Practice Questions

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.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.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.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 tangent and the normal lines at the point √3, 1 to the circle 𝑥2 + 𝑦2 = 4 and the 𝑥 -axis form a triangle. The area of this triangle (in square units) is: 1 2 (1) (2) 3 √3 4 1 (3) (4) √3 √3

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.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.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.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.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 0 ≤x < π2 , then the number of values of x for which sin x −sin 2x + sin 3x = 0, is: (1) 4 (2) 3 (3) 2 (4) 1

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 the area of an equilateral triangle inscribed in the circle x2 + y2 + 10x + 12y + c = 0 is 27√3 sq. units, then c is equal to: (1) 25 (2) 13 (3) −25 (4) 20

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.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.Lines are drawn parallel to the line 4𝑥- 3𝑦+ 2 = 0, at a distance units from the origin. Then which one of 5 the following points lies on any of these lines? JEE Main 2019 (10 Apr Shift 2) JEE Main Previous Year Paper 1 1 1 2 (1) 4, - 3 (2) - 4, 3 (3) -1 - 2 (4) 1 1 4, 3 4, 3

Q69.Let the length of the latus rectum of an ellipse with its major axis along x -axis and centre at the origin, be 8 . If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it? (1) (4√2, 2√2) (2) (4√3, 2√2) (3) (4√3, 2√3) (4) (4√2, 2√3)

Q69.The tangent to the parabola 𝑦2 = 4𝑥 at the point where it intersects the circle 𝑥2 + 𝑦2 = 5 in the first quadrant, passes through the point: (1) 1 3 (2) -1 4 4, 4 3, 3 1 1 3 7 (3) - 4, 2 (4) 4, 4

Q69.If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is: (1) 120 (2) 60 13 13 13 13 (3) (4) 5 2

Q69.If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from O on AB is : (1) (x2 + y2)(x + y) = R2xy (2) (x2 + y2)3 = 4R2x2y2 (3) (x2 + y2) 2 = 4R2x2y2 (4) (x2 + y2) 2 = 4Rx2y2

Q69.A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two adjacent vertices of the rectangle are (−8, 5) and (6, 5), then the area of the rectangle (in sq. units ) is: (1) 72 (2) 98 (3) 56 (4) 84

Q69.A square is inscribed in the circle x2 + y2 −6x + 8y −103 = 0 with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is: (1) 6 (2) √137 (3) √41 (4) 13