UPSEE Solved Model Paper 1

Let two numbers are x any y then x, a, b,c,y are in A.P.
Let common difference of this A.P. = d
Then we can take
x = b-2d
a = b-d
b = b
y = b + 2d
now, a + b + c = 15
⇒ (b-d) + b + (b + d) = 15
⇒ b = 5
x + y = (b - 2d) + (b + 2d)
x + y = 2b
x+ y = 10 ......(i)
Now, x, p, q, r, y are in H.P.
Then

1

x

,

1

p

,

1

q

,

1

r

,

1

y

will be in A.P.
Let common difference of this A.P. = d'
Then we can take

1

x

=

1

q

−2d′

1

p

=

1

q

−d′

1

q

=

1

q

1

r

=

1

q

+d′

1

y

=

1

q

+2d′
Now,

1

p

+

1

q

+

1

r

=

5

3

⇒

3

q

=

5

3

⇒

1

q

=

5

9

and

1

x

+

1

y

=

2

q

and

1

x

+

1

y

=

10

9

x+y

xy

=

10

9

⇒

10

xy

=

10

9

(x+y=10)
xy = 9 ... (ii)
x - y = √(x2+y2)−4xy
= √(10)2−4.9
𝑥 − 𝑦 = 8 . . . . . . (𝑖𝑖𝑖)
from (i) and (iii)
x = 9
y = 1