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HOTs for Maths Olympiad - 5 - Class 10 MCQ


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10 Questions MCQ Test Olympiad Preparation for Class 10 - HOTs for Maths Olympiad - 5

HOTs for Maths Olympiad - 5 for Class 10 2024 is part of Olympiad Preparation for Class 10 preparation. The HOTs for Maths Olympiad - 5 questions and answers have been prepared according to the Class 10 exam syllabus.The HOTs for Maths Olympiad - 5 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for HOTs for Maths Olympiad - 5 below.
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HOTs for Maths Olympiad - 5 - Question 1

Read the given statements and select the incorrect option.

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 1

All the given statements are correct:
A. Arithmetic mean of first 10 natural numbers 
B. Median of first 10 natural numbers (average of 5th and 6th terms) 
C. Mode is undefined as all numbers appear only once.

HOTs for Maths Olympiad - 5 - Question 2

Which of the following statements about matrices is incorrect?

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 2

Matrix multiplication is not commutative, so the product of two matrices is not necessarily the same when the order is reversed. Therefore, Option A is incorrect.

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HOTs for Maths Olympiad - 5 - Question 3

Read the following statements carefully and state 'T' for true and 'F' for false.

(i) The value of sin 45° is √2/2.
(ii) The value of cos 60° is 1/2.
(iii) The value of tan 90° is 0.

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 3

(i) The value of sin 45° is √2/2. True.
(ii) The value of cos 60° is 1/2. True.
(iii) The value of tan 90° is undefined, not 0. False.

HOTs for Maths Olympiad - 5 - Question 4

Read the following statements carefully and state ‘T’ for true and ‘F’ for false.

(i) The derivative of 
(ii) The integral of 
(iii) The second derivative of 

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 4

HOTs for Maths Olympiad - 5 - Question 5

Fill in the blanks and select the correct option.

(i) The area of a triangle with vertices at (1,2), (4, 6), and (5, 8) is P.
(ii) The length of the median to the side joining (4,6) and (5, 8) is Q.

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 5

HOTs for Maths Olympiad - 5 - Question 6

Fill in the blanks and select the correct option.

(i) The distance between the points (x1, y1) and (x2, y2) is given by
 and (x2, y2) = (4, 6), the distance is P.
(ii) The midpoint of the same points is Q.

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 6

HOTs for Maths Olympiad - 5 - Question 7

Read the following statements and select the correct option.

Statement-I: The perimeter of a rectangle is given by 2 (l + b), where l is the length and b is the breadth.

Statement-II: The area of a rectangle is given by 2lb, where l is the length and b is the breadth.

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 7

The perimeter of a rectangle is correctly given by 2(l + b). However, the area of a rectangle is given by l × b, not 2lb. Therefore, Statement-I is true, but Statement-II is false.

HOTs for Maths Olympiad - 5 - Question 8

Read the following statements and select the correct option.

Statement-I: The roots of the equation x2 + 4x + 4 = 0, are real and equal.
Statement-II: The discriminant of the quadratic equation ax2 + bx  + c = 0 is b2 - 4ac

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 8

The roots of x2 + 4x + 4 = 0 are real and equal because the discriminant b2 - 4ac = 42 - 4(1) (4) =0. The discriminant formula b2 - 4ac is correct for any quadratic equation. Therefore, both statements are true.

HOTs for Maths Olympiad - 5 - Question 9

Solve the following and select the correct option.

(i) If the roots of the quadratic equation ax2 + bx + c = 0 are in the ratio 3:5, find the value of b2/ac
(ii) If the sum of the first 10 terms of an arithmetic progression is 155, find the first term given that the common difference is 2.

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 9


HOTs for Maths Olympiad - 5 - Question 10

Solve the following and select the correct option.

(i) If a = 3 and b = 4, find the value of 
(ii) The hypotenuse of a right-angled triangle is 13 cm, and one of its legs is 5 cm.

Find the other leg.

Detailed Solution for HOTs for Maths Olympiad - 5 - Question 10


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