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Question Paper Class IX
Mathematics Set 3
Page 2

 

Ques 7. In the following figure, determine the values of a, b, and c.

Ans:
Ðb = 70° [vertically opposite angles]
Ðb + Ða = 180° (Linear pair)
70o + Ða = 180°
Ða = 180° - 70° = 110
Ðc = 70° [Pair of corresponding angles]
\ Ða = 110°
Ðb = 70°
Ðc = 70°

Ques 8. If f(x) = 2x-3/x-2, then find f(1/2)

Ans:

Putting the value of x = 1/2 in the (1)

Ques 9. Factorize x2 + 14x +45
Ans:
= x2 + 5x + 9x + 45
= x (x+5) +9 (x+5)
= (x+5) (x+9)

Ques 10. If (x-a) is factor of polynomial x6-ax5+x4-ax3+3x-a+2 then find a
Ans:
A = 10 Let p(x)=x6-ax5+x4-ax3+3x-a+2 -(1)
Because (x-a) is its factor
\ P(a) = 0
Put x=a in (1)
P(a) = a6-a+a4-a(a)3+3(a)-a+2
a6-a6+a4-a4+3a-a+2
= 2a+2
But P(a) = 0
\ 2a +2 = 0
\2a = -2
a = -2/2 = -1

Ques 11. Divide polynomial (p(x) = 5x2+3x+1 by g(x) = 2x

Ans:
P(x) = 5x2 + 3x + 1, g(x) = 2x

Quotient = g(x) = 5/2x + 3/2
Remainder = 1
Remainder ¹ 1. So g(x) is not factor of P(x)


Ques 12. Multiply (i) (3x-4) (x+5)
(ii) (x-2) (2x+3)
Ans:
(i) 3x2 + 15x - 4x - 20
= 3x2 + 11x - 20
(ii) 2x2 + 3x - 4x - 6
= 2x2 - x -6

Ques 13. Simplify Öx-2 y3
Ans:
Öx-2 y3 = (x-2 y3)1/2
= (x-2)1/2 x (y3)1/2
= x-2x1/2 x y3x1/2
= x-1 x y3/2
= y3/2/x

Ques 14. If a and b are tow real numbers then prove that a+b, a-b, ab are real.
If b ¹ 0 then prove that a/b is a rational number.
Ans:
Let a = 2/5 and b = 1/2 be two rational numbers
\ a+b = 2/5 + 1/3 = 6+5/15 = 11/15
11/15 is also a rational number
Þ a+b is a rational number.
now a-b = 2/5 - 1/3 = 6-5/15 = 1/15 which is a rational number
\ a-b is a rational number.
Also
axb = 2/5 x 1/3 = 2/15 is a rational number
\ab is also a rational number.

Ques 15. Find the value of 0.565656 ............
Ans:
Let x = 0.565656 = 0.56 -(1)
Multiply equation (i) by 100 x =56.5656.... = 56.56 -(2)
Substract equation (1) from equation (2) we get
100 - x = 56 - 0.56
99x = 56
\ x = 56/99


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