Practice Questions

Q61.Let p(x) be a quadratic polynomial such that p(0) = 1. If p(x) leaves remainder 4 when divided by x −1 and it leaves remainder 6 when divided by x + 1 then: (1) p(−2) = 19 (2) p(2) = 19 (3) p(−2) = 11 (4) p(2) = 11

Q61.If, for a positive integer 𝑛, the quadratic equation, 𝑥𝑥+ 1 + 𝑥+ 1𝑥+ 2 + . .. + 𝑥+ 𝑛-¯ 1𝑥+ 𝑛= 10𝑛 has two consecutive integral solutions, then 𝑛 is equal to: (1) 12 (2) 9 (3) 10 (4) 11 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q62.Let z ∈C, the set of complex numbers. Then the equation, 2|z + 3i| −|z −i| = 0 represents: (1) A circle with radius 8 (2) An ellipse with length of minor axis 16 3 9 (3) An ellipse with length of major axis 16 (4) A circle with diameter 10 3 3

Q62.Let 𝜔 be a complex number such that 2𝜔+ 1 = 𝑧 where 𝑧= √-3 . If 1 1 1 1 -𝜔2 - 1 𝜔2 = 3𝑘, 1 𝜔2 𝜔7 Then 𝑘 can be equal to: (1) – 𝑧 (2) 1 𝑧 (3) -1 (4) 1

Q62.The equation Im( iz−2z−i ) + 1 = 0, z ∈C, z ≠i represents a part of a circle having radius equal to : (1) 1 (2) 2 (3) 3 (4) 1 4 2

Q63.The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is: (1) 7! (2) 5 × 6! (3) 6 × 6! (4) 5 × 7!

Q63.If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is: (1) 47th (2) 45th (3) 46th (4) 44th

Q63.A man 𝑋 has 7 friends, 4 of them are ladies and 3 are men. His wife 𝑌 also has 7 friends, 3 of them are ladies and 4 are men. Assume 𝑋 and 𝑌 have no common friends. Then the total number of ways in which 𝑋 and 𝑌 together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of 𝑋 and 𝑌 are in this party is: (1) 485 (2) 468 (3) 469 (4) 484

Q64. If three positive numbers a , b and c are in A.P. such that abc = 8, then the minimum possible value of b is: (1) 4 23 (2) 2 (3) 4 31 (4) 4

Q64.If the arithmetic mean of two numbers a and b, a > b > 0 , is five times their geometric mean, then a+ba−b is equal to: (1) 7√3 (2) 3√2 12 4 (3) √6 (4) 5√6 2 12

Q64.For any three positive real numbers 𝑎, 𝑏 and 𝑐. If 925𝑎2 + 𝑏2 + 25𝑐2 - 3𝑎𝑐= 15𝑏3𝑎+ 𝑐. Then (1) 𝑏, 𝑐 and 𝑎 are in G.P. (2) 𝑏, 𝑐 and 𝑎 are in A.P. (3) 𝑎, 𝑏 and 𝑐 are in A.P. (4) 𝑎, 𝑏 and 𝑐 are in G.P.

Q65.The value of 21𝐶1-10𝐶1 + 21𝐶2-10𝐶2 + 21𝐶3-10𝐶3 + 21𝐶4-10𝐶4 + … + 21𝐶10-10𝐶10 is (1) 221 - 211 (2) 221 - 210 (3) 220 - 29 (4) 220 - 210

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

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

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.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

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

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

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.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.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.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