Practice Questions

Q67.Suppose that the points ℎ, 𝑘, 1, 2 and -3, 4 lie on the line 𝐿1 . If a line 𝐿2 passing through the points ℎ, 𝑘 and 𝑘 4, 3 is perpendicular to 𝐿1, then ℎ equals: (1) -1 (2) 3 7 (3) 0 (4) 1 3

Q67.Let S = {θ ∈[−2π, 2π] : 2 cos2 θ + 3 sin θ = 0}. Then the sum of the elements of S is: (1) π (2) 13π 6 (3) 5π (4) 2π 3

Q67.The equation 𝑦= 𝑠𝑖𝑛𝑥sin⁡𝑥+ 2 - sin2⁡( 𝑥+ 1 ) represents a straight line lying in: (1) first, third and fourth quadrants (2) second and third quadrants only (3) first, second and fourth quadrants (4) third and fourth quadrants only 5𝜋 5𝜋

Q67.A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of 10 1 1 3 + 1 is (2 2(3) 3 ) (1) 1 : 4(16) 1 1 3 (2) 4(36) 3 : 1 3 (3) 2(36) 1 1 3 : 1 (4) 1 : 2(6)

Q67.The coefficient of t4 in the expansion of 3 ( 1−t61−t ) is JEE Main 2019 (09 Jan Shift 2) JEE Main Previous Year Paper (1) 10 (2) 14 (3) 15 (4) 12

Q67.All the pairs (x, y), that satisfy the inequality 2√sin2x−2sinx+5 ⋅ 1 ≤1 also satisfy the equation: 4sin2y (1) 2 sin x = sin y (2) sin x = 2 sin y (3) |sin x| = |sin y| (4) 2|sin x| = 3 sin y

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

Q67.The total number of irrational terms in the binomial expansion of 1 1 60 is 5 −3 10 (7 ) (1) 48 (2) 55 (3) 54 (4) 49

Q67.The value of sin10°sin30°sin50°sin70° is: (1) 1 (2) 1 36 16 (3) 1 (4) 1 18 32

Q67.Let S be the set of all α ∈R such that the equation, cos2x + αsinx = 2α −7 has a solution. Then S is equal to: (1) [3, 7] (2) [2, 6] (3) [1, 4] (4) R

Q67.For any 𝜃∈ 4, 2, the expression 3sin𝜃- cos𝜃4 + 6sin𝜃+ cos𝜃2 + 4 sin6𝜃 equals: (1) 13 - 4cos2𝜃+ 6cos4𝜃 (2) 13 - 4cos2𝜃+ 6sin2𝜃cos2𝜃 (3) 13 - 4cos6𝜃 (4) 13 - 4cos4𝜃+ 2sin2𝜃cos2𝜃

Q67.The smallest natural number 𝑛 , such that the coefficient of 𝑥 in the expansion of 𝑥2 + is 𝑛𝐶23 , is 𝑥3 (1) 58 (2) 38 (3) 35 (4) 23 3

Q67.Two sides of a parallelogram are along the lines, x + y = 3 and x −y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is: (1) (3, 6) (2) (2, 6) (3) (2, 1) (4) (3, 5)

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.The maximum value of 3 cos θ + 5 sin(θ −π6 ) for any real value of θ is : (1) √19 (2) √31 (3) √79 (4) √34 2

Q68.If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4 (x −a2) = 0 and the other two vertices are the points of intersection of the parabola and y -axis, is 250 sq. units, then a value of 'a' is : (1) 5√5 (2) 5 (21/3) (3) (10)33 (4) 5

Q68.If the line 3x + 4y −24 = 0 intersects the x-axis is at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is: (1) (4, 4) (2) (3, 4) (3) (4, 3) (4) (2, 2)

Q68.The number of solutions of the equation 1 + sin4𝑥= cos23𝑥, 𝑥∈- , is: 2 2 (1) 5 (2) 7 (3) 3 (4) 4

Q68.The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, −3), then its radius is (1) 3√2 (2) 3 (3) 2 (4) 2√2

Q68.Slope of a line passing through P(2, 3) and intersecting the line x + y = 7 at a distance of 4 units from P, is (1) √7−1 (2) 1–√7 √7+1 1+√7 (3) √5−1 (4) 1–√5 √5+1 1+√5

Q68.In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. if x2 −c2 = y, where c is the length of the third side of the triangle, then the circumradius of the triangle is (1) 3 y (2) c 2 √3 (3) 3c (4) √3y

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.If the two lines x + (a −1)y = 1 and 2x + a2y = 1, (a ∈R −{0,1}) are perpendicular, then the distance of their point of intersection from the origin is (1) 2 (2) √2 √5 5 (3) 2 (4) 5 √25

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

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.