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

Show that the points (1, –1, 3) and (3, 4, 3) are equidistant from the plane 5x + 2y – 7z + 8 = 0

Find the distance of the point (1, 2, –1) from the plane x - 2y + 4z - 10 = 0 .

 A rod of 108 meters long is bent to form a rectangle. Find its dimensions if the area is maximum. Let x be the length and y be the breadth of the rectangle. 

Write the negation of the following.

Tirupati is in Andhra Pradesh.

Write the negation of the following.

3 is not a root of the equation x² + 3x – 18 = 0

Write the negation of the following.

`sqrt2` is a rational number.

Write the negation of the following.

Polygon ABCDE is a pentagon.

Write the negation of the following.

Write the negation of the following.

x + 8 > 11 or y – 3 = 6

Write the negation of the following.

11 < 15 and 25 > 20

Write the negation of the following.

Quadrilateral is a square if and only if it is a rhombus.

Write the negation of the following.

It is cold and raining.

Write the negation of the following.

If it is raining then we will go and play football.

Write the negation of the following.

All-natural numbers are whole numbers.

Write the negation of the following.

∀ n ∈ N, n² + n + 2 is divisible by 4.

Write the negation of the following.

∃ x ∈ N such that x – 17 < 20

Using the rule of negation write the negation of the following with justification.

∼ q → p

Using the rule of negation write the negation of the following with justification.

p ∧ ∼ q

Using the rule of negation write the negation of the following with justification.

p ∨ ∼ q

Using the rule of negation write the negation of the following with justification.

(p ∨ ∼ q) ∧ r