Practice Questions

Q79.The equation of the plane which contains the y-axis and passes through the point (1, 2, 3) is: (1) x + 3z = 10 (2) x + 3z = 0 (3) 3x + z = 6 (4) 3x −z = 0

Q79.If →a = 2, →b = 5 and →a×→b = 8, then →a⋅→b is equal to: (1) 6 (2) 4 (3) 3 (4) 5

Q79.Consider the three planes P1 : 3x + 15y + 21z = 9 P2 : x −3y −z = 5, and P3 : 2x + 10y + 14z = 5 Then, which one of the following is true? (1) P2 and P3 are parallel. (2) P1, P2 and P3 all are parallel. (3) P1 and P2 are parallel. (4) P1 and P3 are parallel.

Q81.There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is

Q81.If log3 2, log3(2x −5), log3(2x −72 ) are in an arithmetic progression, then the value of x is equal to _____.

Q82.If 𝑆= + + + + … , then 160 𝑆 is equal to . 5 52 53 54

Q82.For real numbers α and β, consider the following system of linear equations: x + y −z = 2, x + 2y + αz = 1 and 2x −y + z = β. If the system has infinite solutions, then α + β is equal to ______.

Q83.If the value of 1 + 1 1 1 + + + … . . upto ∞ is 𝑙, then 𝑙2 is equal to 3 32 33 .

Q85.The missing value in the following figure is

Q85.The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1)(1, 1) is 18 units, is a circle of diameter d. Then d2 is equal to −1), for x ≤0 2 (x

Q86.The value of the integral ∫π0 |sin 2x|dx is ________.

Q86.The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is 5x8+7x6

Q86.Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (−5, 0). If the locus of the point P is a circle of radius r, then 4r2 (in the nearest integer) is equal to __________.

Q89.If the projection of the vector ˆi + 2ˆj + ˆk on the sum of the two vectors 2ˆi + 4ˆj −5ˆk and −λˆi + 2ˆj + 3ˆk is 1, then λ is equal to _______.

Q90.Suppose the line 𝑥- 2 = 𝑦- 2 = 𝑧+ 2 lies on the plane 𝑥+ 3𝑦- 2𝑧+ 𝛽= 0 . Then ( 𝛼+ 𝛽) is equal to 𝛼 -5 2 . JEE Main 2021 (31 Aug Shift 2) JEE Main Previous Year Paper

Q90.A fair coin is tossed n− times such that the probability of getting at least one head is at least 0. 9. Then the minimum value of n is _______. JEE Main 2021 (25 Jul Shift 2) JEE Main Previous Year Paper

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

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)

Q52.The imaginary part of (3 2√−54) −(3 −2√−54) ,can be (1) −√6 (2) −2√6 (3) 6 (4) √6

Q56.If the co-ordinates of two points A and B are (√7, 0) and (−√7, 0) respectively and conic, 9x2 + 16y2 = 144, then PA + PB is equal to : (1) 16 (2) 8 (3) 6 (4) 9

Q57.The contrapositive of the statement "If I reach the station in time, then I will catch the train" is (1) If I do not reach the station in time, then I will (2) If do not reach the station in time, then I will not catch the train. catch the train. (3) If I will catch the train, then I reach the station in (4) If I will not catch the train, then I do not reach time. the station in time.

Q57.Which of the following statement is a tautology? (1) p ∨(~q) →p ∧q (2) ~(p ∧~q) →p ∨q (3) ~(p ∨~q) →p ∧q (4) ~(p ∨~q) →p ∨q JEE Main 2020 (08 Jan Shift 2) JEE Main Previous Year Paper

Q58.Contrapositive of the statement : 'If a function f is differentiable at a , then it is also continuous at a ', is (1) If a function f is continuous at a , then it is not differentiable at a . (2) If a function f is not continuous at a , then it is not differentiable at a . (3) If a function f is not continuous at a . then it is differentiable at a . (4) If a function f is continuous at a , then it is differentiable at a .