List of practice Questions

A mixture contains milk and water in the ratio 8 ∶ x. If 3 liters of water is added in 33 liters of mixture, the ratio of milk and water becomes 2 ∶ 1, then value of x is:

Let the tangent drawn to the parabola $y ^2=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x+2 y=5$. Then the normal to the hyperbola $\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$ at the point $(\alpha+4, \beta+4)$ does NOT pass through the point :

Match List - I with List - II 
                                   List I                                                                                  List II
A \(N _2( g )+3 H _2( g ) \rightarrow 2 NH _3( g )\)                                                                   I \(Cu\)  
B \(CO ( g )+3 H _2( g ) \rightarrow CH _4( g )+ H _2 O ( g )\)                                      II \(Cu / ZnO - Cr _2 O _3\) 
C \(CO ( g )+ H _2( g ) \rightarrow HCHO ( g )\)                                               III \(Fe _x O _y+ K _2 O + Al _2 O _3\) 
D \(CO ( g )+2 H _2\) (g) \(\rightarrow CH _3 OH ( g )\)                                                             IV \(Ni\) 
Choose the correct answer from the optionsgiven below :

Match List - I with List - II 
List-I (Compound)                                              List-II (Shape)
A \(BrF _5\)                                                                    I bent 
B \(\left[ CrF _6\right]^{3-}\)                                                             II square pyramidal
C \(O _3\)                                                                     III trigonal bipyramidal 
D \(PCl _5\)                                                                    IV octahedral 
Choose the correct answer from the optionsgiven below :

Match List - I with List - II 
 

List-I (Processes/Reactions)		List-II (Catalyst)
A	$2 SO _2( g )+ O _2( g ) \rightarrow 2 SO _3( g )$	I	$Fe ( s )$
B	$4 NH _3( g )+5 O _2( g ) \rightarrow$$4 NO ( g )+6 H _2 O ( g )$	II	$Pt ( s )- Rh ( s )$
C	$N _2( g )+3 H _2( g ) \rightarrow 2 NH _3( g )$	III	$V _2 O _5$
D	Vegetable oil $(l)+ H _2 \rightarrow$Vegetable ghee(s	IV	$Ni ( s )$

Choose the correct answer from the options given below:

Let \(ABC\) be a triangle such that \(\overrightarrow{ BC }=\vec{ a }\), \(\overrightarrow{ CA }=\vec{ b }, \overrightarrow{ AB }=\vec{ c },|\vec{ a }|=6 \sqrt{2},|\vec{ b }|=2 \sqrt{3}\) and \(\vec{ b } \cdot \vec{ c }=12\) Consider the statements :\((S1): |(\vec{ a } \times \vec{ b })+(\vec{ c } \times \vec{ b })|-|\vec{ c }|=6(2 \sqrt{2}-1)\)\((S2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then

Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P \left( E _1\right)=\frac{2+3 p }{6}$, $P \left( E _2\right)=\frac{2- p }{8}$ and $P \left( E _3\right)=\frac{1- p }{2}$ If the maximum and minimum values of $p$ are $p _1$ and $p _2$, then $\left( p _1+ p _2\right)$ is equal to :

Given two statements below: 
Statement I: In $Cl _2$ molecule the covalent radius is double of the atomic radius of chlorine. 
Statement II: Radius of anionic species is always greater than their parent atomic radius Choose the most appropriate answer from options given below:

The curve y(x) = ax³ + bx² + cx + 5 touches the x-axis at the point P (–2, 0) and cuts the y-axis at the point Q, where y is equal to 3. Then the local maximum value of y(x) is :

Match List-I with List-II, match the gas evolved during each reaction:
 

List-I		List-II
(A)	$\left( NH _4\right)_2 Cr _2 O _7 \xrightarrow{\Delta}$	(I)	$H _2$
(B)	$KMnO _4+ HCl \rightarrow$	(II)	$N _2$
(C)	$Al + NaOH + H _2 O \rightarrow$	(III)	$O _2$
(D)	$NaNO _3 \xrightarrow{\Delta}$	(IV)	$Cl _2$

Choose the correct answer from the options given below:

Let the solution curve of the differential equation $x d y=\left(\sqrt{x^2+y^2}+y\right) d x, x>0$, intersect the line $x =1$ at $y =0$ and the line $x=2$ at $y=\alpha$. Then the value of $\alpha$ is :

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$ is equal to:

The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively If $P(X=1)=\frac{4}{243}$, then $P(X=4$ or 5$)$ is equal to :

Which reactant will give the following alcohol on reaction with one mole of phenyl magnesium bromide \(( PhMgBr )\) followed by acidic hydrolysis?

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)$ is :

Match List-I with List-II
 

List-I		List-II
(A)	Cd(s)+2Ni(OH)3(s)→CdO(s)+2Ni(OH)2(s)+H2O(l)	(I)	Primary battery
(B)	Zn(Hg)+HgO(s)→ZnO(s)+Hg(l)	(II)	Discharging of secondary battery
(C)	2PbSO4(s)+2H2O(l)→Pb(s)+PbO2(s)+2H2SO4(aq)	(III)	Fuel cell
(D)	2H2(g)+O2(g)→2H2O(l)	(IV)	Charging of secondary battery

Choose the correct answer from the options given below:

Identify the correct statement for the below given transformation

Choose the correct option for the following reactions

Statements about Enzyme Inhibitor Drugs are given below:

1. There are Competitive and Noncompetitive inhibitor drugs
2.  These can bind at the active sites and allosteric sites
3.  Competitive Drugs are allosteric site blocking drugs
4.  Non-competitive Drugs are active site blocking drugs 

Choose the correct answer from the options given below :

Terylene polymer is obtained by condensation of :