HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

In ∆ABC, if sin²A + sin²B = sin²C, then show that a² + b² = c² 

Find the polar co-ordinates of point whose Cartesian co-ordinates are `(1, sqrt(3))`

In ΔABC, a = 3, b = 4 and sin A = `3/4`, find ∠B

Find the Cartesian co-ordinates of point whose polar co-ordinates are `(4, pi/3)`

With usual notations, prove that `(cos "A")/"a" + (cos "B")/"b" + (cos "C")/"c" = ("a"^2 + "b"^2 + "c"^2)/(2"abc")`

In ∆ABC, prove that `("b" - "c")^2 cos^2 ("A"/2) + ("b" + "c")^2 sin^2 ("A"/2)` = a² 

In ∆ABC, if a = 13, b = 14, c = 15, then find the value of cos B

In ΔABC, if a cos A = b cos B, then prove that ΔABC is either a right angled or an isosceles triangle.

In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`

In ∆ABC, if `(2cos "A")/"a" + (cos "B")/"b" + (2cos"C")/"c" = "a"/"bc" + "b"/"ca"`, then show that the triangle is a right angled

In ∆ABC, prove that `sin  ((A - B)/2) = ((a - b)/c) cos  C/2` 

If the angles A, B, C of ΔABC are in A.P. and its sides a, b, c are in G.P., then show that a², b², c² are in A.P.

In ∆ABC, prove that `(cos^2"A" - cos^2"B")/("a" + "b") + (cos^2"B" - cos^2"C")/("b" + "c") + (cos^2"C" - cos^2"A")/("c" + "a")` = 0

In ΔABC, prove that `("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")` = 0

In ΔABC, prove that `("b"^2 - "c"^2)/"a" cos"A" + ("c"^2 - "a"^2)/"b" cos"B" + ("a"^2 - "b"^2)/"c" cos "C"` = 0

In ∆ABC, if ∠A = `pi/2`, then prove that sin(B − C) = `("b"^2 - "c"^2)/("b"^2 + "c"^2)`

The displacement of a particle at time t is given by s = 2t³ – 5t² + 4t – 3. The time when the acceleration is 14 ft/sec², is 

The edge of a cube is decreasing at the rate of 0.6 cm/sec then the rate at which its volume is decreasing when the edge of the cube is 2 cm, is

A particle moves along the curve y = 4x² + 2, then the point on the curve at which y – coordinate is changing 8 times as fast as the x – coordinate is

The displacement of a particle at time t is given by s = 2t³ – 5t² + 4t – 3. Find the velocity when 𝑡 = 2 sec