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IIT JEE 2008
Paper I


Formats Worksheet / Test Paper Quiz Review
: Multiple choice

Your Performance  

1.

1. Consider the two curves

C1 : y2 = 4 x

C2 : x2 + y2 − 6x + 1 = 0

Then,

  C1 and C2 touch each other only at one point

  C1 and C2 touch each other exactly at two points

  C1 and C2 intersect (but do not touch) at exactly two points

  C1 and C2 neither intersect nor touch each other

  Half-n-half Clue
 

2.

2. If 0 < x < 1, then
√(1 + x2 ) [ {x cos (cot−1 x) + sin (cot−1 x)}2 −1 ]1/2 =

 
x

√(1 + x2)

  x

  x√(1 + x2)

  √(1 + x2)

  Half-n-half Clue
 

3.

3. The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a^, b^, c^such that
a^b^ = b^c^ = c^a^ =
1

2
.
Then, the volume of the parallelopiped is

 
√3

2

 
1

√2

 
1

2√2

 
1

√3

  Half-n-half Clue
 

4.

4. Let a and b be non-zero real numbers. Then, the equation

(a x2 + b y2 + c) (x2 − 5 x y + 6 y2) = 0


represents

  four straight lines, when c = 0 and a, b are of the same sign

  two straight lines and a circle, when a = b, and c is of sign opposite to that of a

  two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a

  a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a

  Half-n-half Clue
 

5.

5. Let
g (x) = (x − 1)n

log cosm (x − 1)
;
0 < x < 2, m and n are integers, m ≠ 0, n > 0, and let p be the left hand derivative of |x − 1| at x = 1.
If
lim
x→1+
g(x) = p

then

  n = 1, m = 1

  n = 1, m = −1

  n = 2, m = 2

  n > 2, m = n

  Half-n-half Clue
 

6.

6. The total number of local maxima and local minima of the function
f (x) = { (2 + x)3 , −3 < x ≤ −1
x2/3 ,
−1 < x < 2
is

  0

  1

  2

  3

  Half-n-half Clue
 

7.

7. A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T . If S is not the centre of the circumcircle, then

 
1

PS
+ 1

ST
< 2

(QS × SR)

 
1

PS
+ 1

ST
> 2

(QS × SR)

 
1

PS
+ 1

ST
< 4

QR

 
1

PS
+ 1

ST
> 4

QR

 
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