MATHS SECTION – I Single Correct Choice Type Q.1 to Q.7 has four choices (A), (B), (C), (D) out of which only one is correct and carry 3 marks each. There is NEGATIVE marking. 1 mark will be deducted for each wrong answer.
1. Any circle through the point of intersection of the lines x + 3 y = 1 and 3 x − y = 2 if intersects these lines at points P and Q, then the angle subtended by the arc PQ at its centre is (a) 180 o (b) 90 o (c) 120 o (d) Depends on centre and radius 2. If the chord y = mx + 1 of the circle x 2 + y 2 = 1 subtends an angle of measure 45 o at the major segment of the circle then value of m is (a) 2 (b) – 2 (c) – 1 (d) None of these 2 3. The equation of the common tangent of the parabolas x = 108 y and y 2 = 32 x , is (c) 3 x + 2y = 36 (b) 2 x + 3y + 36 = 0 (d) 3 x + 2y + 36 = 0 (a) 2 x + 3y = 36 4. The equation of parabola whose focus is (5, 3) and directrix is 3 x − 4 y + 1 = 0 , is (a) (4 x + 3y) 2 − 256 x − 142 y + 849 = 0 (b) (4 x − 3y) 2 − 256 x − 142 y + 849 = 0 (c) (3 x + 4 y) 2 − 142 x − 256 y + 849 = 0 (d) (3 x − 4 y) 2 − 256 x − 142 y + 849 = 0 5.
6.
lim
3x − a − x + a = x−a
(a)
2a
x →a
lim
y →0
(b)
1 / 2a
(c)
2a
(d)
1 / 2a
x tan x + sec x
(c)
x sec x + tan x
(d)
None of these
(b)
lim𝑥→∞ 𝑓(𝑥) = 2
(x + y) sec( x + y) − x sec x = y
(a) sec x(x tan x + 1) (b) 7. (a) (c)
f (x) = (𝑥/2 + 𝑥)2 , then
lim𝑥→∞ 𝑓(𝑥) = −4
lim𝑥→∞ 𝑓(𝑥) = 𝑒 −4
(d)
lim𝑥→∞ 𝑓(𝑥) =
1 9
SECTION – III Comprehension Type Q.8 to Q.10 are based upon a paragraph. Each question has four choices (A), (B), (C), (D) out of which only one is correct and carry 5 marks each. There is NEGATIVE marking. 1 mark will be deducted for each wrong answer.
Consider the circle S : x 2 + 8.
9.
and the line L : y = 3x – 1. If the line L cuts circle at A and B then
Length of the chord AB equals 2 (a) (b) √5 √5 5 (c) (d) √2 √10 The angle subtended by the chord AB in the minor arc of S is (a) (c)
10.
y2 − 4x − 1 = 0
3𝜋 4 2𝜋 3
(b) (d)
5𝜋 6 𝜋 4
Acute angle between line L and the circle S is 𝜋 𝜋 (a) (b) (c)
