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High Order Thinking Skills (HOTs) - 5 - Class 9 MCQ


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10 Questions MCQ Test Mathematics Olympiad for Class 9 - High Order Thinking Skills (HOTs) - 5

High Order Thinking Skills (HOTs) - 5 for Class 9 2024 is part of Mathematics Olympiad for Class 9 preparation. The High Order Thinking Skills (HOTs) - 5 questions and answers have been prepared according to the Class 9 exam syllabus.The High Order Thinking Skills (HOTs) - 5 MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for High Order Thinking Skills (HOTs) - 5 below.
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High Order Thinking Skills (HOTs) - 5 - Question 1

ill in the blanks and select the correct option.

(i) A rectangle has a length of 15 cm and width of 10 cm. If the length is increased by 20% and the width is decreased by 10%, the new area of the rectangle is P cm2.
(ii) A right-angled triangle has legs of lengths 6 cm and 8 cm. The length of the hypotenuse is Q cm.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 1

(i) New length = 15 cm + 20% of 15 cm = 15 + 3 = 18 cm
New width = 10 cm - 10% of 10 cm = 10 - 1 = 9 cm
New area = 18 cm * 9 cm = 162 cm2 (So, P = 180)
(ii) Hypotenuse = √(62 + 82) = √(36 + 64) = √100 = 10 cm (So, Q = 10)

High Order Thinking Skills (HOTs) - 5 - Question 2

Fill in the blanks and select the correct option.
(i) The sum of the interior angles of a polygon with 10 sides is P degrees.
(ii) The area of a square is 144 cm². The length of its diagonal is Q cm.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 2

(i) Sum of interior angles of a polygon = (n-2) * 180 = (10-2) * 180 = 1440 degrees (So, P = 1440)
(ii) Side of the square = √144 = 12 cm
Diagonal = Side * √2 = 12 * √2 cm (So, Q = 12√2)

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High Order Thinking Skills (HOTs) - 5 - Question 3

Fill in the blanks and select the correct option.
(i) The number of diagonals in a hexagon is P.
(ii) The length of each side of an equilateral triangle with an area of 9√3 cm2 is Q cm.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 3

(i) Number of diagonals in a polygon = n(n-3)/2 = 6(6-3)/2 = 9 (So, P = 9)
(ii) Area of equilateral triangle = (√3/4) * a2 = 9√3
a2 = 36
a = √36 = 6 cm (So, Q = 6)

High Order Thinking Skills (HOTs) - 5 - Question 4

Fill in the blanks and select the correct option.
(i) The surface area of a sphere with radius 7 cm is P cm2.
(ii) The volume of a cube with side 5 cm is Q cm3.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 4

(i) Surface area of a sphere = 4πr2 = 4 * π * 72 = 616 cm² (So, P = 616)
(ii) Volume of a cube = side3 = 53 = 125 cm3 (So, Q = 125)

High Order Thinking Skills (HOTs) - 5 - Question 5

Fill in the blanks and select the correct option.
(i) The sum of the first 20 natural numbers is P.
(ii) The sum of the squares of the first 10 natural numbers is Q.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 5

(i) Sum of first n natural numbers = n(n+1)/2 = 20(21)/2 = 210 (So, P = 210)
(ii) Sum of squares of first n natural numbers = n(n+1)(2n+1)/6 = 10(11)(21)/6 = 385 (So, Q = 385)

High Order Thinking Skills (HOTs) - 5 - Question 6

Fill in the blanks and select the correct option.
(i) The perimeter of a rectangle is 54 cm. If its length is 16 cm, its width is P cm.
(ii) The circumference of a circle with a radius of 7 cm is Q cm.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 6

(i) Perimeter = 2(l + w)
54 = 2(16 + w)
54 = 32 + 2w
2w = 22
w = 11 cm (So, P = 11)
(ii) Circumference = 2πr = 2 * π * 7 = 44 cm (So, Q = 44)

High Order Thinking Skills (HOTs) - 5 - Question 7

Fill in the blanks and select the correct option.
(i) The value of P if (x - 2)(x - 3) = x2 - Px + 6.
(ii) The value of Q if the mean of the first 5 prime numbers is Q.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 7

(i) Expanding (x - 2)(x - 3) gives x2 - 5x + 6, so P = 5 (So, P = 5)
(ii) The first 5 prime numbers are 2, 3, 5, 7, 11.
Mean = (2+3+5+7+11)/5 = 28/5 = 5.6 (So, Q = 5.6)

High Order Thinking Skills (HOTs) - 5 - Question 8

Fill in the blanks and select the correct option.
(i) The area of a trapezium with bases 10 cm and 6 cm, and height 5 cm is P cm2.
(ii) The area of a triangle with base 8 cm and height 12 cm is Q cm2.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 8

(i) Area of a trapezium = 1/2 * (sum of parallel sides) * height
= 1/2 * (10 + 6) * 5 = 40 cm² (So, P = 40)
(ii) Area of a triangle = 1/2 * base * height
= 1/2 * 8 * 12 = 48 cm² (So, Q = 48)

High Order Thinking Skills (HOTs) - 5 - Question 9

Fill in the blanks and select the correct option.
(i) If the quadratic equation x2 - 7x + 10 = 0 has roots α and β, then the value of α + β is P.
(ii) If the arithmetic mean of 8, 10, 12, 14, and 16 is Q.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 9

(i) Sum of the roots of the quadratic equation ax² + bx + c = 0 is -b/a = 7 (So, P = 7)
(ii) Arithmetic mean = (8 + 10 + 12 + 14 + 16) / 5 = 60 / 5 = 12 (So, Q = 12)

High Order Thinking Skills (HOTs) - 5 - Question 10

Fill in the blanks and select the correct option.
(i) The LCM of 12 and 15 is P.
(ii) The HCF of 24 and 36 is Q.

Detailed Solution for High Order Thinking Skills (HOTs) - 5 - Question 10

(i) LCM of 12 and 15 = 60 (So, P = 60)
(ii) HCF of 24 and 36 = 12 (So, Q = 12)

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