Practice Questions

Q73.If the system of linear equations, x + y + z = 6 x + 2y + 3z = 10 3x + 2y + λz = μ has more than two solutions, then μ −λ2 , is equal to. JEE Main 2020 (07 Jan Shift 2) JEE Main Previous Year Paper 1 loge( 1−2x1+3x ), when x ≠0 , is continuous, then k is by f(x) = x

Q73.If 1 , α, β ∈(0, π2 ), then tan(α + 2β), is equal to √1+cos2α = 17 and √1−cos2β2 = √10

Q73.The sum of distinct values of λ for which the system of equations : (λ −1) x + (3λ + 1) y + 2λz = 0 (λ −1) x + (4λ −2) y + (λ + 3) z = 0 2x + (3λ + 1) y + 3 (λ −1) z = 0 , Has non-zero solutions, is ....... .

Q73.Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + xy2 + x2y, for all real x and y. If lim f(x)x = 1, then f ′(3) is equal to : x→0

Q73.If y = ∑6k=1 k cos−1{ 53 cos kx −45 sin kx} then dxdy at x = 0 is

Q73.If the line, 2 x −y + 3 = 0 is at a distance 1 and 2 from the lines 4x −2y + α = 0 and 6x −3y + β = 0 √5 √5 respectively, then the sum of all possible values of α and β is ____________.

Q73.If lim x−1 = 820, (n ∈N) then the value of n is equal to.... x→1

Q73.If the lines x + y = a and x −y = b touch the curve y = x2 −3x + 2 at the points where the curve intersects the x−axis, then ab is equal to … → → →

Q73.If for x ≥0, y = y(x) is the solution of the differential equation, (x + 1)dy = y(2) = 0 then y(3) is equal to ________ ((x + 1)2 + y −3)dx, →

Q73.The diameter of the circle, whose Centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2 is x2 x2 x2 x2 lim −cos = 2−k then the value of k is 2 −cos 4 + cos 2 cos x8 1 (1 4 )}

Q73.If the variance of the following frequency distribution: JEE Main 2020 (04 Sep Shift 2) JEE Main Previous Year Paper Class: 10 −20 20 −30 30 −40 Frequency: 2 x 2 is 50, then x is equal to _______

Q73. sin( x1 ) + 5x2 , x < 0 ⎧ x5 Let f : R →R be defined as f(x) = 0 , x = 0 . The value of λ for which f ′′(0) exists, ⎨ 1 ) + λx2 , x > 0 ⎩x5 cos( x is___.

Q73.Let S be the set of all integer solutions (x, y, z) of the system of equations x −2 y + 5 z = 0 −2 x + 4 y + z = 0 −7 x + 14 y + 9 z = 0 such that 15 ≤x2 + y2 + z2 ≤150. Then, the number of elements in the set S is equal to ..........

Q73.If the curves, x2 −6x + y2 + 8 = 0 and x2 −8y + y2 + 16 −k = 0, (k > 0) touch each other at a point, then the largest value of k is ____________. → → → → π If →a

Q74.Suppose that a function f : R →R satisfies f(x + y) = f(x) f(y) for all x, y ε R and f(1) = 3. If ∑ni=1 f(i) = 363 , then n is equal to ..... . JEE Main 2020 (06 Sep Shift 2) JEE Main Previous Year Paper → →

Q74.If the vectors, p = (a + 1)ˆi + aˆj + aˆk,→q = aˆi + (a + 1)ˆj + aˆk and →r= aˆi + aˆj + (a + 1)ˆk(a ∈R) are 2 2 coplanar and q = 0 , then the value of λ is ________ 3(→p.→q) −λ→r×→

Q74.If x→0{ x ε R and A4 = [aij]. If a11 = 109, then a22 is equal to_____________.

Q74.Let {x} and [x] denote the fractional part of x and the greatest integer ≤x respectively of a real number x. if n > 1) are three consecutive terms of a G.P. then n is equal ∫n0 {x}dx, ∫n0 [x]dx and 10(n2 −n), (n ∈N, to__ 2 2 2 , is equal to : + ˆj × × + ˆk × ×

Q74.Let [t] denote the greatest integer less than or equal to t. Then the value of ∫21 |2x −[3x]|dx is

Q74.If the tangent to the curve y = ex at a point (c, ec) and the normal to the parabola y2 = 4x at the point (1, 2) intersect at the same point on the x−axis, then the value of c is ..... + μ ∈R. If Q(α, β, γ) is

Q74.The number of all 3 × 3 matrices A, with entries from the set {−1, 0, 1} such that the sum of the diagonal elements of AAT is 3, is ___________.

Q74.If the function f defined on (−13 , 1/3) { k , when x = 0 equal to.

Q74.Let a line y = mx(m > 0), intersect the parabola, y2 = x, at a point P, other than the origin. Let the tangent to it a P , meet the x-axis at the point Q. If area (ΔOPQ) = 4 square unit, then m is equal to

Q74.The integral ∫20 ||x −1| −x|dx is equal to

Q74.If the equation of a plane P , passing through the intersection of the planes, x + 4y −z + 7 = 0 and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b ∈R, then the distance of the point (3, 2, −1) from the plane P is … …