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  c^{2} = a (b + c) 
B  a^{2} = c (a + b) 
C  b^{2} = a (b + c) 
D  (1 / a + 1 / b + 1 / c) = 1 
Question 2 
The area bounded by y = tan(x), y = cot(x) and xaxis in 0 ≤ x ≤ π/2
A  3log_{e}2 
B  log_{e}2 
C  2log_{e}2 
D  5log_{e}2 
Question 3 
If f (x) + f (y) = f (x + y) and ∫^{3}_{0} f (x) dx = λ then ∫^{3}_{3} f (x) dx =
A  2λ 
B  2λ 
C  0 
D  ½ 
Question 4 
Let f (2) = 4 and f ’ (2) = 2. Then lim_{x→ 2} (^{ x f (2)  2f (x) }⁄_{ (x2) }) is equal to
A  8 
B  4 
C  0 
D  4 
Question 5 
If the normal at the point “t_{1}” on the curve xy = c^{2} meets the curve again at “t_{2}”, then
A  (t_{1})^{3}t_{2} = 1 
B  (t_{1})^{3}t_{2} = 1 
C  (t_{2})^{3}t_{1} = 1 
D  (t_{2})^{3}t_{1} = 1 
Question 6 
Let f (x) = (e^{x} + 1)/ (e^{x} + 1) and ∫^{1}_{0} x (^{ex + 1}⁄_{ex  1}) dx = λ , then ∫^{1}_{1} t f (t) dt equals
A  0 
B  2λ 
C  λ 
D  3λ 
Question 7 
The positive value of λ for which the lines y – 2x – 6 = 0, 3y + x – 4 = 0, λy + 4x + λ^{2} = 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 2x^{4} – 2x^{2} + x + 3 equals
A  3 + i/2 
B  3 – i/2 
C  (3 + i)/2 
D  (3 – i)/2 
Question 9 
The ratio of the greatest value of 2 – cosx + sin^{2}x to its least value is
A  5/4

B  9 / 4 
C  13 / 4 
D  15 / 4 
Question 10 
If y = 4x – 5 is tangent to the curve y^{2} = px^{3} + 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 
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