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Class 10 Exam  >  Class 10 Tests  >  HOTs for Maths Olympiad - 6 - Class 10 MCQ

HOTs for Maths Olympiad - 6 - Class 10 MCQ


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10 Questions MCQ Test - HOTs for Maths Olympiad - 6

HOTs for Maths Olympiad - 6 for Class 10 2024 is part of Class 10 preparation. The HOTs for Maths Olympiad - 6 questions and answers have been prepared according to the Class 10 exam syllabus.The HOTs for Maths Olympiad - 6 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 - 6 below.
Solutions of HOTs for Maths Olympiad - 6 questions in English are available as part of our course for Class 10 & HOTs for Maths Olympiad - 6 solutions in Hindi for Class 10 course. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free. Attempt HOTs for Maths Olympiad - 6 | 10 questions in 15 minutes | Mock test for Class 10 preparation | Free important questions MCQ to study for Class 10 Exam | Download free PDF with solutions
HOTs for Maths Olympiad - 6 - Question 1
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Read the given statements and select the incorrect option.

Detailed Solution for HOTs for Maths Olympiad - 6 - Question 1

All the given statements are correct:
A. The circumference formula 2r is correct.
B. The area formula πr2 is correct.
C. The diameter being twice the radius is correct.

HOTs for Maths Olympiad - 6 - Question 2
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Read the given statements and select the incorrect option.

Detailed Solution for HOTs for Maths Olympiad - 6 - Question 2

The roots of x2 − 2x + 1 = 0 are 1 and 1 (double root), not 1 and -1.

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HOTs for Maths Olympiad - 6 - Question 3
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Read the following statements carefully and state ‘T’ for true and ‘F’ for false.

(i) The slope of the line passing through the points (2, 3) and (4, 7) is 2.
(ii) The equation of the line with slope m and y-intercept c is y = mx + c
(iii) Parallel lines have equal slopes.

Detailed Solution for HOTs for Maths Olympiad - 6 - Question 3

(i) The slope of the line passing through (2, 3) and (4, 7) is  True
(ii) The equation of a line with slope m and y-intercept c is y = mx + c. True.
(iii) Parallel lines have equal slopes. True.

HOTs for Maths Olympiad - 6 - Question 4
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Read the following statements carefully and state ‘T’ for true and ‘F’ for false.

(i) The probability of getting a head in a single toss of a fair coin is 0.5.
(ii) The probability of rolling a sum of 7 with two fair six-sided dice is 1/6.
(iii) The probability of drawing an ace from a standard deck of 52 cards is 1/13.
Detailed Solution for HOTs for Maths Olympiad - 6 - Question 4

(i) The probability of getting a head in a single toss of a fair coin is 0.5. True.
(ii) The probability of rolling a sum of 7 with two fair six-sided dice is 6/36 = 1/6.True.
(iii) The probability of drawing an ace from a standard deck of 52 cards is 4/52 = 1/13. True.

HOTs for Maths Olympiad - 6 - Question 5
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Fill in the blanks and select the correct option.

(i) If the system of equations 2x + 3y = 7 and 4x + ky = 14 has no solution, then the value of k is P.

(ii) If the system of equations 5x + 4y = 3 and 10x + 8y = k has infinitely many solutions, then the value of k is Q.
Detailed Solution for HOTs for Maths Olympiad - 6 - Question 5

(i) For no solution, the coefficients of xxx and yyy in the two equations must be proportional, but not equal. Therefore,

(ii) For infinitely many solutions, the coefficients of x and y must be proportional and the constant term must also follow the same proportion.

HOTs for Maths Olympiad - 6 - Question 6
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Fill in the blanks and select the correct option.

(i) The roots of the equation x2 + px + q = 0 are in the ratio 2:3. If the roots are 2/3 and 2, then the value of p is P.
(ii) The value of q is Q
Detailed Solution for HOTs for Maths Olympiad - 6 - Question 6

(i) If the roots are in the ratio 2:3, let the roots be 2k and 3k. The sum of the roots is given by −p/a = 2k + 3k = 5k. Thus, p=−5k.
(ii) The product of the roots is given by q/a = (2k) (3k) = 6k2. Hence, q = 6k2

HOTs for Maths Olympiad - 6 - Question 7
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Read the following statements and select the correct option.

Statement-I: The sum of the interior angles of a triangle is always 180 degrees.
Statement-II: The sum of the exterior angles of a triangle is always 360 degrees.
Detailed Solution for HOTs for Maths Olympiad - 6 - Question 7

The sum of the interior angles of any triangle is always 180 degrees, and the sum of the exterior angles of any polygon, including a triangle, is always 360 degrees. Therefore, both statements are true.

HOTs for Maths Olympiad - 6 - Question 8
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Read the following statements and select the correct option.

Statement-I: The sum of the interior angles of a polygon with n sides is (n -2) x 180°.

Statement-Il: The sum of the exterior angles of any polygon is always 360°.
Detailed Solution for HOTs for Maths Olympiad - 6 - Question 8

Statement-I is correct because the formula for the sum of interior angles of a polygon with n sides is (n - 2) x 180°.
Statement-II is also correct because the sum of the exterior angles of any polygon is always 360°.

HOTs for Maths Olympiad - 6 - Question 9
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Solve the following and select the correct option.

(i) Find the value of k for which the system of equations 3x + 4y = 5 and 6x + ky = 10 has no solution.
(ii) The base of a triangle is 5 cm more than its height. If the area of the triangle is 30 cm2, find its base and height.
Detailed Solution for HOTs for Maths Olympiad - 6 - Question 9

HOTs for Maths Olympiad - 6 - Question 10
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Solve the following and select the correct option.

(i) Find the area of a parallelogram with base 10 cm and height 5 cm.
(ii) If the area of a circle is 154 cm2, find its radius. Use π = 22/7.
Detailed Solution for HOTs for Maths Olympiad - 6 - Question 10


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