NY Regents Exam   Teasers   IQ Tests   Chemistry   Biology   GK   C++   Recipes   Search <  a href="/cgi/members/home.cgi" class="toplink">Members   Sign off

IIT JEE 2008 Paper II

 Formats Worksheet / Test Paper Quiz Review
: Multiple choice

1.

1. A particle P starts from the point z0 = 1 + 2i, where i = √–1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1. From z1 the particle moves √2 units in the direction of the vector i^+ j^and then it moves through an angle π /2 in anticlockwise direction on a circle with centre at origin, to reach a point z2. The point z2 is given by
 6 + 7i – 7 + 6i 7 + 6i – 6 + 7i

Half-n-half Clue

2.

2.
 Let the function g : (− ∞, ∞) → (− π 2 , π 2 ) be given by g(u) = 2 tan−1 (eu) − π 2 . Then, g is
 even and is strictly increasing in (0, ∞) odd and is strictly decreasing in (– ∞, ∞) odd and is strictly increasing in (– ∞, ∞) neither even nor odd, but is strictly increasing in (– ∞, ∞)

Half-n-half Clue

3.

3. Consider a branch of the hyperbola

x2 – 2 y2 – 2 √2 x – 4 √2 y – 6 = 0

with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is

 1 – √ 2 3

 √ 3 2 − 1

 1 + √ 2 3

 √ 3 2 + 1

Half-n-half Clue

4.

4. The area of the region between the curves
 y = √ 1 + sin x cos x
and
 y = √ 1 − sin x cos x
bounded by the lines x = 0 and x = π /4 is

 √2 − 1 ∫ 0 t (1 + t2) √(1 − t2) dt

 √2 − 1 ∫ 0 4t (1 + t2) √(1 − t2) dt

 √2 + 1 ∫ 0 4t (1 + t2) √(1 − t2) dt

 √2 + 1 ∫ 0 t (1 + t2) √(1 − t2) dt

Half-n-half Clue

5.

5. Consider three points P = (– sin (βα), – cos β), Q = (cos (βα), sin β) and R = (cos (βα + θ), sin (βθ)), where 0 < α , β, θ < π /4. Then,
 P lies on the line segment RQ Q lies on the line segment PR R lies on the line segment QP P, Q, R are non-collinear

Half-n-half Clue

6.

6. An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is
 2, 4 or 8 3, 6 or 9 4 or 8 5 or 10

Half-n-half Clue

7.

7. Let two non-collinear unit vectors a^and b^ form an acute angle. A point P moves so that at any time t the position vector OP (where O is the origin) is given by a^cos t + b^sin t. When P is farthest from origin O, let M be the length of OP be the unit vector along OP. Then

 u^ = a^ − b^ | a^ − b^ | and M = ( 1+ 2a^. b^)1/2

 u^ = a^ − b^ | a^− b^ | and M = ( 1+a^. b ^)1/2

 u^ = a^ + b^ | a^+ b^ | and M = ( 1+ a^. b^)1/2

 u^ = a^ + b^ | a^+ b^ | and M = ( 1+ 2a^. b ^)1/2

Half-n-half Clue