HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)

Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)

Write the negation of p → q

In ∆ABC, if cos A = `(sinB)/(2sinC)`, then ∆ABC is ______.

In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______.

In ∆ABC, if b² + c² − a² = bc, then ∠A = ______.

If polar co-ordinates of a point are `(3/4, (3pi)/4)`, then its Cartesian co-ordinate are ______

In ∆ABC, prove that ac cos B − bc cos A = a² − b² 

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.