Practice Questions

Q65.Let Sn = 131 + 13+231+2 + 13+23+331+2+3 + … + 13+23+…n31+2+…,+n . If 100 Sn = n, then n is equal to: (1) 200 (2) 199 (3) 99 (4) 19 10 x+1 x−1

Q65.If the sum of the first n terms of the series √3 + √75 + √243 + √507 + … is 435√3, then n equals: (1) 13 (2) 15 (3) 29 (4) 18

Q66.If 5tan2⁡𝑥- cos2⁡𝑥= 2cos⁡ 2𝑥+ 9, then the value of cos⁡4𝑥 is 3 1 (1) - (2) 5 3 2 7 (3) (4) - 9 9

Q66.If (27)999 is divided by 7, then the remainder is (1) 3 (2) 1 (3) 6 (4) 2

Q66.The coefficient of x−5 in the binomial expansion of ( x 32 −x 31 +1 − x−x 21 ) where x ≠0,1 is (1) −1 (2) 4 (3) 1 (4) −4

Q67.The lengths of two adjacent sides of a cyclic quadrilateral are 2 units and 5 units and the angle between them is 60o . If the area of the quadrilateral is 4√3 sq. units, then the perimeter of the quadrilateral is (1) 12.5 units (2) 13 units (3) 13.2 units (4) 12 units

Q67.Let 𝑘 be an integer such that the triangle with vertices 𝑘, - 3𝑘, 5, 𝑘 and -𝑘, 2 has area 28 sq. units. Then the orthocenter of this triangle is at the point: (1) 2, - 1 (2) 1, 3 2 4 3 1 (3) 1, - (4) 2, 4 2

Q67.The locus of the point of intersection of the straight lines, tx −2y −3t = 0 and x −2ty + 3 = 0 (t ∈R), is: (1) A hyperbola with the length of conjugate axis 3 (2) A hyperbola with eccentricity √5 (3) An ellipse with the length of major axis 6 (4) An ellipse with eccentricity 2 √5

Q68.A square, of each side 2 , lies above the x -axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30° with the positive direction of the x-axis , then the sum of the x- JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper coordinates of the vertices of the square is : (1) 2√3 −2 (2) √3 −2 (3) 2√3 −1 (4) √3 −1

Q68.The radius of a circle, having minimum area, which touches the curve 𝑦= 4 - 𝑥2 and the lines, 𝑦= 𝑥 is: (1) 2√2 + 1 (2) 2√2 - 1 (3) 4√2 - 1 (4) 4√2 + 1 1

Q68.If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles cos−1( 71 ) and sec−1(7) at the center respectively, then the distance between these chords is: (1) 8 (2) 16 √7 7 (3) 4 (4) 8 √7 7

Q69.If the common tangents to the parabola, x2 = 4y and the circle, x2 + y2 = 4 intersect at the point P , then the distance of P from the origin (units), is: + (1) 2(3 2√2) (2) 3 + 2√2 + (3) √2 + 1 (4) 2(√2 1) JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper

Q69.The eccentricity of an ellipse whose centre is at the origin is . If one of its directrices is 𝑥= - 4 , then the 2 equation of the normal to it at 1, 3 is: 2 (1) 2𝑦- 𝑥= 2 (2) 4𝑥- 2𝑦= 1 (3) 4𝑥+ 2𝑦= 7 (4) 𝑥+ 2𝑦= 4

Q69.A line drawn through the point P(4, 7) cuts the circle x2 + y2 = 9 at the points A and B. Then PA ⋅PB is equal to. (1) 74 (2) 53 (3) 56 (4) 65

Q70.If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 units, then |c| is equal to: (1) 8√3 (2) 10√3 (3) 2√3 (4) 16√3

Q70.A hyperbola passes through the point 𝑃√2, √3 and has foci at ± 2, 0. Then the tangent to this hyperbola at 𝑃 also passes through the point (1) 3√2, 2√3 (2) 2√2, 3√3 (3) √3, √2 (4) -√2, - √3 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper cot𝑥- cos𝑥

Q70.If a point P(0, −2) and Q is any point on the circle, x2 + y2 −5x −y + 5 = 0 , then the maximum value of (PQ)2 is (1) 8 + 5√3 (2) 47+10√6 2 (3) 14 + 5√3 (4) 25+ √6 2

Q71. lim equals 𝑥→𝜋 𝜋- 2𝑥3 2 1 1 (1) (2) 24 16 (3) 1 (4) 1 8 4

Q71. The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, −1) and (−2, 2) is (1) √3 (2) √3 2 4 (3) 2 (4) 1 √5 2

Q71.Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is 3 5 and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is: (1) 32 (2) 80 (3) 40 (4) 8

Q72.The 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 equal, then the (2) If the squares of two numbers are not equal, then numbers are not equal the numbers are equal (3) If the squares of two numbers are not equal, then (4) If the squares of two numbers are equal, then the the numbers are not equal numbers are equal

Q72.The statement 𝑝→𝑞→~𝑝→𝑞→𝑞 is (1) A tautology (2) Equivalent to ~𝑝→𝑞 (3) Equivalent to 𝑝→~𝑞 (4) A fallacy

Q72. lim √3x−3 is equal to x→3 √2x−4− √2 (1) 1 (2) 1 √2 2√2 (3) √3 (4) √3 2

Q73.The sum of 100 observations and the sum of their squares are 400 & 2475, respectively. Later on, three observations 3, 4 & 5 were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is (1) 8. 25 (2) 8. 50 (3) 9. 00 (4) 8. 00

Q73.A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is: 12 (1) (2) 6 5 (3) 4 (4) 6 25