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Q88.If β†’a = Ξ±Λ†i + Ξ²Λ†j + 3Λ†k, β†’b= βˆ’Ξ²Λ†i βˆ’Ξ±Λ†j βˆ’Λ†k and β†’c= Λ†i βˆ’2Λ†j βˆ’Λ†k such that β†’aβ‹…β†’b= 1 and β†’bβ‹…β†’c= βˆ’3, then β†’ 1 Γ— is equal to _______. 3 ((β†’a b) β‹…β†’c)

202117 Mar Shift 1Vectors
MathsMedium

Q88.If β†’a and b are unit vectors and (β†’a b) (7β†’a b) (β†’a b) then the angle between β†’a and b (in degrees) is _________. βˆ’2 (7β†’a β†’ β†’ b), yβˆ’2

202125 Jul Shift 2Vectors
MathsMedium

Q88.A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then ( Ο€4 + 1)k is equal to

202126 Aug Shift 1Applications of Derivatives
MathsMedium

Q88.If y = y(x), y ∈[0, Ο€2 ) is the solution of the differential equation sec y dxdy βˆ’sin(x + y) βˆ’sin(x βˆ’y) = 0, with y(0) = 0, then 5yβ€²( Ο€2 ) is equal to _____. JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper β†’ β†’ β†’

202127 Jul Shift 1Differential Equations
MathsMedium

Q88.Let f(x) and g(x) be two functions satisfying f(x2) + g(4 βˆ’x) = 4x3 and g(4 βˆ’x) + g(x) = 0, then the value of ∫4βˆ’4 f(x2)dx is

202118 Mar Shift 1Definite Integration & Area
MathsMedium

Q88.Let a function g : [0, 4] β†’R be defined as max {t3 βˆ’6t2 + 9t βˆ’3}, 0 ≀x ≀3 ⎧ g(x) = 0≀t≀x ⎨ ⎩ 4 βˆ’x, 3 < x ≀4 then the number of points in the interval (0, 4) where g(x) is NOT differentiable, is _________. JEE Main 2021 (20 Jul Shift 2) JEE Main Previous Year Paper

202120 Jul Shift 2Matrices
MathsMedium

Q88.The difference between degree and order of a differential equation that represents the family of curves given a > 0 is _______. + √a2 ), by y2 = a(x

202126 Feb Shift 1Differential Equations
MathsMedium

Q88.If the curve, y = y(x) represented by the solution of the differential equation (2xy2 βˆ’y)dx + x dy = 0, passes through the intersection of the lines, 2x βˆ’3y = 1 and 3x + 2y = 8, then |y(1)| is equal to ___ .

202125 Feb Shift 2Differential Equations
MathsMedium

Q88.Let β†’a, b,β†’cbe three mutually perpendicular vectors of the same magnitude and equally inclined at an angle ΞΈ, β†’ with the vector β†’a+ b +β†’c. Then 36 cos2 2ΞΈ is equal to

202120 Jul Shift 1Vectors
MathsMedium

Q88.The number of distinct real roots of the equation 3x4 + 4x3 βˆ’12x2 + 4 = 0 is _________. + C, x > 0 where C is the constant of integration, then the +

202127 Aug Shift 1Applications of Derivatives
MathsMedium

Q88.Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x3 βˆ’3x2 βˆ’12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4A is equal to ______.

202126 Aug Shift 2Applications of Derivatives
MathsMedium

Q88.Let y = y(x) be the solution of the differential equation dy = eΞ±x+ydx; Ξ± ∈N. If y(loge 2) = loge 2 and y(0) = loge( 12 ), then the value of Ξ± is equal to ___. β†’ β†’

202127 Jul Shift 2Differential Equations
MathsMedium

Q89.Let the mirror image of the point (1, 3, a) with respect to the plane β†’rβ‹…(2Λ†i βˆ’Λ†j + Λ†k) Then the value of |a + b| is equal to ___ . y+6

202118 Mar Shift 23D Geometry
MathsMedium

Q89.Let β†’a = Λ†i βˆ’Ξ±Λ†j + Ξ²Λ†k, b = 3Λ†i + Ξ²Λ†j βˆ’Ξ±Λ†k and β†’c= βˆ’Ξ±Λ†i βˆ’2Λ†j + Λ†k, where Ξ± and Ξ² are integers. If β†’aβ‹… b = βˆ’1 and β†’ β†’ is equal to ______. Γ— b β‹…β†’c= 10, then (β†’a b) β‹…β†’c

202127 Jul Shift 2Vectors
MathsMedium

Q89.If ∫ b( x2+x+12x+1 ) (x2+x+1)2 dx = a tanβˆ’1( 2x+1√3 ) + value of 9(√3a b) is equal to _________. β†’ β†’

202127 Aug Shift 1Indefinite Integration
MathsMedium

Q89.If the lines xβˆ’k k is _______. 1 = 2 = zβˆ’33 and x+13 = y+22 = z+31 are co-planar, then the value of

202125 Jul Shift 23D Geometry
MathsMedium

Q89.Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, βˆ’3, 1) and (2, 3, βˆ’5) at the right angles. If a, b, c, d are integers, then the minimum value of (a2 + b2 + c2 + d2) is

202118 Mar Shift 13D Geometry
MathsMedium

Q89.The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A4 is equal to β†’

202125 Feb Shift 1Definite Integration & Area
MathsMedium

Q89.Let β†’a = Λ†i + Λ†j + Λ†k, b and β†’c= Λ†j βˆ’Λ†k be three vectors such that β†’aΓ— b =β†’cand β†’aβ‹… b = 1. If the length of β†’ projection vector of the vector b on the vector β†’aΓ—β†’cis l, then the value of 3l2 is equal to _____.

202127 Jul Shift 1Vectors
MathsMedium

Q89.Let x be a vector in the plane containing vectors β†’a = 2Λ†i βˆ’Λ†j + Λ†k and b = Λ†i + 2Λ†j βˆ’Λ†k. If the vector x is 17√6 β†’ 2 is 2 , then the value of x is equal to _______. perpendicular to (3Λ†i + 2Λ†j βˆ’Λ†k) and its projection on β†’a

202117 Mar Shift 2Vectors
MathsMedium

Q89.Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x βˆ’y + z + 3 = 0 and let R(3, 5, Ξ³) be a point of this plane. Then the square of the length of the line segment SR is

202127 Aug Shift 23D Geometry
MathsMedium

Q89.The square of the distance of the point of intersection of the line xβˆ’1 2 = yβˆ’23 = z+16 and the plane 2 x βˆ’y + z = 6 from the point (βˆ’1, βˆ’1, 2) is

202131 Aug Shift 13D Geometry
MathsMedium

Q89.Let three vectors β†’π‘Ž, →𝑏 and →𝑐 be such that →𝑐 is coplanar with β†’π‘Ž and →𝑏, β†’π‘ŽΒ· →𝑐= 7 and →𝑏 is perpendicular to →𝑐, 2 where β†’π‘Ž= - ^𝑖+ ^𝑗+ ^π‘˜ and →𝑏= 2 ^𝑖+ ^π‘˜, then the value of 2 β†’π‘Ž+ →𝑏+ →𝑐 is

202124 Feb Shift 1Vectors
MathsMedium

Q89.The area of the region S = {(x, y) : 3x2 ≀4y ≀6x + 24} is______.

202126 Aug Shift 1Definite Integration & Area
MathsMedium

Q89.If the area of the triangle formed by the x-axis, the normal and the tangent to the circle (x βˆ’2)2 + (y βˆ’3)2 = 25 at the point (5, 7) is A, then 24A is equal to _________.

202124 Feb Shift 2Circles
MathsMedium

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