High Order Thinking Skills (HOTs) - 2 - Class 9 MCQ

The diagonals of a rhombus do indeed bisect each other at right angles, making Statement-I true. However, the diagonals of a parallelogram are not necessarily equal; they bisect each other but can be of different lengths, making Statement-II false.

The first five prime numbers are 2,3,5,7, and 11. Their arithmetic mean is (2+3+5+7+ 11) /5=28/5=5.6, making Statement-I true. However, the harmonic mean of the first five prime numbers is calculated as making Statement-II false.

The determinant of the matrix is 1.4 -2.3 = 4-6 = -2, making Statement-I true. The inverse of the matrix but considering the negative determinant, it does not match exactly, so Statement-II is false.

In a right triangle, by the Pythagorean theorem, the hypotenuse is the longest side, making Statement-I true. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, making Statement-II also true.

If a point is equidistant from the endpoints of a segment, it must lie on the perpendicular bisector of the segment, making Statement-I true. The locus of points equidistant from two given points is indeed the perpendicular bisector of the segment joining those points, making Statement-II also true.

A parallelogram with all sides equal and diagonals intersecting at right angles is actually a rhombus, not necessarily a square, making Statement-I false. All squares are rectangles because they have all the properties of rectangles (opposite sides equal and all angles right angles), but not all rectangles are squares because they may not have all sides equal, making Statement-II true.

The sum of the first n natural numbers is indeed given by the formula  making Statement-I true. The sum of the first n odd natural numbers is given by n² , making Statement-II also true.

The area of a trapezium is indeed given by ,  making Statement-I true. However, the diagonals of a trapezium are not necessarily equal; they are only equal in an isosceles trapezium, so Statement-II is false.

First, let's calculate the interior angle of a regular octagon.
A regular polygon with n sides has an interior angle given by the formula:

For a regular octagon (n=8):

So, Statement-I is true.
Next, let's calculate the exterior angle of a regular octagon.
The exterior angle of a regular polygon is given by the formula:

So, Statement-II is also true.

Therefore, both Statement-I and Statement-II are true.

Hence, the correct option is:C

(i) Substitute x=3 and x=−1 into the polynomial: