High Order Thinking Skills (HOTs) - 1 - Class 9 MCQ

The sum of the interior angles of a polygon with n sides is given by the formula (n-2) x 180 degrees. For a hexagon (n=6), this is (6−2)×180=720 degrees, so Statement-I is true. A quadrilateral with one pair of opposite sides equal and parallel is indeed called a parallelogram, making Statement-II also true.

Solving 2x+3=7, we get 2x=4, thus x=2, so Statement-I is true. However, the given statement claims that x=2, which is true. The equation y=2x+1 represents a linear function, and its graph is indeed a straight line, so Statement-II is true.

The area of a triangle is given by 1/2 ×base×height. For the given triangle, this is 1/2 ​ x10x5=25 square cm, so Statement-I is true. The area of a circle is given by πr² . For a radius of 7 cm, the area is 49π square cm, not  154π, so Statement-II is false.

The volume of a cube is given by side length cubed. For a side length of 4 cm , the volume is 4³= 64 cubic cm , so Statement-I is true. The perimeter of a rectangle is 2 (length + width). For given dimensions, this is 2(5+3)=16 cm, so Statement-II is also true.

Factoring the quadratic equation x²-5x+6, we get (x-2)(x-3)=0, so the roots are 2 and 3, making Statement-I true. For any quadratic equation ax²+bx+c=0, the sum of the roots is indeed given by -b/a,
making Statement-II also true.

The GCD of 24 and 36 is 12 since 12 is the largest number that divides both 24 and 36 without leaving a remainder, so Statement-I is true. The LCM of 5 and 7 is 35 because 35 is the smallest number that both 5 and 7 divide without a remainder, making Statement-II also true.

The sum of the interior angles of a triangle is 180 degrees. For angles 50 and 60 degrees, the third angle is 180−50−60=70 degrees, so Statement-I is true. The exterior angle of a triangle is indeed equal to the sum of the two opposite interior angles, so Statement-II is true.

When a fair coin is tossed, there are two possible outcomes: heads and tails, each with a probability of 1/2, so Statement-I is true. A standard die has six faces numbered 1 to 6, with three even numbers (2, 4, 6). The probability of rolling an even number is 3/6 = 1/2, not 1/3, so Statement-II is false.

The distance formula between two points (x₁,y₁) and  (x₂,y₂) is indeed , making Statement-I true. The midpoint formula for the segment connecting two points is , so Statement-II is also true.

For a quadratic equation ax²+bx+c=0, the product of the roots is given by c/a. Here, the product is 3/2, making Statement-I true. The sum of the roots is given by -b/a, which is 5/2, but since the sum should be positive 5/2, Statement-II is true. Therefore, Statement-I is true but Statement-II is also correct.