HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

`int (log x)/(log ex)^2` dx = _________

Show that the homogeneous equation of degree 2 in x and y represents a pair of lines passing through the origin if h² − ab ≥ 0.

Write the following compound statements symbolically.

Triangle is equilateral or isosceles

Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.

Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra

Write the following statements in symbolic form

Even though it is not cloudy, it is still raining

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)`