Question

1. Prove that 5+3 is an irrational number , where is an irrational number.

2. Find the zeros of the polynomial f(x) =4

(or)

If α,β are the zeros of the polynomial f(x)= 6x2+x-2 , find the value of +



3. One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting (a) red card or spade (b) neither spade nor king.



SECTION - B

II. ANSWER THE FOLLOWING : 4X3=12

4. Solve ax+by = a - b; bx-ay= a+b

5. Determine whether the quadratic equation x2+5x+5=0 have real roots and if so, find the roots.

(or)

Solve for x : 1 -

−3 +5 6

6. The sum of 5th and 9th terms of an A.P is 72 and the sum of 7th and 12th terms is 97. Find the A.P.

7. The vertices of ABC are A(5,5) , B(1,5) and C( 9,1) . A line is drawn to intersect sides AB and AC at P and Q respectively, such that = = 3. Find the length of

4

the line segment PQ.

SECTION - C

III. ANSWER THE FOLLOWING : 3X4=12

8. Draw the graphs of the equations 2x+y = 6 and 2x-y+2=0. Shade the region bounded by these lines and x - axis. Find the area of the shaded region.

(or)

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and that by one boy alone to finish the work.

9. If the equation (1+m2)x2+2mcx+(c2-a2) = 0 has equal roots, prove that c2=a2(1+m2).

10. The ratio of the sum of m and n terms of an A.P is m2:n2. Show that the ratio of the mth and nth terms is (2m-1) : (2n-1).​

Answer 1

1 let us assum that 5-√3 is rational number so we can find two integers a , b. Where a and b are two co - primes number. So it arise contradiction due to our wrong assumption that 5 - √3 is rational number. Hence, 5 -√3 is irrational number.

2 The given polynomial f(x)

= 4√3 x^2 +5x - 2√3

= 4√3 x^2 + 8x - 3x - 2√3

= 4x(√3 x +2) - √3 (√3 x +2)

= (√3x+2)(4x-√3)

Hence the zeroes are -2/√3 and √3/4

3 3/26 and 6/13

4 ax+by=a-b

ax=a-b-by

x=a-b-by/a←

bx-ay=a+b

substituting

b(a-b-by/a)-ay=a+b

ab-b²-b²y/a-ay=a+b

ab-b²-b²y-a²y/a=a+b

ab-b²-(b²+a²)y=a²+ab

-(b²+a²)y=a²+ab-ab+b²

(b²+a²)y=-(a²+b²)

y=-(a²+b²)/a²+b²

y=-1←

substituting value of y

x=a-b-b(-1)/a

x=a-b+b/a

x=a/a

x=1

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