HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Choose the correct alternative:
The point on the line 2x − 3y = 5 is equidistance from (1, 2) and (3, 4) is

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If the two straight lines x + (2k − 7)y + 3 = 0 and 3kx + 9y − 5 = 0 are perpendicular then the value of k is

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If a vertex of a square is at the origin and its one side lies along the line 4x + 3y − 20 = 0, then the area of the square is

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If the lines represented by the equation 6x² + 41xy – 7y² = 0 make angles α and β with x-axis then tan α tan β =

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θ is acute angle between the lines x² – xy – 6y² = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`

Represent graphically the displacement of 45 cm, 30° north of east

Represent graphically the displacement of 80 km, 60° south of west

Find the derivatives of the following functions with respect to corresponding independent variables:

f(x) = x – 3 sin x

Find the derivatives of the following functions with respect to corresponding independent variables:

y = sin x + cos x

Find the derivatives of the following functions with respect to corresponding independent variables:

f(x) = x sin x

Find the derivatives of the following functions with respect to corresponding independent variables:

y = cos x – 2 tan x

Find the derivatives of the following functions with respect to corresponding independent variables:

g(t) = t³ cos t

Find the derivatives of the following functions with respect to corresponding independent variables:

g(t) = 4 sec t + tan t

Find the derivatives of the following functions with respect to corresponding independent variables:

y = e^x sin x

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `tan x/x`

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `sinx/(1 + cosx)`

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `x/(sin x + cosx)`

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `(tanx - 1)/secx`

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `sinx/x^2`

Find the derivatives of the following functions with respect to corresponding independent variables:

y = tan θ (sin θ + cos θ)