Practice Questions

Q60.Sulphur (S) containing amino acids from the following are: (a) isoleucine (b) cysteine (c) lysine (d) methionine (e) glutamic acid (1) b, c, e (2) a, b, c (3) b, d (4) a, d

Q60.The homoleptic and octahedral complex of Co2+ and H2O has ______ unpaired electron(s) in the t2g set of orbitals.

Q60.A trisubstituted compound 'A', C10H12O2 gives neutral FeCl3 test positive. Treatment of compound 'A' with NaOH and CH3Br gives C11H14O2, with hydroiodic acid gives methyl iodide and with hot conc. NaOH gives a compound B, C10H12O2. Compound 'A' also decolorises alkaline KMnO4. The number of 𝜋 bond/s present in the compound 'A' is _____ .

Q60.Number of ambidentate ligands in a representative metal complex M ( en ) ( SCN ) is _________ . [en = 4 ethylenediamine]

Q61.If the value of real number α > 0 for which x2 −5αx + 1 = 0 and x2 −αx −5 = 0 have a common real roots is 3 then β is equal to ________ √2β

Q64.If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is (1) 103 (2) 102 (3) 101 (4) 104

Q65.The largest natural number n such that 3n divides 66! is _______

Q65.If 2𝑛𝐶3: 𝑛𝐶3 = 10: 1, then the ratio 𝑛2 + 3𝑛: 𝑛2 - 3𝑛+ 4 is (1) 35: 16 (2) 27: 11 (3) 65: 37 (4) 2: 1

Q65.If tan15° + + + tan195° = 2a, then the value of 𝑎+ is : tan75° tan105° 𝑎 (1) 4 (2) 4 - 2√3 (3) 2 (4) 5 - 3 2√3

Q67.Statement ( 𝑃⇒𝑄) ∧( 𝑅⇒𝑄) is logically equivalent to (1) 𝑃⇒𝑅∨𝑄⇒𝑅 (2) 𝑃∧𝑅⇒𝑄 (3) 𝑃⇒𝑅∧𝑄⇒𝑅 (4) 𝑃∨𝑅⇒𝑄

Q67.If 2n+1P n−1 : 2n−1P n = 11 : 21 , then n2 + n + 15 is equal to :

Q67.The negation of the expression 𝑞∨( ( ~𝑞) ∧𝑝) is equivalent to (1) ( ~𝑝) ∧( ~𝑞) (2) 𝑝∧( ~𝑞) (3) ( ~𝑝) ∨( ~𝑞) (4) ( ~𝑝) ∨𝑞

Q67.The negation of the statement 𝑝∨𝑞∧𝑞∨~𝑟 is (1) 𝑝∨𝑟∧~𝑞 (2) ~𝑝) ∨𝑟∧~𝑞 (3) ~𝑝∨~𝑞∨~𝑟 (4) ~𝑝∨~𝑞∧~𝑟

Q68.Negation of p ∧(q ∧~(p ∧q)) is (1) (~(p ∧q)) ∨p (2) p ∨q (3) ~(p ∨q) (4) (~(p ∧q)) ∧q

Q69.The statement ( 𝑝∧( ~𝑞) ) ∨( ( ~𝑝) ∧ 𝑞) ∨( ( ~𝑝) ∧ ( ~𝑞) ) is equivalent to _____ (1) ~𝑝∨𝑞 (2) ~𝑝∨~𝑞 (3) 𝑝∨~𝑞 (4) 𝑝∨𝑞 Q70. 1 2 3 Let for 𝐴= 𝛼3 1 , 𝐴= 2. If |2 adj ( 2 adj ( 2𝐴) ) | = 32𝑛, then 3𝑛+ 𝛼 is equal to 1 1 2 (1) 9 (2) 11 (3) 12 (4) 10

Q69.The statement ~𝑝∨~𝑝∧𝑞 is equivalent to (1) ~𝑝∧𝑞 (2) 𝑝∧𝑞∧~𝑝 (3) ~𝑝∧𝑞∧𝑞 (4) ~𝑝∨𝑞 JEE Main 2023 (10 Apr Shift 2) JEE Main Previous Year Paper

Q70.Let H be the hyperbola, whose foci are (1 ± √2, 0) and eccentricity is √2 . Then the length of its latus rectum is: (1) 3 (2) 52 (3) 2 (4) 32

Q72.Among the two statements (S1) : (p ⇒q) ∧(p ∧(~q)) is a contradiction and (S2) : (p ∧q) ∨((~p) ∧q) ∨(p ∧(~q)) ∨((~p) ∧(~q)) is a tautology (1) only (S2) is true (2) only (S1) is true (3) both are false (4) both are true

Q72.Let p and q be two statements. Then ~(p ∧(p →~q) is equivalent to (1) p ∨(p ∧(~q)) (2) p ∨((~p) ∧q) (3) (~p) ∨q (4) p ∨(p ∧q)

Q72.Which of the following statements is a tautology? (1) p →(p ∧(p →q)) (2) (p ∧q) →(~(p) →q) (3) (p ∧(p →q)) →~q (4) p ∨(p ∧q)

Q72.The statement (p ∧(~q)) ⇒(p ⇒(~q)) is (1) equivalent to (~p) ∨(~q) (2) a tautology (3) equivalent to p ∨q (4) a contradiction

Q72.The converse of ((~p) ∧q) ⇒r is (1) ((~p) ∨q) ⇒r (2) (~r) ⇒p ∧q (3) (~r) ⇒((~p) ∧q) (4) (p ∨(~q)) ⇒(~r)

Q73.Negation of (p →q) →(q →p) is (1) (p~) ∨p (2) q ∧(~p) (3) (~q) ∧p (4) p ∨(~q)

Q73.The negation of (p ∧(−q)) ∨(−p) is equivalent to (1) p ∧(−q) (2) p ∧q (3) p ∨(q ∨(−p)) (4) p ∧(q ∧(−p))

Q75.Let A = {1, 2, 3, 4, 5, 6, 7} . Then the relation R = {(x, y) ∈A × A : x + y = 7} is (1) an equivalence relation (2) symmetric but neither reflexive nor transitive (3) transitive but neither symmetric nor reflexive (4) reflexive but neither symmetric nor transitive A−1 = αA + βI and α + β = −2, then 4α2 + β2 + λ2 is equal to :