Practice Questions

Q60.The correct sequence of amino acids present in the tripeptide given below is: (1) Val - Ser - Thr (2) Leu - Ser - Thr (3) Thr - Ser - Val (4) Thr - Ser - Leu

Q60.The increasing order of pKa of the following amino acids in aqueous solution is Glycine, Aspartate, Lysine, Arginine. (1) Arginine < Lysine < Glycine < Aspartate (2) Aspartate < Glycine < Arginine < Lysine (3) Glycine < Aspartate < Arginine < Lysine (4) Aspartate < Glycine < Lysine < Arginine

Q60.Among the following compounds, which one is found in RNA? (1) (2) (3) (4)

Q60. The correct match between Item I and Item II is: (1) (A) →(Q, R); (B) →(S); (C) →(P) (2) (A) →(R); (B) →(Q); (C) →(P) (3) (A) →(R); (B) →(S); (C) →(Q) (4) (A) →(Q); (B) →(S); (C) →(R)

Q60.Which of the following statements is not true about RNA? (1) It controls the synthesis of protein (2) It usually does not replicate (3) It has always double standard α - helix structure (4) It is present in the nucleus of the cell

Q60.Maltose on treatment with dilute HCl gives: (1) D-Glucose (2) D-Fructose (3) D-Galactose (4) D-Glucose and D- Fructose

Q60.Number of stereo centers present in linear and cyclic structures of glucose are respectively: (1) 4 and 4 (2) 5 and 5 (3) 4 and 5 (4) 5 and 4

Q60.The correct structure of histidine in a strongly acidic solution (pH = 2) is (1) (2) (3) (4)

Q60.The peptide that gives positive ceric ammonium nitrate and carbylamine tests is: (1) Gln −Asp (2) Asp −Gln (3) Lys −Asp (4) Ser −Lys

Q61.Let 𝛼 and 𝛽 be the roots of the equation 𝑥2 + 2𝑥+ 2 = 0, then 𝛼15 + 𝛽15 is equal to (1) -512 (2) 128 (3) 512 (4) -256

Q61.The number of all possible positive integral value of α for which the roots of the quadratic equation 6x2 −11x + α = 0 are rational numbers is: (1) 5 (2) 3 (3) 4 (4) 2

Q61.If α and β are the roots of the quadratic equation x2 + xsinθ −2sinθ = 0, θ ∈(0, 2π ) , then α12+β12 is equal to : (α−12+β−12).(α−β)24 (1) 26 (2) 212 (sinθ+8)12 (sinθ−4)12 (3) 212 (4) 212 (sinθ+8)12 (sinθ−8)6 , has magnitude , then −z is equal to:

Q61.If λ be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m −4)x + 2 = 0, then the least value of m for which λ + λ1 = 1, is : JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) 2 −√3 (2) −2 + √2 (3) 4 −2√3 (4) 4 −3√2 α −

Q61.The number of integral values of m for which the quadratic expression (1 + 2m) x2 −2(1 + 3m)x + 4(1 + m), x ∈R is always positive, is (1) 7 (2) 3 (3) 6 (4) 8

Q61.If three distinct numbers 𝑎, 𝑏, 𝑐 are in G.P. and the equations 𝑎𝑥2 + 2𝑏𝑥+ 𝑐= 0 and 𝑑𝑥2 + 2𝑒𝑥+ 𝑓= 0 have a common root, then which one of the following statements is correct? (1) 𝑑 𝑒 𝑓 are in A.P. (2) 𝑑, 𝑒, 𝑓 are in A.P. 𝑎, 𝑏, 𝑐 (3) 𝑑, 𝑒, 𝑓 are in G.P. (4) 𝑑 𝑒 𝑓 are in G.P. 𝑎, 𝑏, 𝑐

Q61.The value of λ such that sum of the squares of the roots of the quadratic equation, x2 + (3 −λ) x + 2 = λ has the least value is: (1) 2 (2) 49 (3) 15 (4) 1 8

Q61.If 𝛼 and 𝛽 are the roots of the equation 375 𝑥2 - 25𝑥- 2 = 0, then 𝑛 𝛽𝑟 is equal to: ∑ 𝑟= 1 lim ∑ 𝑟=𝑛 1 𝛼𝑟+ 𝑛→∞lim 𝑛→∞ (1) 1 (2) 21 12 346 (3) 7 (4) 29 116 358

Q61.Let p, q ∈ Q . If 2 −√3 is a root of the quadratic equation x2 + px + q = 0, then (1) p2–4q + 12 = 0 (2) q2 + 4p + 14 = 0 (3) p2–4q–12 = 0 (4) q2–4p–16 = 0

Q61.Consider the quadratic equation (c −5)x2 −2cx + (c −4) = 0, c ≠5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is (1) 11 (2) 12 (3) 18 (4) 10

Q61.The sum of the solutions of the equation √𝑥- 2 + √𝑥√𝑥- 4 + 2 = 0, 𝑥> 0 is equal to (1) 10 (2) 9 (3) 12 (4) 4 JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper

Q61.The number of real roots of the equation 5 + 2𝑥- 1 = 2𝑥2𝑥- 2 is : (1) 2 (2) 3 (3) 1 (4) 4 π

Q61.If m is chosen in the quadratic equation (m2 + 1)x2 −3x + (m2 + 1)2 = 0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is: (1) 4√3 (2) 10√5 (3) 8√3 (4) 8√5

Q61.If α, β and γ are three consecutive terms of a non-constant G.P. Such that the equations αx2 + 2βx + γ = 0 and x2 + x −1 = 0 have a common root, then α(β + γ) is equal to: (1) βγ (2) αβ (3) αγ (4) 0

Q61.If one real root of the quadratic equation 81x2 + kx + 256 = 0 is cube of the other root, then a value of k is : (1) -81 (2) 100 (3) 144 (4) -300 where x and y are real numbers then y −x equals

Q61.Let α and β be the roots of the quadratic equation x2 sin θ −x(sin θ cos θ + 1) + cos θ = 0 (0 < θ < 45∘), and (−1)n is equal to : α < β. Then ∑∞n=0 (αn + βn ) 1 (1) 1−cos θ − 1+sin1 θ (2) 1+cos1 θ + 1−sin1 θ 1 (3) 1−cos θ + 1+sin1 θ (4) 1+cos1 θ − 1−sin1 θ JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper