List of practice Questions

Let $x, y$ and $z$ be positive real numbers Suppose $x, y$ and $z$ are the lengths of the sides of a triangle opposite to its angles $X, Y$ and $Z$, respectively If $\tan \frac{x}{2}+\tan \frac{z}{2}=\frac{2 y}{x+y+z}$ then which of the following statements is/are TRUE?

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $c_1y = (c_2 +c_3 )e^{x+c_4}$ is

In the reaction scheme shown below, Q, R, and S are the major products.

The correct structure of

Let $f:[0,2] \rightarrow R$ be the function defined by
$f(x)=(3-\sin (2 \pi x)) \sin \left(\pi x-\frac{\pi}{4}\right)-\sin \left(3 \pi x+\frac{\pi}{4}\right)$ If $\alpha, \beta \in[0,2]$ are such that $\{x \in[0,2]: f(x) \geq 0\}=[\alpha, \beta]$, then the value of $\beta-\alpha$ is ______

$5.00\, mL$ of $0.10 \,M$ oxalic acid solution taken in a conical flask is titrated against $NaOH$ from a burette using phenolphthalein indicator. The volume of $NaOH$ required for the appearance of permanent faint pink color is tabulated below for five experiments. What is the concentration, in molarity, of the $NaOH$ solution?

Exp. No.	Vol. of NaOH (mL)
1	12.5
2	10.5
3	9.0
4	9.0
5	9.0

Corner points of the feasible region determined by the system of linear constraints are $(0, 3), (1, 1)$ and $(3, 0)$. Let $z = px = qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the minimum of $z$ occurs at $(3, 0)$ and $(1, 1)$ is

Choose the correct statement(s) among the following

Consider the following compounds in the liquid form:
$O _{2}, HF , H _{2} O , NH _{3}, H _{2} O _{2}, CCl _{4}, CHCl _{3}, C _{6} H _{6}, C _{6} H _{5} Cl$
When a charged comb is brought near their flowing stream, how many of them show deflection as per the following figure?

Consider the following four compounds I, II, III and IV. Choose the correct statement(s)

In an experiment, $m$ grams of a compound $X$ (gas/liquid/solid) taken in a container is loaded in a balance as shown in figure I below. In the presence of a magnetic filed, the pan with $X$ is either deflected upwards (figure II), or deflected downwards (figure III), depending on the compound $X$. Identify the correct statements(s)

The $1^{\text {st }}, 2^{\text {nd }}$, and the $3^{\text {rd }}$ ionization enthalpies, $I_{1}, I_{2}$, and $I_{3}$, of four atoms with atomic numbers $n, n+1$, $n+2$, and $n+3$, where 𝑛 < 10, are tabulated below. What is the value of n?

Atomic Number	Ionization Enthalpy (kJ/mol)
Atomic Number	I₁	I₂	I₃
n	1681	3374	6050
n+1	2081	3952	6122
n+2	469	4562	6910
n+3	738	1451	7733

The structure of a peptide is given below:

If the absolute values of the net charge of the peptide at $pH =2, pH =6$, and $pH =11$ are $\left| z _{1}\right|,\left| z _{2}\right|$, and $\left| z _{3}\right|$, respectively, then what is $\left|z_{1}\right|+\left|z_{2}\right|+\left|z_{3}\right|$ ?

Which of the following plots is (are) correct for the given reaction? ([P] $_{0}$ is the initial concentration of $P$ )

If a line makes an angle of $\pi/3$ with each of $x$ and and $y$-axis, then the acute angle made by $z$-axis is

A uniform electric field, E=-400$\sqrt3\vec{Y}$YNC^-1is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 2√10 × 10⁶ ms⁻¹. This particle is aimed to hit a target T, which is 5 m away from its entry point into the field schematically in the figure. Take $\frac{q}{m}$ = 10¹⁰ckg^-1.

A uniform electric field