HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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The equation of the tangent to the curve y = `1 - e^(x/2)` at the point of intersection with Y-axis is

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If the tangent at (1, 1) on y² = x(2 – x)² meets the curve again at P, then P is

Solve the following : If the curves ax² + by² = 1 and a'x² + b'y² = 1, intersect orthogonally, then prove that `(1)/a - (1)/b = (1)/a' - (1)/b'`.

Solve the following : Determine the area of the triangle formed by the tangent to the graph of the function y = 3 – x² drawn at the point (1, 2) and the coordinate axes.

Solve the following : Find the equation of the tangent and normal drawn to the curve y⁴ – 4x⁴ – 6xy = 0 at the point M (1, 2).

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The principal solutions of equation sin θ = `- 1/2` are ______.

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The principal solutions of equation cot θ = `sqrt3` are ______.

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The general solution of sec x = `sqrt(2)` is ______.

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If cos pθ = cos qθ, p ≠ q, then ______.

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If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are

If `sqrt3`cos x - sin x = 1, then general value of x is ______.

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In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are

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In ΔABC if c² + a² – b² = ac, then ∠B = ____.

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In ΔABC, ac cos B - bc cos A = _______

If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to

`"cos"^-1 ("cos" (7pi)/6)` = _________.

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The value of cot (tan^-12x + cot^-12x) is

The principal value of sin^–1 `(- sqrt3/2)` is ______.

If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.

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If tan^-1(2x) + tan^-1(3x) = `pi/4`, then x = _____