JEE MAIN

1. If f (x, y) is a polynomial of degree 3 such that
   f (0, 0) = f (±1, 0) = f (0, ± 1) = f (2, 2) = 0, then
   f (a, b) = 0 for a + b =

(a)

21

20 (b)

19

21 (c)

21

19

(d)

20

21

2. The inradius of a right angled triangle with integer
   sides is 2011. The number of such triangles is
   (a) 2 (b) 3 (c) 5 (d) 7


3. The radius of the largest circle with centre ⎜⎝⎛ 21 ,^0 ⎞⎠⎟

inscribed in the ellipse x^2 + 2y^2 = 2 is

(a)

1

2 (b) 1 (c)

3

2 (d)

1

2

4. In triangle ABC, C=π
   2

, D and E are points on the

side AC such that AD = 11, DE = 5.

If CAB : CDB : CEB = 1 : 2 : 3, then BC =

(a) 8 (b) 9 (c)

44

5 (d)

15

2

5. The normal to the curve 2y + 5x^5 – 10x^3 + x + 6 = 0
   at the point (0, –3) is a tangent to the curve at the
   point
   (a) (2, –44) (b) (–2, 38)
   (c) (1, –1) (d) (–1, –4)
   JEE ADVANCED


6. If

N

(^114) r rr
1
2 15
7
!! !( )!

∑= − , then 5 N is divisible by
(a) 2 (b) 3 (c) 11 (d) 31
COMPREHENSION
Consider 5-digit numbers formed using the digits 0, 1,
2, 3, 4, 5 without repetition of digits.

7. The number of numbers divisible by 4 is
   (a) 48 (b) 54 (c) 66 (d) 144
   8. The number of numbers divisible by 12 is
   (a) 54 (b) 66 (c) 108 (d) 144
   INTEGER MATCH
   9. If y = f (x) is the orthogonal trajectory of the circles

(x – c)^2 + y^2 = 1, x ≥ 0, f (0) = 1 and fx()=

3

2 ,

then e^2 x + 1 is

MATRIX MATCH

10. Match the following columns.
    Column I Column II

(P) tdt

t

dt

e tt

x

e

x

1 11 +^212

+

+

∫∫=

/

tan

/

cot

()

(1)^1

4

(Q) dx

( sinxxcos )

/

+

∫ 4 =

0

π 2

(2)

1

3

(R) I x

x

1 dx

1

0

1

=

−

∫

tan and

I x

x

dx I

(^20) I
2
1
2
= ∫
sin
,
π/

(3)
1
2
(S) Iffx and
t
t
dt
x
()= ln
1 ∫^1 +
F(x) = f(x) + f^1
x
⎛
⎝⎜
⎞
⎠⎟,then F(e) =
(4) 1
(5) 2
P Q R S
(a) 4 2 1 5
(b) 4 2 3 3
(c) 3 4 2 3
(d) 5 1 2 4
See Solution Set of Maths Musing 165 on page no. 84
M
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