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10th Maths 4.2

NCERT Class 10th solution of Exercise 4.1 NCERT Class 10th solution of Exercise 4.3 NCERT Class 10th solution of Exercise 4.4 NCERT Class 10th Maths Projects Exercise 4.2 Q1. Find the roots of the following quadratic equation by factorisation : i)

$x^2-3x-10=0,$ ii)

$2x^2+x-6=0,$ iii)

$sqrt2x^2+7x+5sqrt2=0,$ iv)

$2x^2-x+1/8=0,$ v)

$100x^2-20x+1=0.$ Sol. : i)

$x^2-3x-10=0$

$x^2-5x+2x-10=0$

$x(x-5)+2(x-5)=0$

$(x-5)(x+2)=0$

$x-5=0$

$x=5$

$x+2=0$

$x=-2$ Answer :

$x=5, x=-2$ . ii)

$2x^2+x-6=0$

$2x^2+4x-3x-6=0$

$2x(x+2)-3(x+2)=0$

$(x+2)(2x-3)=0$

$x+2=0$

$x=-2$ ,

$2x-3=0$

$x=3/2$ Answer :

$x=-2, x=3/2$ . iii)

$sqrt2x^2+7x+5sqrt2=0$

$sqrt2x^2+5x+2x+5sqrt2=0$

$x(sqrt2x+5)+sqrt2(sqrt2x+5)=0$

$(sqrt2x+5)(x+sqrt2)=0$

$sqrt2x+5=0$

$x=-5/sqrt2$

$x+sqrt2=0$

$x=-sqrt2$ Answer :

$x=-5/sqrt2, x=-sqrt2$ . iv)

$2x^2-x+1/8=0$

$16x^2-8x+1=0$

$16x^2-4x-4x+1=0$

$4x(4x-1)-1(4x-1)=0$

$(4x-1)(4x-1)=0$

$(4x-1)^2=0$

$4x-1=0$

$x=1/4$ Answer : each

$x=1/4$ . v)

$100x^2-20x+1=0$

$100x^2-10x-10x+1=0$ `10x(10x-1)-1(10x-1)=0...

NCERT Class 10th solution of Exercise 4.2 NCERT Class 10th solution of Exercise 4.3 NCERT Class 10th solution of Exercise 4.4 NCERT Class 10th Maths Projects Exercise 4.1 Q1. Check whether the following are quadratic equations : i)

$(x+1)^2=2(x-3)$ ii)

$x^2-2x=(-2)(3-x)$ iii)

$(x-2)(x+1)=(x-1)(x+3)$ iv)

$(x-3)(2x+1)=x(x+5)$ v)

$(2x-1)(x-3)=(x+5)(x-1)$ vi)

$x^2+3x+1=(x-2)^2$ vii)

$(x+2)^3=2x(x^2-1)$ viii)

$x^3-4x^2-x+1=(x-2)^3$ Sol. : i)

$(x+1)^2=2(x-3)$

$x^2+2x+1=2x-6$

$x^2+2x+1-2x+6=0$

$x^2+7=0$ Answer : Yes. ii)

$x^2-2x=(-2)(3-x)$

$x^2-2x=-6+2x$

$x^2-2x+6-2x=0$

$x^2-4x+6=0$ Answer : Yes. iii)

$(x-2)(x+1)=(x-1)(x+3)$

$x(x+1)-2(x+1)=x(x+3)-1(x+3)$

$x^2+x-2x-2=x^2+3x-x-3$

$x^2-x-2=x^2+2x-3$

$x^2-x-2-x^2-2x+3=0$

$-3x+1=0$

$3x-1=0$ Answer : No. iv)

$(x-3)(2x+1)=x(x+5)$

$x(2x+1)-3(2x+1)=x^2+5x$

$2x^2+x-6x-3-x^2-5x=0$

$x^2-10x-3=0$ Answer : Yes. v)

$(2x-1)(x-3)=(x+5)(x-1)$

$2x(x-3)-1(x-3)=x(x-1)+5(x-1)$

$2x^2-6x-x+3=x^2-x+5x-5$

$2x^2-7x+3=x^2+4x-5$

$2x^2-7x+3-x^2-4x+5=0$

$x^2-11x+8=0$ Answe...

10th Maths 3.6

NCERT Class 10th solution of Exercise 3.1 NCERT Class 10th solution of Exercise 3.2 NCERT Class 10th solution of Exercise 3.3 NCERT Class 10th solution of Exercise 3.4 NCERT Class 10th solution of Exercise 3.5 NCERT Class 10th solution of Exercise 4.1 NCERT Class 10th Maths Projects Exercise 3.6 Q1. Solve the following pairs of equations by reducing them to a pair of linear equations : i)

$1/(2x)+1/(3y)=2 ; 1/(3x)+1/(2y)=13/6$ ii)

$2/sqrtx+3/sqrty=2 ; 4/sqrtx-9/sqrty=-1$ iii)

$4/x+3y=14 ; 3/x-4y=23$ iv)

$5/(x-1)+1/(y-2)=2 ; 6/(x-1)-3/(y-2)=1$ v)

$(7x-2y)/xy=5 ; (8x+7y)/xy=15$ vi)

$6x+3y=6xy ; 2x+4y=5xy$ vii)

$10/(x+y)+2/(x-y)=4 ; 15/(x+y)-5/(x-y)=-2$ viii)

$1/(3x+y)+1/(3x-y)=3/4 ; 1/(2(3x+y))-1/(2(3x-y))=-1/8$ Sol. : i)

$1/(2x)+1/(3y)=2$ ___________(1)

$1/(3x)+1/(2y)=13/6$ _________(2) Let

$1/x=p$ and

$1/y=q$ then

$p/2+q/3=2$

$3p+2q=12$ ________________(3)

$p/3+q/2=13/6$

$2p+3q=13$ ________________(4) from equation (3)

$q=(12-3p)/2$ Put in equation (4)

$2p+3((12-3p)/2)=13$ `4p+36-9p=2...

10th Maths 3.5

NCERT Class 10th solution of Exercise 3.1 NCERT Class 10th solution of Exercise 3.2 NCERT Class 10th solution of Exercise 3.3 NCERT Class 10th solution of Exercise 3.4 NCERT Class 10th solution of Exercise 3.6 NCERT Class 10th Maths Projects Exercise 3.5 Q1. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method. (i)

$x-3y-3=0; 3x-9y-2=0$ (ii)

$2x+y=5; 3x+2y=8$ (iii)

$3x-5y=20; 6x-10y=40$ (iv)

$x-3y-7=0; 3x-3y-15=0$ Sol. : i)

$x-3y-3=0$ _______(1)

$3x-9y-2=0$ ______(2)

$a_1/a_2=1/3, b_1/b_2=(-3)/-9=1/3,$ and

$c_1/c_2=(-3)/-2=3/2$

$a_1/a_2=b_1/b_2nec_1/c_2$ Answer : No solution. ii)

$2x+y=5$ ________(1)

$3x+2y=8$ _______(2)

$a_1/a_2=2/3, b_1/b_2=1/2,$ and

$c_1/c_2=(-5)/-8=5/8$

$a_1/a_2neb_1/b_2nec_1/c_2$ By Cross Multiplication Method :

$x/(b_1c_2-b_2c_1)=y/(c_1a_2-c_2a_1)=1/(a_1b_2-a_2b_1)$

$x/((1)(-8)-(2)(-5))=y/((-5)(3)-(-8)(2))=1/((2)(2)-(3)(1))$ `x/...

10th Maths 3.4

NCERT Class 10th solution of Exercise 3.1 NCERT Class 10th solution of Exercise 3.2 NCERT Class 10th solution of Exercise 3.3 NCERT Class 10th solution of Exercise 3.5 NCERT Class 10th solution of Exercise 3.6 NCERT Class 10th Maths Projects Exercise 3.4 Q1. Solve the following pair of linear equations by the elimination method and the substitution method : i)

$x+y=5$ and

$2x-3y=4$ ii)

$3x+4y=10$ and

$2x-2y=2$ iii)

$3x-5y-4=0$ and

$9x=2y+7$ iv)

$x/2+(2y)/3=-1$ and

$x-y/3=3$ Sol. : i) By Elimination Method :

$x+y=5$ ___________(1)

$2x-3y=4$ __________(2) Multiply equation (1) by

$3$ and equation (2) by

$1$ ,

$3x+3y=15$ ________(3)

$2x-3y=4$ __________(4) By Equation (3) + (4)

$3x+3y+2x-3y=15+4$

$5x=19$

$x=19/5$ Put in equation (1)

$19/5+y=5$

$y=5-19/5$

$y=(25-19)/5$

$y=6/5$ By Substitution Method : from equation (1)

$y=5-x$ __________(5) Substituting this value in equation (2)

$2x-3(5-x)=4$

$2x-15+3x=4$

$5x=4+15$

$5x=19$

$x=19/5$ put in equation (5)

$y=5-19/5$

$y=(25-19)/5$

$y=6/5$ Answer : `...

Exercise 3.3 NCERT Class 10th solution of Exercise 3.1 NCERT Class 10th solution of Exercise 3.2 NCERT Class 10th solution of Exercise 3.4 NCERT Class 10th solution of Exercise 3.5 NCERT Class 10th solution of Exercise 3.6 NCERT Class 10th Maths Projects Exercise 3.3 Q1. Solve the following pair of linear equations by the substitution method : i)

$x+y=14; x-y=4$ ii)

$s-t=3; s/3+t/2=6$ iii)

$3x-y=3; 9x-3y=9$ iv)

$0.2x+0.3y=1.3; 0.4x+0.5y=2.3$ v)

$sqrt2x+ sqrt3y=0; sqrt3x-sqrt8y=0$ vi)

$(3x)/2-(5y)/3=-2; x/3+y/2=13/6$ Sol. : i)

$x+y=14$ ________(1)

$x-y=4$ _________(2) from equation (2)

$x=y+4$ _________(3) Substituting this value in equation (1)

$y+4+y=14$

$2y=14-4$

$2y=10$

$y=10/2$

$y=5$ Put in equation (3)

$x=14-5$

$x=9$ Answer :

$x=9, y=5$ . ii)

$s-t=3$ ___________(1)

$s/3+t/2=6$ _______(2) from equation (1)

$s=t+3$ __________(3) Substituting this value in equation (2)

$(t+3)/3+t/2=6$

$(2(t+3)+3t)/6=6$

$2t+6+3t=36$

$5t=36-6$

$5t=30$

$t=30/5$

$t=6$ Put in equation (3)

$s=6+3$

$s=9$ An...

NCERT Class 10th solution of Exercise 3.1 NCERT Class 10th solution of Exercise 3.3 NCERT Class 10th solution of Exercise 3.4 NCERT Class 10th solution of Exercise 3.5 NCERT Class 10th solution of Exercise 3.6 NCERT Class 10th Maths Projects Exercise 3.2 Q1. From the pair of linear equations in the following problems, and find their solutions graphically. i)

$10$ students of Class

$X$ took part in a Mathematics quiz. If the number of girls is

$4$ more than the number of boys, find the number of boys and girls who took part in the quiz. ii)

$5$ pencils and

$7$ pens together cost

$₹50$ , whereas

$7$ pencils and

$5$ pens together cost

$₹46$ . Find the cost of one pencil and that one pen. Sol. : i) Let the number of boys in Mathematical qize are

$x$ , and the number of girls in Mathematical qize are

$y$ According to question

$x+y=10$ ______(1) and

$y=x+4$ _______(2) from equation (1) when

$x=4$

$4+y=10$

$y=10-4$

$y=6$ when

$x=6$

$6+y=10$

$y=10-6$

$y=4$ from equation (2) when

$x=0$

$y=0+4$

$y=4$ ...

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10th Maths 4.2

10th Maths 4.1

10th Maths 3.6

10th Maths 3.5

10th Maths 3.4

10th Maths 3.3

10th Maths 3.2