a x+b y=0,(a \neq b)$ and the circle $x^2+y^2-2 x=0$ are $A (\alpha, 0)$ and $B (1, \beta)$ The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is :

If the circles $x^2+y^2+6 x+8 y+16=0$ and $x^2+y^2+2(3-\sqrt{3}) x+x+2(4-\sqrt{6}) y$ $= k +6 \sqrt{3}+8 \sqrt{6}, k >0$ touch internally at the point $P(\alpha, \beta)$, then $(\alpha+\sqrt{3})^2+(\beta+\sqrt{6})^2$ is equal to _______

Let $S_1$ and $S_2$ be respectively the sets of all $a \in R -\{0\}$ for which the system of linear equations $ a x+2 a y-3 a z=1$ $ (2 a+1) x+(2 a+3) y+(a+1) z=2$ $(3 a+5) x+(a+5) y+(a+2) z=3$ has unique solution and infinitely many solutions Then

Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point $(x, y)$ on it is directly proportional to $\left(\frac{-y}{x}\right)$ If the curve passes through the point $(1,2)$ and $(8,1)$, then $\left|y\left(\frac{1}{8}\right)\right|$ is equal to

Let $x=2$ be a local minima of the function $f(x)=2 x^4-18 x^2+8 x+12$, $x \in(-4,4)$ If $M$ is local maximum value of the function $f$ in $(-4,4)$, then $M =$

The sum $1^2-2 \cdot 3^2+3 \cdot 5^2-4 \cdot 7^2+5 \cdot 9^2-\ldots+15 \cdot 29^2$ is_____

Let the area of the region $\left\{(x, y):|2 x-1| \leq y \leq\left|x^2-x\right|, 0 \leq x \leq 1\right\}$ be $A$ Then $(6 A +11)^2$ is equal to ____

$\displaystyle\lim _{n \rightarrow \infty} \frac{1}{2^n}\left(\frac{1}{\sqrt{1-\frac{1}{2^n}}}+\frac{1}{\sqrt{1-\frac{2}{2^n}}}+\frac{1}{\sqrt{1-\frac{3}{2^n}}}+\ldots +\frac{1}{\sqrt{1-\frac{2^n-1}{2^n}}}\right)$ is equal to

Let $f(x)=\begin{cases}x^2 \sin \left(\frac{1}{x}\right) & , x \neq 0 \\ 0 & , x=0\end{cases}$Then at $x=0$