- If the circles x^2 + y^2 – 4rx – 2ry + 4r^2 = 0 and
x^2 + y^2 = 25 touch each other, then r satisfies
(a) 4r^2 + 10r ± 25 = 0
(b) 5r^2 + 10r ± 16 = 0
(c) 4r^2 ± 10r + 25 = 0
(d) 4r^2 ± 10r – 25 = 0
- If the points (0, 0), (1, 0), (0, –1) and (λ, 3λ) are
concyclic, then λ is
(a) 5 (b) 1/5 (c) –5 (d) –1/5
- The shortest distance of the point (9, –12) from the
circle x^2 + y^2 = 16, is
(a) 7 units (b) 11 units
(c) 15 units (d) 4 units
- One extremity of a diameter of the circle
x^2 + y^2 – 8x – 4y + 15 = 0 is (2, 1), the other extremity
is
(a) (0, 0) (b) (6, 3)
(c) (4, 2) (d) (–3, –6)
- The triangle PQR is inscribed in the circle
x^2 + y^2 = 25. If Q and R have coordinates (3, 4) and
(–4, 3) respectively, then ∠QPR is equal to
(a) π/2 (b) π/3 (c) π/4 (d) π/6
- The equation of a circle which passes through the
point (h, k) and touches the y-axis at origin, is
(a) h^2 (x^2 + y^2 ) = (h^2 + k^2 )x
(b) h^2 (x^2 + y^2 ) = (h^2 + k^2 )y
(c) k^2 (x^2 + y^2 ) = (h^2 + k^2 )x
(d) k^2 (x^2 + y^2 ) = (h^2 + k^2 )y
- If ax^2 + (2a – 3)y^2 – 6x + ay – 3 = 0 represents a
circle, then its radius is
(a) 1 (b) 6 (c) 1/2 (d) 3/2
- Locus of a point which divides chord at a distance
1 unit from the centre of the circle x^2 + y^2 = 1 in the
ratio 2 : 1 is
(a) x^2 + y^2 = 2 (b) x^2 + y^2 = 4
(c) x^2 + y^2 = 8 (d) x^2 + y^2 = 16
CATEGORY-II
Every correct answer will yield 2 marks. For incorrect response,
25% of full mark (1/2) would be deducted. If candidate marks
more than one answer, negative marking will be done.
- If intercept on the line y = x by the circle
x^2 + y^2 – 2x = 0 is AB, then equation of the circle
with AB as diameter is
(a) x^2 + y^2 + x + y = 0
(b) x^2 + y^2 – x + y = 0
(c) x^2 + y^2 – x – y = 0
(d) x^2 + y^2 + x – y = 0
32. The equation of the circle described on the chord
3 x + y + 5 = 0 of the circle x^2 + y^2 = 16 as diameter
is
(a) x^2 + y^2 + 3x + y + 11 = 0
(b) x^2 + y^2 – 3x – y – 11 = 0
(c) x^2 + y^2 + 3x + y – 11 = 0
(d) x^2 + y^2 + 3x – y – 11 = 0
33. In a triangle ABC, if a
cos^22 C ccos Ab,
22
3
2
+= then
the sides a, b, c
(a) satisfy a + b = c (b) are in A.P.
(c) are in G.P. (d) are in H.P.
- The number of integral values of k for which the
equation 3cosx + 4sinx = 2k + 1 has a solution, is
(a) 3 (b) 6 (c) 4 (d) 5
- The number of ways in which the letters of the word
‘COMBINE’ can be arranged so that the word begin
and end with a vowel, is
(a) 30 (b) 504 (c) 360 (d) 720
CATEGORY-III
In this section more than 1 answer can be correct. Candidates
will have to mark all the correct answers, for which 2 marks
will be awarded. If candidate marks one correct and one
incorrect answer then no marks will be awarded. But if,
candidate makes only correct, without making any incorrect,
formula below will be used to allot marks.
2×(no. of correct response/total no. of correct options)
- If nC 4 , nC 5 and nC 6 are in A.P., then n is
(a) 8 (b) 9 (c) 14 (d) 7
- If 0 ≤ x ≤ 2 π and |cosx| ≤ sinx, then
(a) the set of values of x is ππ
42
⎡ ,
⎣⎢
⎤
⎦⎥
(b) the number of solutions that are integral
multiples of π/4 is three
(c) the sum of the largest and the smallest solution
is 3π/4
(d) x∈⎡
⎣⎢
⎤
⎦⎥
∪⎡
⎣⎢
⎤
⎦⎥
ππ π π
42 2
3
4
,,
- In a ΔABC, tanA and tanB are the roots of the
equation ab(x^2 + 1) = c^2 x, where a, b and c are the
sides of the triangle. Then
(a) tan(AB)
ab
ab
− = −
22
2
(b) cotC = 0
(c) sin^2 A + sin^2 B = 1
(d) none of these
