{"id":624298,"date":"2023-09-01T07:44:22","date_gmt":"2023-09-01T07:44:22","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=624298"},"modified":"2023-09-01T07:44:27","modified_gmt":"2023-09-01T07:44:27","slug":"kc-sinha-exercise-7-2-mathematics-solution-class-10-chapter-7-quadratic-equations","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-7-2-mathematics-solution-class-10-chapter-7-quadratic-equations\/","title":{"rendered":"KC Sinha: Exercise 7.2 – Mathematics Solution Class 10 Chapter 7 Quadratic Equations"},"content":{"rendered":"\n\n\n\n\n

Question 1 A <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong>
(x \u2212 2) (x + 1) = (x \u2212 1) (x + 3)<\/strong><\/p>\n\n\n\n

Sol :
Given; (x \u2212 2) (x + 1) = (x \u2212 1) (x + 3)
\u21d2 x2<\/sup> + x \u2212 2x \u2212 2 = x2<\/sup> + 3x \u2212 x \u2212 3
\u21d2 x2<\/sup> \u2212 x \u2212 2 \u2212 x2<\/sup> \u2212 2x + 3 = 0
\u21d2 \u22123x + 1 = 0
\u2235 The highest power of x in the equation is 1;
\u2234 It is not a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 1 B <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong>
(x \u2212 2)2<\/sup> + 1 = 2x \u2212 3<\/strong><\/p>\n\n\n\n

Sol :
Given; (x \u2212 2)2<\/sup> + 1 = 2x \u2212 3
\u21d2 x2<\/sup> \u2212 2x + 4 + 1 = 2x \u2212 3
\u21d2 x2<\/sup> \u2212 2x + 5 \u2212 2x + 3 = 0
\u21d2 x2<\/sup> \u2212 4x + 8 = 0
\u2235 The highest power of x in the equation is 2;
\u2234 It is a quadratic equation<\/p>\n\n\n\n

\n\n\n\n

Question 1 C <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong>
x (x + 1) + 8 = (x + 2) (x \u2212 2)<\/strong><\/p>\n\n\n\n

Sol :
Given; x (x + 1) + 8 = (x + 2) (x \u2212 2)
\u21d2 x2<\/sup> + x + 8 = x2<\/sup> \u2212 22<\/sup>
\u21d2 x2<\/sup> + x + 8 \u2212 x2<\/sup> + 4 = 0
\u21d2 x + 12 = 0
\u2235 The highest power of x in the equation is 1;
\u2234 It is not a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 1 D <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong>
(x \u2212 3) (2x + 1) = x (x + 5)<\/strong><\/p>\n\n\n\n

Sol :
Given; (x \u2212 3) (2x + 1) = x (x + 2)
\u21d2 2x2<\/sup> + x \u2212 6x \u2212 3 = x2<\/sup> + 5x
\u21d2 2x2<\/sup> + x \u2212 6x \u2212 3 \u2212 x2<\/sup> \u2212 5x = 0
\u21d2 x2<\/sup> \u2212 10x \u2212 3 = 0
\u2235 The highest power of x in the equation is 2;
\u2234 It is a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 1 E <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong>
x (2x + 3) = x2<\/sup> + 1<\/strong><\/p>\n\n\n\n

Sol :
Given; x (2x + 3) = x2<\/sup> + 1
\u21d2 2x2<\/sup> + 3x = x2<\/sup> + 1
\u21d2 2x2<\/sup> + 3x \u2212 x2<\/sup> \u2212 1 = 0
\u21d2 x2<\/sup> +3x \u2212 1 = 0
\u2235 The highest power of x in the equation is 2;
\u2234 It is a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 1 F <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong>
x2<\/sup> + 3x + 1 = (x \u2212 2)2<\/sup><\/strong><\/p>\n\n\n\n

Sol :
Given; x2<\/sup> + 3x + 1 = (x \u2212 2)2<\/sup>
\u21d2 x2<\/sup> + 3x + 1 = x2<\/sup> \u2212 4x + 4
\u21d2 x2<\/sup> + 3x + 1 \u2212 x2<\/sup> \u2212 4x \u2212 4 = 0
\u21d2 \u2212x \u2212 3 = 0
\u2235 The highest power of x in the equation is 1;
\u2234 It is not a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 1 G <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong>
(x + 1) (x \u2212 1) = (x + 2) (x + 3)<\/strong><\/p>\n\n\n\n

Sol :
Given; (x + 1) (x \u2212 1) = (x + 2) (x + 3)
\u21d2 x2<\/sup> \u2212 12<\/sup> = x2<\/sup> + 5x + 6
\u21d2 x2<\/sup> \u2212 1 \u2212 x2<\/sup> \u2212 5x \u2212 6 = 0
\u21d2 \u22125x \u2212 7 = 0
\u2235 The highest power of x in the equation is 1;
\u2234 It is not a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 1 H <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong><\/p>\n\n\n\n

(x \u2212 1)2<\/sup> = (x + 1)2<\/sup><\/strong>
Sol :
Given; (x \u2212 1)2<\/sup> = (x + 1)2<\/sup>
\u21d2 x2<\/sup> \u2212 x + 12<\/sup> = x2<\/sup> + x + 12<\/sup>
\u21d2 x2<\/sup> \u2212 x + 1 \u2212 x2<\/sup> \u2212 x \u2212 1 = 0
\u21d2 \u22122x = 0
\u2235 The highest power of x in the equation is 1;
\u2234 It is not a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 2 A <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong><\/p>\n\n\n\n

(x + 2)3<\/sup> = x3<\/sup> \u2212 4<\/strong>
Sol :
Given; (x + 2)3<\/sup> = x3<\/sup> \u2212 4
\u21d2 x3<\/sup> + 6x2<\/sup> + 12x + 23<\/sup> = x3<\/sup> \u2212 4
\u21d2 x3<\/sup> + 6x2<\/sup> + 12x + 23<\/sup>\u2212 x3<\/sup> + 4 = 0
\u21d2 6x2<\/sup> + 12x + 12 = 0
\u2235 The highest power of x in the equation is 2;
\u2234 It is a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 2 B <\/h4>\n\n\n\n

Check whether the following are quadratic equations:<\/strong><\/p>\n\n\n\n

x\u22121x=8
Sol :
Given; x\u22121x=8
\u21d2 x2<\/sup> \u2212 1 = 8x
\u21d2 x2<\/sup> \u2212 8x \u2212 1 = 0
\u2235 The highest power of x in the equation is 2;
\u2234 It is a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 2 C <\/h4>\n\n\n\n

Check whether the following are quadratic equations :<\/strong><\/p>\n\n\n\n

2×2\u22123x\u2212\u2212\u221a+5=0<\/strong>
Sol :
Given; 2×2\u22123x\u2212\u2212\u221a+5=0
\u21d2 2×2+5=3x\u2212\u2212\u221a
\u21d2 (2×2+5)2=(3x\u2212\u2212\u221a)2
\u21d2 4x4<\/sup> + 20x2<\/sup> + 25 = 9x
\u21d2 4x4<\/sup> + 20x2<\/sup> \u2212 9x + 25 = 0
\u2235 The highest power of x in the equation is 4;
\u2234 It is not a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 2 D <\/h4>\n\n\n\n

Check whether the following are quadratic equations :<\/strong><\/p>\n\n\n\n

x2+1x=5<\/strong>
Sol :
Given; x2+1x=5
\u21d2 x3<\/sup> + 1 = 5x
\u21d2 x3<\/sup>\u2212 5x + 1 = 0
\u2235 The highest power of x in the equation is 3;
\u2234 It is not a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 2 E <\/h4>\n\n\n\n

Check whether the following are quadratic equations :<\/strong><\/p>\n\n\n\n

x2\u22121×2=8<\/strong>
Sol :
Given; x2\u22121×2=8
\u21d2 x4<\/sup>\u2212 1 = 8x2<\/sup>
\u21d2 x4<\/sup>\u2212 8x2<\/sup>\u2212 1 = 0
\u2235 The highest power of x in the equation is 4;
\u2234 It is not a quadratic equation.<\/p>\n\n\n\n

\n\n\n\n

Question 3 A <\/h4>\n\n\n\n

Represent the following situations mathematically:<\/strong>
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.<\/strong><\/p>\n\n\n\n

Sol :
Let \u2018x\u2019 be the number of marbles John had.
\u2234 Jivanti will have 45 \u2212 x marbles.
[\u2235 the total number of marbles is 45]
As both of them lost 5 marbles each; marbles they now have will be x \u2212 5 and 40 \u2212 x respectively.
\u21d2 Product of the number of marbles = (x \u2212 5) (40 \u2212 x)<\/p>\n\n\n\n

\u2234 40x \u2212 x2<\/sup> \u2212 200 + 5x = 124 [\u2235 the product is 124]
\u21d2 x2<\/sup> \u2212 45x + 324 = 0<\/p>\n\n\n\n

\n\n\n\n

Question 3 B <\/h4>\n\n\n\n

Represent the following situations mathematically:<\/strong><\/p>\n\n\n\n

A shopkeeper buys a number of books for Rs. 80. If he had bought four more books for the same amount, the book would have cost Re. 1 less.<\/strong>
Sol :
Let \u2018x\u2019 be the number of books bought by the shopkeeper.
\u2234 Cost of one book = Rs. 80 \u00f7 x.
[\u2235 the total cost of books is Rs. 80]
\u2234 Cost of one book when he buys 4 more books for same rate = Rs. 80 \u00f7 (x + 4).
When he buys four more books for the same amount; it will cost Re. 1 per book less than the previous.
\u2234 80 \u00f7 (x + 4) = (80 \u00f7 x) \u2212 1
\u21d2 80x+4=80x\u22121
\u21d2 80x = (x + 4) (80 \u2212 x)
\u21d2 80x = 80x \u2212 x2<\/sup> + 320 \u2212 4x
\u21d2 x2<\/sup> + 4x + 320 = 0<\/p>\n\n\n\n

\n\n\n\n

Question 3 C <\/h4>\n\n\n\n

Represent the following situations mathematically:<\/strong><\/p>\n\n\n\n

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs. 750. We would like to find out the number of toys produced on that day.<\/strong>
Sol :
Let \u2018x\u2019 be the number of toys produced on that day.
\u2234 Cost of production of each toy that day= Rs. 55 \u2212 x.<\/p>\n\n\n\n

[\u2235 The cost of production of each toy (in rupees) is 55 minus the number of toys produced in a day]
\u2234 Cost of production of x toys = Rs. x (55 \u2212 x)
[\u2235 On a particular day, the total cost of production was Rs. 750.]
\u2234 x (55 \u2212 x) = 750
\u21d2 x2<\/sup> \u2212 55x + 750 = 0<\/p>\n\n\n\n

\n\n\n\n

Question 3 D <\/h4>\n\n\n\n

Represent the following situations mathematically:<\/strong><\/p>\n\n\n\n

The sum of the squares of two positive integers is 117. If the square of the smaller number equals four times the larger number, we need to find the integers.<\/strong>
Sol :
Let \u2018x\u2019 and \u2018y\u2019 be the smaller and larger integer respectively.
\u2234 x2<\/sup> + y2<\/sup> = 117.
[\u2235 The sum of the squares of two positive integers is 117]
\u2234 x2<\/sup> = 4y
[\u2235 the square of the smaller number equals four times the larger number.]
\u2234 y2<\/sup> + 4y \u2013 117 = 0<\/p>\n\n\n\n

\n\n\n\n

Question 4 A <\/h4>\n\n\n\n

Represent the following situations in the form of the quadratic equation.<\/strong><\/p>\n\n\n\n

Divide 16 into two parts such that twice of the square of larger part exceeds the square of the smaller part by 164.<\/strong>
Sol :
Let \u2018x\u2019 be the one part and the other part will be 16 \u2212 x.
[\u2235 16 is being divided]
\u2235 Twice of the square of larger part exceeds the square of the smaller part by 164.
\u2234 2x2<\/sup> = (16 \u2013 x)2<\/sup> + 164
\u2234 2x2<\/sup> = 256 \u2013 32x + x2<\/sup> + 164
\u21d2 x2<\/sup> + 32x \u2212 420 = 0<\/p>\n\n\n\n

\n\n\n\n

Question 4 B <\/h4>\n\n\n\n

Represent the following situations in the form of the quadratic equation.<\/strong><\/p>\n\n\n\n

One year ago, a man was eight times as old as his son. Now, his age is equal to the square of his son’s age.<\/strong>
Sol :
Let \u2018y\u2019 and \u2018x\u2019 be the present age of the man and son.
\u2235 One year ago the man was eight times as old as his son.
\u2234 y \u2013 1 = 8 (x \u2212 1)
\u2235 Now, his age is equal to the square of his son’s age.
\u2234 y = x2<\/sup>
\u2234 x2<\/sup> \u2212 1 = 8 (x \u2212 1)
\u21d2 x2<\/sup> \u2212 8x + 7 = 0<\/p>\n\n\n\n

\n\n\n\n

Question 4 C <\/h4>\n\n\n\n

Represent the following situations in the form of the quadratic equation.<\/strong><\/p>\n\n\n\n

A train travels a distance of 300 km at a constant speed. If the speed of the train ‘is increased by 5 km an hour. The journey would have taken two hours less.<\/strong>
Sol :
Let \u2018x\u2019 be the speed of the train in km per hour.
\u2234 Time taken to cover 300 km = 300x
[\u2235 Time = Distance  speed .]
\u2234 Time taken when speed is increased by 5 = \\frac{300}{x+5}<\/p>\n\n\n\n

300x+5
\u2235 The journey would have taken two hours less when speed is decreased.<\/p>\n\n\n\n

\n
KC Sinha Solutions<\/a><\/div>\n\n\n\n
KC Sinha Class 10 Solutions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Question 1 A  Check whether the following are quadratic equations:(x \u2212 2) (x + 1) = (x \u2212 1) (x + 3) Sol :Given; (x \u2212 2) (x + 1) = (x \u2212 1) (x + 3)\u21d2 x2 + x \u2212 2x \u2212 2 = x2 + 3x \u2212 x \u2212 3\u21d2 x2 \u2212 x \u2212 2 \u2212 x2 \u2212 2x […]<\/p>\n","protected":false},"author":302,"featured_media":624299,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[24],"tags":[],"boards":[],"class_list":["post-624298","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-10","entry"],"yoast_head":"\nKC Sinha: Exercise 7.2 - Mathematics Solution Class 10 Chapter 7 Quadratic Equations - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"Question 1 A  Check whether the following are quadratic equations:(x \u2212 2) (x + 1) = (x \u2212 1) (x + 3) Sol :Given; 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