IIT JEE Mathematics Final Problem Revision Set 16

1. The value of λ for which the system of equations

x + y+ λz = 4
x - 2y + z +4 = 0
2x - y - z = 2 has no solution is

a. -3
b. 0
c. -2
d. 3

2. Let y(x) be a function of x satisfying the relation l0g (x+y)= 2xy, then y'(x) at x = 0 is equal to

a. 1/3
b. 0
c. 1
d. 2

3. If an area lying between the curves y = ax² and x = ay² is 1 square unit, then a is equal to

a. 1/2
b. 1/3
c. 1/√3
d. √3

4. the definite integral ∫ (0 to 1) √[(1-x)/(1+x)] is equal to

a. 1
b. π/2 + 1/2
c. π/2 - 1
d. π

5. A set contains (2n+1) elements. The number of subsets of the set which contain at the most n elements is

a. 2²ⁿ
b. 2ⁿ
c. 2^n-1
d. 2ⁿ⁺¹

Problems 1 to 4 are from JEE 2004