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Solution: Since, 1, 2 and 3 are the remainders of , and , respectively. Question 11 Show that 12 n cannot end with the digit 0 or 5 for any natural number n. Solution: If any number ends with the digit 0 or 5, it is always divisible by 5. If 12 n ends with the digit zero or five it must be divisible by 5. This is possible only if prime factorisation of 12 n contains the prime number 5. Question 12 On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively.
What is the minimum distance each should walk so that each can cover the same distance in complete steps? Solution: We have to lind the LCM of 40 cm, 42 cm and 45 cm to get the required minimum distance. Hence, write its decimal expansion, without actual division. Hence, 0. Solution: On dividing n by 3, let q be the quotient and r be the remainder. So, in this case, only n is divisible by 3.
Question 3 Prove that one of any three consecutive positive integers must be divisible by 3. On dividing n by 3, let q be the quotient and r be the remainder. Hence, one of any three consecutive positive integers must be divisible by 3. Question 4 For any positive integer n, prove that n � n is divisible by 6. Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Give reasons for your answer. Solution: False We know that, if two triangles are similar, then their corresponding angles are equal.
Is the following statement true? Solution: False Two quadrilaterals are similar if their corresponding angles are equal and corresponding sides must also be proportional. Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar?
Solution: True Here, the corresponding two sides and the perimeters of two triangles are proportional, then the third side of both triangles will also in proportion.
If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar?
Solution: False Because, according to SAS similarity criterion, if one angle of a triangle is equal to an angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. Here, one angle and two sides of two triangles are equal but these sides not including equal angle, so given statement is not correct. AP Hence proved. Find the altitude of an equilateral triangle of side 8 cm. Solution: Let ABC be an equilateral triangle of side 8 cm i.
Then, D is the mid-point of BC. Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle Ncert Exemplar Class 10 Maths Byjus Paper is 48 cm 2 , find the area of the larger triangle. If PN. Areas of two similar triangles are 36 cm 2 and cm 2. If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle. This website uses cookie or similar technologies, to enhance your browsing experience and provide personalised recommendations.
By continuing to use our website, you agree to our Privacy Policy and Cookie Policy. Home 20 Trending Quiz Feedback Add to home. Chapter Name. Chapter 1 Real Numbers. Chapter 2 Polynomials. Chapter 4 Quadratic Equations. Chapter 5 Arithmetic Progression. Chapter 6 Triangles. Chapter 7 Coordinate Geometry. Chapter 8 Introduction to Trigonometry and its Applications.
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