List of practice Questions

Find the range of \(\frac{1}{7}-\sin5x\)
If the complex number (1 + 2i cosθ) / (1 - 3i cosθ) is purely imaginary, then find the number of values of θ in the interval [-2π, 2π].
If set A = { z: |z - 1| ≤ 1} and set B = { z: |z - 5i| ≤ |z - 5| }, if z = a + ib, where a, b ∈ I, then find the sum of modulus squares of A ∩ B.
If f(x) = 3ax3 + bx2 + cx + 1 and f(1) = 41, f'(1) = 2 and f''(2)= 4, then find (a2 + b2 + c2).
When 4 dice are rolled, then the probability of 16 as a sum is:
Consider the equation ax2 + bx + c = 0 . Find probability if a, b, c ∈ A where A = {1,2,3, ... , 8} that the equation has equal roots.
Consider a equation  P(x)= ax2 + bx + c =0. If a,b,c ∈ A, were A = {1, 2, 3, 4, 5, 6} . Then the probability that P(x) has real and distinct roots?
Bag X contains five one-rupee coins, four five rupee coins. Bag Y contains 4 one rupee and 5 five rupees. Bag Z contains 3 one-rupee coins and 6 five rupee coins. If 1 rupee coin is selected at random, what is the probability it is drawn from bag Y?
Tetrahedral dice having outcomes (1, 2, 3, 4) has 3 outcomes a, b, c (which are visible). Probability that ax2 + bx + c = 0 has real roots is m/n (m, n are coprime), then m + n =?

\(A\) is a neutral organic compound (M.F.: \(C_8H_9ON\)). On treatment with aqueous \(Br_2/HO^-\), \(A\) forms a compound \(B\) which is soluble in dilute acid. \(B\) on treatment with aqueous \(NaNO_2/HCl\) (0--5\(^\circ\)C) produces a compound \(C\) which on treatment with \(CuCN/NaCN\) produces \(D\). Hydrolysis of \(D\) produces \(E\) which is also obtainable from the hydrolysis of \(A\). \(E\) on treatment with acidified \(KMnO_4\) produces \(F\). \(F\) contains two different types of hydrogen atoms. The structure of \(A\) is 

What happens when methane undergoes combustion in systems A and B respectively?
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The diameter of colloidal particles in solution should not be much smaller than wavelength of light to show Tyndall effect. 
Reason R : The light scatters in all directions when the size of particles is large enough. 
In the light of the above statements, choose the correct answer from the options given below
The covalency and oxidation state respectively of boron in [BF4]-, are
Given below are two statements related to Ellingham diagram:
Statement-I: Ellingham diagrams can be constructed for formation of oxides, sulfides and halides of metals. 
Statement-II : It consists of plots of ΔfH° vs T for formation of oxides of elements. 
In the light of the above statements, choose the most appropriate 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 Isotopes of hydrogen have almost same chemical properties, but difference in their rates of reaction. 
Reason: R Isotopes of hydrogen have different enthalpy of bond dissociation. 
In the light of the above statements, choose the most appropriate answer from the options given below
better method for preparation of bef2 among the following is
The correct group of halide ions which can be oxidised by oxygen in acidic medium is
Which of the following complexes will exhibit maximum attraction to an applied magnetic field?
The total number of stereoisomers for the complex [Cr(ox)2Clbr]3- (where oxalate) is:
Given below are two statements:
Statement I: Tropolone is an aromatic compound and has 8л electrons. 
Statement II: electrons of >C = O group in tropolone is involved in aromaticity. 
In the light of the above statements, choose the correct answer from the options given below
Match the List I with List II
1- Bromopropane is reacted with regents in List I to give products in List II
 List I-Reagent List II-Product
(A)KOH(alc)INitrile
(B)KCL(alc)IIEster
(C)AgNo2IIIAlkene
(D)H3CC00AgIIINitroalkane
Choose the correct answer from the options given below:
The major products for the following reaction is
major products for the following reaction jee main
Match the List I with List II
 List I List II
(A)Weak intermolecular forces of attraction IHexamethylenedia mine + adipic acid 
(B)Hydrogen bondingIIAlEt3 + TiCl4 
(C)Heavily branched polymerIII2-chloro-1, 3-butadiene
(D)High density polymerIIIphenol+ formaldehyde

choose the correct answer from the options given below:

Which of the following compound is optically active?
Among the following four aromatic compounds, which one will have the lowest melting point?