Practice Questions

Q50. The number of groups present in a tripeptide Asp – Glu – Lys is ____

Q50.The mass percentage of nitrogen in histamine is ________

Q50.The number of chiral carbons in chloramphenicol is ____________.

Q50.A solution of phenol in chloroform when treated with aqueous NaOH gives compound Pas a major product. The mass percentage of carbon in P is ______ .

Q50.The number of chiral carbon(s) present in peptide, lle-Arg-Pro, is ................

Q50.For the disproportionation reaction 2 Cu+(aq) ⇌Cu(s) + Cu2+(aq) at 298K,ln K (where K is the equilibrium constant) is _______ ×10−1 Given : (E°Cu2+ / Cu+= 0. 16V E°Cu+ / Cu= 0. 52V RTF = 0. 025)

Q50.The number of chiral centres in penicillin is _________.

Q51.If α and β are the roots of the equation 2x(2x + 1) = 1, then β is equal to : (1) 2α(α + 1) (2) −2α(α + 1) (3) 2α(α −1) (4) 2α2

Q51.Let α and β be the roots of the equation x2 −x −1 = 0 . If pk = (α)k + (β)k, k ≥1, then which one of the following statements is not true? (1) p3 = p5 −p4 (2) p5 = 11 (3) (p1 + p2 + p3 + p4 + p5) = 26 (4) p5 = p2 ⋅p3

Q51.The set of all real values of λ for which the quadratic equation (λ2 + 1)x2 −4λx + 2 = 0 always have exactly one root in the interval (0, 1) is : (1) (−3, −1) (2) (0, 2) (3) (1, 3] (4) (2, 4]

Q51.Let S , be the set of all real roots of the equation, 3x(3x −1) + 2 = |3x −1| + |3x −2|, then (1) contains exactly two elements. (2) is a singleton. (3) is an empty set. (4) contains at least four elements.

Q51.The product of the roots of the equation 9x2 −18 x + 5 = 0 is : (1) 59 (2) 2581 (3) 275 (4) 259 ¯¯

Q51.If α and β be two roots of the equation x2 −64x + 256 = 0. Then the value of 1 1 + ( β5 ) ( α5 ) JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper (1) 2 (2) 3 (3) 1 (4) 4

Q51.Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3 , then its other root lies in (1) (−1, 0) (2) (1, 3) (3) (–3, –1) (4) (0, 1) 1 1 2 2 +

Q51.If α and β are the roots of the equation, 7x2 −3x −2 = 0, then the value of α + β is equal to: 1−α2 1−β2 (1) 27 (2) 1 32 24 (3) 3 (4) 27 8 16

Q51.If the equation x2 + bx + 45 = 0, b ∈R has conjugate complex roots and they satisfy |z + 1| = 2√10, then (1) b2 −b = 30 (2) b2 + b = 72 (3) b2 −b = 42 (4) b2 + b = 12

Q51.Let λ ≠0 be in R. If α and β are the roots of the equation, x2 −x + 2λ = 0 and α and γ are the roots of the equation, 3x2 −10x + 27λ = 0, then βγλ is equal to: (1) 27 (2) 18 (3) 9 (4) 36 a + b is equal to:

Q51.If A = {x ∈R : |x| < 2} and B = {x ∈R : |x −2| ≥3}; then (1) A ∩B = (−2, −1) (2) B −A = R −(−2, 5) (3) A ∪B = R −(2, 5) (4) A −B = [−1, 2)

Q51.Let α and β be the roots of the equation, 5x2 + 6x −2 = 0. If Sn = αn + βn, n = 1, 2, 3, . . . . , then (1) 6S6 + 5S5 = 2S4 (2) 5S6 + 6S5 + 2S4 = 0 (3) 5S6 + 6S5 = 2S4 (4) 6S6 + 5S5 + 2S4 = 0 1+sin 9 +i cos

Q51.The number of real roots of the equation, e4x + e3x −4e2x + ex + 1 = 0 is: (1) 1 (2) 3 (3) 2 (4) 4

Q51.Consider the two sets: A = {m ∈R : both the roots of x2 −(m + 1)x + m + 4 = 0 are real } and B = [−3, 5) Which of the following is not true? (1) A −B = (−∞, −3) ∪(5, ∞) (2) A ∩B = {−3} (3) B −A = (−3, 5) (4) A ∪B = R

Q51.Let [t] denote the greatest integer ≤t. Then the equation in x, [x]2 + 2[x + 2] −7 = 0 has : (1) exactly two solutions (2) exactly four integral solutions (3) no integral solution (4) infinitely many solutions

Q51.Let α and β be two real roots of the equation (k + 1)tan2x −√2 ⋅λ tan x = (1 −k), where k(≠−1) and λ are real numbers. If tan2(α + β) = 50, then a value of λ is (1) 10√2 (2) 10 (3) 5 (4) 5√2

Q52.The value of 30 ( −1+i√31−i ) is : (1) 65 (2) 215 i (3) −215 (4) −215 i

Q52.If α and β are the roots of the equation x2 + px + 2 = 0 and α1 and β1 are the roots of the equation + α1 ) is equal to : 2x2 + 2qx + 1 = 0, then (α −1α )(β −1β )(α + β1 )(β (1) 9 4 (9 + q2) (2) 49 (9 −q2) (3) 4 9 (9 + p2) (4) 94 (9 −p2)