WBJEE - Mathematics (Category - 2) Model Test
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Question 1 |
Let nPr - 1 ⁄ a = nPr ⁄ b = nPr + 1 ⁄ c , then which of the following hold good
A | c2 = a (b + c) |
B | a2 = c (a + b) |
C | b2 = a (b + c) |
D | (1 / a + 1 / b + 1 / c) = 1 |
Question 2 |
The area bounded by y = tan(x), y = cot(x) and x-axis in 0 ≤ x ≤ π/2
A | 3loge2 |
B | loge2 |
C | 2loge2 |
D | 5loge2 |
Question 3 |
The ratio of the greatest value of 2 – cosx + sin2x to its least value is
A | 5/4
|
B | 9 / 4 |
C | 13 / 4 |
D | 15 / 4 |
Question 4 |
If the normal at the point “t1” on the curve xy = c2 meets the curve again at “t2”, then
A | (t1)3t2 = 1 |
B | (t1)3t2 = -1 |
C | (t2)3t1 = -1 |
D | (t2)3t1 = 1 |
Question 5 |
Let f (x) = (ex + 1)/ (ex + 1) and ∫10 x (ex + 1⁄ex - 1) dx = λ , then ∫1-1 t f (t) dt equals
A | 0 |
B | 2λ |
C | λ |
D | 3λ |
Question 6 |
If y = 4x – 5 is tangent to the curve y2 = px3 + q at (2,3), then
A | p = 2, q = -7
|
B | p = -2, q = 7 |
C | p = -2, q = -7 |
D | p = 2, q = 7 |
Question 7 |
The positive value of λ for which the lines y – 2x – 6 = 0, 3y + x – 4 = 0, λy + 4x + λ2 = 0 are concurrent is
A | λ = 2 |
B | λ = 3 |
C | λ = 4 |
D | λ = 5 |
Question 8 |
If x = (1 + i) / 2 (where i = √-1 ), then the expression 2x4 – 2x2 + x + 3 equals
A | 3 + i/2 |
B | 3 – i/2 |
C | (3 + i)/2 |
D | (3 – i)/2 |
Question 9 |
If f (x) + f (y) = f (x + y) and ∫30 f (x) dx = λ then ∫3-3 f (x) dx =
A | -2λ |
B | 2λ |
C | 0 |
D | ½ |
Question 10 |
Let f (2) = 4 and f ’ (2) = 2. Then limx→ 2 ( x f (2) - 2f (x) ⁄ (x-2) ) is equal to
A | -8 |
B | 4 |
C | 0 |
D | -4 |
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