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onsider the matrices

onsider the matrices :A=[2−53 m],B=[20 m]and X=[xy]. Let the set of all m, for which the system of

Let the inverse

Let the inverse trigonometric funcThe number of real solutions of the equation 2sin−1x+3cos−1x=2π/5,

If (1/α+1+1/α+2+….+1/α+1012) −(1/2⋅1+1/4⋅3+1/6⋅5+….+1/2024⋅2023)

If (1/α+1+1/α+2+….+1/α+1012) −(1/2⋅1+1/4⋅3+1/6⋅5+….+1/2024⋅2023) =12024, then α is equal to

The square of

The square of the distance of the image of the point (6,1,5) in the line x−1/3=y/2=z−2/4, from the

Let A, B

Let A, B and C be three points on the parabolay2 = 6x and let the line segment AB meet the line Lt

For a differentiable

For a differentiable function f:IR→IR, suppose f′(x)=3f(x)+α, where α∈IR,f(0)=1 and limx→−∞f(x)=7. T

Let the set

Let the set of all values of p, for which f(x) = (p2 –6p + 8) (sin22x – cos2 2x) + 2(2 – p)x + 7

Consider the circle

Consider the circle C : x2 + y2 = 4 and the parabolaP : y2 = 8x. If the set of all values of

Let →a=2^i+α^j+^k, ˙b=−^i+^k,

Let →a=2^i+α^j+^k, ˙b=−^i+^k, →c=β^j−^k, where α and β are integers and αβ=−6. Let the values of the

Let α,β; α

Let α,β; α β, be the roots of the equation x2−√2x−√3=0. Let Pn=αn−βn,n∈N. Then (11√3−10√2) P10+(11√

The value of

The value of the integral 2∫−1loge(x+√x2+1)dx is

If an unbiased

If an unbiased dice is rolled thrice, then theprobability of getting a greater number in the ithroll

Let a,ar,ar2,…....be an

Let a,ar,ar2,…....be an infinite G.P. If ∞∑n=0arn=57 and ∞∑n=0a3r3n=9747,then a + 18r is equal

he integral 3/4∫1/4cos(2cot−1√1−x/1+x)dx

he integral 3/4∫1/4cos(2cot−1√1−x/1+x)dx is equal to:

If logey=3sin−1x, then

If logey=3sin−1x, then (1−x)2 y′′−xy′ at x=12 is equal to

Let B=[1315] and

Let B=[1315] and A be a 2×2 matrix such that AB−1=A−1. If BCB−1=A and C4+αC2+βI=O, then 2β−α is e

The sum of

The sum of coefficients of x^2/3 and x^-2/5 in the binomial expansion of (x^2/3+x^−2/5/2)^9 is

lim x→x/2(∫(π/2)^3 x3(sin(2t^1/3)+cos(t1/3))dt/(x−π/2)^2)

lim x→x/2(∫(π/2)^3 x3(sin(2t^1/3)+cos(t1/3))dt/(x−π/2)^2) is equal

Let the range

Let the range of the function f(x)=12+sin3x+cos3x,x∈IR be [a,b] . If α and β are respectively the

If the variance

If the variance of the frequency distribution is 160,then the value of c N is

Two vertices of

Two vertices of a triangle ABC are A(3,−1) and B (−2,3), and its orthocentre is P(1,1). If the coord

Let the foci

Let the foci of a hyperbola H coincide with the foci of the ellipse E : (x−1)^2/100+(y−1)^2/75=1

The area (in

The area (in square units) of the region enclosed bythe ellipse x2 + 3y2 = 18 in the first quadrant

Let z be

Let z be a complex number such that the real part of z−2iz+2i is zero. Then, the maximum value of