Practice Questions

Q64.If a1, a2, a3, . . . . are in A.P. such that a1 + a7 + a16 = 40, then the sum of the first 15 terms of this A.P is: (1) 280 (2) 120 (3) 150 (4) 200

Q65.If the sum and product of the first three terms in an A. P. are 33 and 1155, respectively, then a value of its 11th term is: (1) −25 (2) −35 (3) 25 (4) −36

Q65.Let 𝑆𝑛 denote the sum of the first 𝑛 terms of an 𝐴. 𝑃. . If 𝑆4 = 16 and 𝑆6 = - 48 , then 𝑆10 is equal to: (1) -320 (2) -380 (3) -260 (4) -410

Q67.Let fk(x) = k1 (sink x + cosk x) for k = 1, 2, 3, … Then for all x ∈R, the value of f4(x) −f6(x) is equal to : (1) 1 (2) 1 12 4 (3) −1 (4) 5 12 12

Q68.A point on the straight line, 3𝑥+ 5𝑦= 15 which is equidistant from the coordinate axes will lie only in: (1) 1𝑠𝑡 and 2𝑛𝑑 quadrants (2) 1𝑠𝑡, 2𝑛𝑑 and 4th (3) 1𝑠𝑡 quadrant (4) 4𝑡ℎ quadrant quadrants

Q68.A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (−1, 1) and (2, 3) . Then the centroid of this triangle is: (1) ( 31 , 1) (2) (1, 73 ) (3) ( 31 , 2) (4) ( 13 , 35 )

Q68.Consider the set of all lines 𝑝𝑥+ 𝑞𝑦+ 𝑟= 0 such that 3𝑝+ 2𝑞+ 4𝑟= 0 . Which one of the following statements is true? 3 1 (1) The lines are not concurrent. (2) The lines are concurrent at the point 4, 2 . (3) The lines are all parallel. (4) Each line passes through the origin.

Q68.If a straight line passing through the point P(−3, 4) is such that its intercepted portion between the coordinate axes is bisected at P , then its equation is : (1) 4x + 3y = 0 (2) 4x −3y + 24 = 0 (3) 3x −4y + 25 = 0 (4) x −y + 7 = 0

Q69.If the straight line 2x −3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β) , then β equals : (1) −5 (2) 353 (3) 5 (4) −353

Q70.If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13 , then the eccentricity of the hyperbola is: (1) 13 (2) 2 12 (3) 13 (4) 13 6 8

Q70.The equation of a tangent to the parabola, x2 = 8y, which makes an angle θ with the positive direction of x− axis, is (1) y = xtanθ + 2cotθ (2) y = xtanθ −2cotθ (3) x = ycotθ + 2tanθ (4) x = ycotθ −2tanθ

Q70.Axis of a parabola lies along 𝑥-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive 𝑥-axis then which of following points does not lie on it? (1) 6, 4√2 (2) 5, 2√6 (3) 8, 6 (4) 4, - 4

Q71.Consider the following three statements: P : 5 is a prime number Q : 7 is a factor of 192 R : LCM of 5 and 7 is 35 Then the truth value of which one of the following statements is true? (1) P ∨(~Q ∧R) (2) (P ∧Q) ∨(~R) (3) (~P) ∨(Q ∧R) (4) (~P) ∧(~Q ∧R)

Q72.For any two statement p and q, the negative of the expression p ∨(~p ∧q) is (1) ~p ∨~q (2) p ∧q (3) ~p ∧~q (4) p ↔q

Q72.Contrapositive of the statement "If two numbers are not equal, then their squares are not equal". is : (1) If the squares of two numbers are not equal, then (2) If the squares of two numbers are equal, then the the numbers are equal. numbers are not equal. (3) If the squares of two numbers are equal, then the (4) If the squares of two numbers are not equal, then numbers are equal. the numbers are not equal.

Q72.If the truth value of the statement 𝑝→~𝑞∨𝑟 is false 𝐹, then the truth values of the statements 𝑝, 𝑞, 𝑟 are respectively JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper (1) 𝑇, 𝐹, 𝑇 (2) 𝑇, 𝐹, 𝐹 (3) 𝑇, 𝑇, 𝐹 (4) 𝐹, 𝑇, 𝑇

Q72.If 5𝑥+ 9 = 0 is the directrix of the hyperbola 16𝑥2 - 9𝑦2 = 144, then its corresponding focus is: (1) -5, 0 (2) 5, 0 5 5 (3) - 3, 0 (4) 3, 0

Q73.The contrapositive of the statement “If you are born in India, then you are a citizen of India”, is (1) If you are not born in (2) If you are a citizen of (3) If you are born in (4) If you are not a citizen India, then you are not India, then you are India, then you are not of India, then you are a citizen of India. born in India. a citizen of India. not born in India.

Q73.Which one of the following statements is not a tautology? (1) 𝑝∨𝑞→𝑝∨( ~𝑞) (2) 𝑝∧𝑞→( ~𝑝∨𝑞) (3) 𝑝→𝑝∨𝑞 (4) 𝑝∧𝑞→𝑝 JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q73.Which one of the following Boolean expression is a tautology? (1) (p ∨q) ∧(~p ∨~q) (2) (p ∧q) ∨(p ∧~q) (3) (p ∨q) ∧(p ∨~q) (4) (p ∨q) ∨(~p ∨~q)

Q74.If p ⇒(q ∨r) is False , then the truth values of p, q, r are respectively, (where T is True and F is False ) (1) T, F, F (2) F, T, T (3) F, F, F (4) T, T, F

Q74.Consider the statement: " P(n) : n2 −n + 41 is prime". Then which one of the following is true? (1) P(3) is false but P(5) is true (2) Both P(3) and P(5) are false (3) Both P(3) and P(5) are true (4) P(5) is false but P(3) is true

Q74.The negation of the Boolean expression ~𝑠∨~𝑟∧𝑠 is equivalent to (1) 𝑟 (2) 𝑠∧𝑟 (3) 𝑠∨𝑟 (4) ~𝑠∧~𝑟

Q75.The Boolean expression ∼(p ⇒(∼q)) is equivalent to (1) (∼p) ⇒q (2) q ⇒∼p (3) p ∨q (4) p ∧q

Q75.If q is false and p ∧q ↔r is true, then which one of the following statements is a tautology? (1) (p ∨r) →(p ∧r) (2) (p ∧r) →(p ∨r) (3) p ∧r (4) p ∨r