Practice Questions

Q66.If f(y) = 1 −(y −1) + (y −1)2 −(y −1)3 + … −(y −1)17 then the coefficient of y2 in it is (1) 17C2 (2) 17C3 (3) 18C2 (4) 18C3

Q66.The middle term in the expansion of (1 −1x ) n (1 −xn) in powers of x is (1) −2nCn−1 (2) −2nCn (3) 2nCn−1 (4) 2nCn

Q66.If n = mC2 , then the value of nC2 is given by JEE Main 2012 (19 May Online) JEE Main Previous Year Paper (1) 3 (m+1C4) (2) m−1C4 (3) m+1C4 (4) 2 (m+2C4)

Q67.The value of cos 255∘+ sin 195∘ is (1) √3−1 (2) √3−1 2√2 √2 (3) −√3−1 (4) √3+1 √2 √2

Q67.Suppose θ and ϕ(≠0) are such that sec(θ + ϕ), sec θ and sec(θ −ϕ) are in A.P. If cos θ = k cos ( ϕ2 ) for some k, then k is equal to (1) ±√2 (2) ±1 (3) ± 1 (4) ±2 √2

Q67.The equation esin x −e−sin x −4 = 0 has (1) infinite number of real roots (2) no real roots (3) exactly one real root (4) exactly four real roots

Q67.If two vertices of a triangle are (5, −1) and (−2, 3) and its orthocentre is at (0, 0), then the third vertex is (1) (4, −7) (2) (−4, −7) (3) (−4, 7) (4) (4, 7)

Q67.If the straight lines x + 3y = 4, 3x + y = 4 and x + y = 0 form a triangle, then the triangle is (1) scalene (2) equilateral triangle (3) isosceles (4) right angled isosceles

Q68.Let L be the line y = 2x, in the two dimensional plane. Statement 1: The image of the point (0, 1) in L is the point ( 54 , 35 ) Statement 2: The points (0, 1) and ( 45 , 35 ) lie on opposite sides of the line L and are at equal distance from it. (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is true, (4) Statement 1 is false, Statement 2 is true. Statement 2 is a correct explanation for Statement 1.

Q68.The area of triangle formed by the lines joining the vertex of the parabola, x2 = 8y, to the extremities of its latus rectum is (1) 2 (2) 8 (3) 1 (4) 4

Q68.The point of intersection of the lines (a3 + 3)x + ay + a −3 = 0 and (a5 + 2)x + (a + 2)y + 2a + 3 = 0 (a real) lies on the y-axis for (1) no value of a (2) more than two values of a (3) exactly one value of a (4) exactly two values of a

Q68.The line parallel to x-axis and passing through the point of intersection of lines ax + 2by + 3b = 0 and bx −2ay −3a = 0, where (a, b) ≠(0, 0) is (1) above x-axis at a distance 2/3 from it (2) above x-axis at a distance 3/2 from it (3) below x-axis at a distance 3/2 from it (4) below x-axis at a distance 2/3 from it

Q69.A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is (1) −14 (2) −4 (3) −2 (4) −12

Q69.The equation of the circle passing through the point (1, 2) and through the points of intersection of x2 + y2 −4x −6y −21 = 0 and 3x + 4y + 5 = 0 is given by (1) x2 + y2 + 2x + 2y + 11 = 0 (2) x2 + y2 −2x + 2y −7 = 0 (3) x2 + y2 + 2x −2y −3 = 0 (4) x2 + y2 + 2x + 2y −11 = 0

Q69.If the line y = mx + 1 meets the circle x2 + y2 + 3x = 0 in two points equidistant from and on opposite sides of x -axis, then (1) 3m + 2 = 0 (2) 3m −2 = 0 (3) 2m + 3 = 0 (4) 2m −3 = 0

Q69.If P1 and P2 are two points on the ellipse x24 + y2 = 1 at which the tangents are parallel to the chord joining the points (0, 1) and (2, 0), then the distance between P1 and P2 is (1) 2√2 (2) √5 (3) 2√3 (4) √10

Q70.Statement 1: y = mx − m1 is always a tangent to the parabola, y2 = −4x for all non-zero values of m. Statement 2: Every tangent to the parabola, y2 = −4x will meet its axis at a point whose abscissa is non- negative. (1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1. (2) Statement 1 is false, Statement 2 is true. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

Q70.The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is (1) 10 (2) 3 3 5 (3) 56 (4) 53

Q70.The number of common tangents of the circles given by x2 + y2 −8x −2y + 1 = 0 and x2 + y2 + 6x + 8y = 0 is (1) one (2) four (3) two (4) three

Q71.If the eccentricity of a hyperbola x2 K 2 is = 1, which passes through (K, 2), is √133 , then the value of 9 −y2b2 (1) 18 (2) 8 (3) 1 (4) 2

Q71.If the foci of the ellipse x2 , then b2 is equal 16 + = 1 coincide with the foci of the hyperbola 144x2 −y281 = 251 b2 to (1) 8 (2) 10 (3) 7 (4) 9

Q71.The chord PQ of the parabola y2 = x, where one end P of the chord is at point (4, −2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is (1) −4 (2) −14 (3) 4 (4) 1 4

Q71.If the mean of 4, 7, 2, 8, 6 and a is 7 , then the mean deviation from the median of these observations is (1) 8 (2) 5 (3) 1 (4) 3

Q72.The normal at (2, 23 ) to the ellipse, x216 + y23 = 1 touches a parabola, whose equation is (1) y2 = −104x (2) y2 = 14x (3) y2 = 26x (4) y2 = −14x sin(π cos2 x)

Q72.If in a triangle ABC, b+c11 = c+a12 = a+b13 , then cos A is equal to (1) 5/7 (2) 1/5 (3) 35/19 (4) 19/35