List of practice Questions

Let B and C be the two points on the line \(y + x = 0\) such that B and C are symmetric with respect to the origin. Suppose A is a point on \(y – 2x = 2\) such that \(\Delta ABC\) is an equilateral triangle. Then, the area of the \(\Delta ABC\) is

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to

Let P = \(\left[\begin{matrix} \frac{\sqrt3}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt3}{2} \end{matrix}\right]\) A = \(\left[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right]\) and Q = PAP^T. If P^TQ²⁰⁰⁷P = \(\left[\begin{matrix} a & b \\ c & d \end{matrix}\right]\), then 2a+b-3c-4d equal to

The slope of tangent at any point (x, y) on a curve y = y(x) is \(\frac{x^2+y^2}{2xy},x>0\) If y(2) = 0, then a value of y(8) is

if \(2x^y+3y^x=20\) then \(\frac{dy}{dx}\) at (2,2) is equal to:

Let \( (\alpha, \beta) \) be the centroid of the triangle formed by the lines \( 15x - y = 82 \), \( 6x - 5y = -4 \), and \( 9x + 4y = 17 \). Then \( \alpha + 2\beta \) and \( 2\alpha - \beta \) are the roots of the equation:

If the set \(\left( Re \left( \frac{z-\bar{z}+z\bar{z}}{2-3z+5\bar{z}}\right) : z ∈ C, Re(z)=3 \right)\) is equal to the interval (α,β), then 24(β-α) is equal to

Let the solution curve y = y(x) of the differential equation\(\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1 + x^6)^{3/2}} y = 2x \exp\left(x^3 - \frac{\tan^{-1}(x^3)}{1 + x}\right)^6\)pass through the origin. Then y(1) is equal to:

Let \(S=\left\{z∈C : \bar{z}=i(z^2+Re(\bar{z}))\right\}\). Then \(\sum\limits_{z∈S}|z|^2\) is equal to

If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation

Let the image of the point P(1, 2, 6) in the plane passing through the points A(1, 2, 0), B(1, 4, 1) and C(0, 5, 1) be Q (α, β, γ). Then (α² + β² + γ²) is equal to

The major product formed in the following reaction is

Match the following List-I and List-II:

List-I	Industry	List-II	Waste Generated
(A)	Steel Plants	(I)	Gypsum
(B)	Thermal Power Plants	(II)	Fly ash
(C)	Fertilizer industries	(III)	Slag
(D)	Ppaer mills	(IV)	Bio-degradable Wastes

Choose the correct answer from the options given below:

Given below arc two statements:
Statement I : In the metallurgy process. sulphide ore is converted to oxide before reduction.
Statement II : Oxide ores in general are easier to reduce.
In the light of the above statements, choose the most appropriate answer from the options given below

In the above reaction. Left hand side and right hand side rings are named as 'A' and 'B' respectively. They undergo ring expansion. The correct statement for this process is:

Match List I with List II

	List I		List II
A	Nitrogen oxides in air	I	Eutrophication
B	Nitrogen oxides in air	II	Eutrophication
C	Carbon dioxide	III	Global warming
D	Phosphate fertilisers in water	IV	Acid rain

Choose the correct answer from the options given below:

The one giving maximum number of isomeric alkenes on dehydrohalogenation reaction is
(excluding rearrangement)

Match List I with List II

List-I	Reaction	List-II	Reagents
(A)	Hoffmann Degradation	(I)	Conc.KOH,\(\triangle\)
(B)	Clemenson reduction	(II)	CHCl₃, NaOH/H₃O⁺
(C)	Cannizaro reaction	(III)	Br₂, NaOH
(D)	Reimer-Tiemann Reaction	(IV)	Zn-Hg/HCl

Choose the correct answer from the option given below:

Given below are two statements :
Statement I: SbCI, is more covalent than SbCI3
Statement II: The higher oxides of halogens also tend to be more stable than the lower ones.
In the light of the above statements, choose the most appropriate answer from the options given below :

For lead storage battery pick the the correct statements.
A. During charging of battery, PbSO4 on anode is converted into PbO2
B. During charging of battery, PbSO4 on cathode is converted into PbO2
C. Lead storage battery, consists of grid of lead packed with PbO2 as anode
D. Lead storage battery has ~ 38% solution of sulphuric acid as an electrolyte
Choose the correct answer from the options given below:

Choose the halogen which is most reactive towards SN1 reaction in the given compounds (A, B, C & D)

Given below are two statements: One is labelled as "Assertion A" and the other is labelled as "Reason R".
Assertion A: In the complex Ni(CO), and Fe(CO)s, the metals have zero oxidation state.
Reason R: Low oxidation states are found when a complex has ligands capable of π-donor character in addition to the o-bonding.
In the light of the above statements, choose the most appropriate answer from the option given below.

The statement/s which are true about antagonists from the following is/are:
A. They bind to the receptor site.
B. Get transferred inside the cell for their action.
C. Inhibit the natural communication of the body.
D. Mimic the natural messenger.
Choose the correct answer from the options given below:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Butan -1- ol has higher boiling point than ethoxyethane.
Reason R: Extensive hydrogen bonding leads to stronger association of molecules.
In the light of the above statements, choose the correct answer from the options given below: