Section A

Solution.1
(x - 3)(x + 3) = 2
x² - 9 = 2
x² - 11 = 0 (equation is quadratic).

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Solution.2

19/200

=

19/2³ x 5²

⇒ terminate after 3 places .

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Solution.3
6 =

5 +

a/7

/2

12 =

35 + a/7

84 - 35 = a ⇒ a = 49

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Solution.4
cot²θ - cosec²θ = 1

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Solution.5
S₁ = a
put n = 1
S₁ = 5

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Solution.6

0 =

2 - 2k/1 + k

2 - 2k = 0
k = 1
Thus (axis) x divides the line segment AB in the Ratio 1 : 1

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Section B

Solution.7
Product of two numbers = L.C.M x H.C.F
∴ HCF is x

LCM is 25x

900 = (25x) x (x)
900 = 25x²
x² = 36
x = 6
So, H.C.F = 6

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Solution.8
In A.P
A = 17
d = -3
l = -40
n^th term from the end = l - (n - 1)d
8^th term from the end = -40 - (8 - 1)(-3)

= - 40 - (7) (-3)

= - 40 + 21

= -19

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Solution.9
It is given that C divides the line segment joining A and B , in the ratio k:1 ,So Co-ordinates of P
are (

9k -1/k + 1

,

8k + 3/k + 1

)
Point P lies on the line x - y - 6 = 0

9k -1/k + 1

-

8k + 3/k + 1

- 6 = 0

9k - 1 - 8k - 3/k + 1

- 6 = 0

k - 4 + 4k - 6 = 0

5k - 10 = 0

k = 2

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Solution.10
The given equation are in the form

ax + by + c = 0

If the given equation have many solutions, then solutions, then equations will represent coincident lines .

condition for which

a₁/a₂

=

b₁/b₂

=

c₁/c₂

1/3

=

3/9

=

7/k

k = 21

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Solution.11
Let there are g green marbles and b blue marbles in the box. Then, total number of marbles in the box

g + b = 35

P(getting a blue marble from the box) =

b/35

b/35

=

3/5

⇒ b = 21



So, total green marbles are = 14

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Solution.12
There are 12 face card in a pack in which 6 are black and 6 are red . If all black face cards are lost

Number of cards left = 52-6 = 46

number of kings (of Red card) = 2

Probability of drawing a king =

2/46

=

1/23

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