Math Assignment / Class X / Chapter 4 / Quadratic Equations
Extra questions of chapter 4 class 10 Quadratic Equations with answer and hints to the difficult questions. Important and useful math assignment for the students of class 10
For better results
ASSIGNMENT FOR 10 STANDARD QUADRATIC EQUATIONS
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Question 36 Out of a number of Saras birds, (1/4)th of the number are moving about in Lotus plants, (1/9)th coupled with (1/4)th, as well as 7 times the square root of the number moving on a hill, 56 birds remain on trees. What is the total number of words. |
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Solution Let total birds = x No. of birds moving in lotus plant
= (1/4)x No. of birds coupled with = (1/9
+1/4)x = (13/36)x No of birds moving on the hill = 7x No. of birds on the tree = 56 Acoording to the question \[
\frac{1}{4}x+\frac{13}{36}x+7\sqrt{x}+56=x\] \[ \frac{22}{36}x+7\sqrt{x}+56=x\] \[
x-\frac{22}{36}x-7\sqrt{x}-56=0\] \[ \frac{14}{36}x-7\sqrt{x}-56=0\] \[\frac{2}{36}x-\sqrt{x}-8=0\] \[ \frac{1}{18}x-\sqrt{x}-8=0\] \[ x-18\sqrt{x}-144=0\] \[ Putting \: \: \: \: \sqrt{x}=y
\: \: \: \Rightarrow\: \: x=y^{2}\] \[ y^{2}-18y-144=0\] \[ y^{2}-24y+6y-144=0\] \[ y(y-24)+6(y-24)=0\] \[ (y-24)(y+6)=0\] \[ \Rightarrow y=24, -6\] \[ y=-6 \: \: is \: \: rejected\] \[ y=\sqrt{x}=24\Rightarrow
x=(24)^{2}=576\] Hence Total Number of birds = 576 |
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Question : 37 7 years ago, age of
Varun was five times the square of the age of Swati. After 3 years, age of
Swati will be 2/5 of the age of Varun. Find their present ages. |
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Solution : Let 7 years ago the
age of Swati = x years Let 7 years ago the
age of Varun = y years ATQ y = 5x2 …………………(1) Present age of
Swati = x + 7 Present age of
Varun = y + 5 After 3 years age
of Swati = x + 10 After 3 years age
of Varun= y + 10 Again ATQ : Age of Swati = (2/5) age of Varun x + 10 = (2/5)[y + 10] 5(x + 10) = 2y + 20 5x + 50 = 2y + 20 Putting y = 5x2 we get 5x + 50 = 2(5x2
) + 20 10x2 - 5x + 20 - 50 = 0 10x2 - 5x
- 30 = 0 2x2 - x
- 6 = 0 (Dividing by 5) (2x + 3)(x - 2) = 0 x = - 3/2 (Rejected) and
x = 2 Putting x = 2 in
equation (1) we get y = 5 (2)2 ⇒ y = 20 Present age of
Swati = x + 7 = 2 + 7 = 9 Present age of
Varun = y + 7 = 20 + 7 = 27 |
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