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# WBJEE 2014 Solved Mathematics Question Paper – Part 11

Mar 31, 2017 18:45 IST

Find WBJEE 2014 Solved Mathematics Question Paper – Part 11 in this article. This paper consists of 5 questions (#51 to #55) from WBJEE 2014 Mathematics paper. Detailed solution of these questions has been provided so that students can match their solutions.

Importance of Previous Years’ Paper:

Previous years’ question papers help aspirants in understanding exam pattern, question format, important topics and assessing preparation. It has also been seen that sometimes questions are repeated in WBJEE Exam. So, this paper will certainly boost your confidence.

WBJEE is a common entrance examinations held at state level for admission to the undergraduate level engineering and medical courses in the state of West Bengal. The Mathematics section of WBJEE 2014 engineering entrance exam consists of 80 questions.

52. The straight lines x + y = 0, 5x + y = 4 and x + 5y = 4 form

(A) an isosceles triangle

(B) an equilateral triangle

(C) a scalene tri ngle

(D) a right angled triangle

Ans: (A)

Sol:

Their point of intersection are (–1, 1) (1, –1) and (2/3, 2/3)

Using distance formula the distance between AB and BC is same so, ABC is isosceles triangle.

(x – α) should be somewhere positive and somewhere negative so α ∈ (0, 2)

Hence, a ∈ (0, 2)

55. The function f(x) = a sin|x| + be|x| is differentiable at x = 0 when

(A) 3a + b = 0

(B) 3a – b = 0

(C) a + b = 0

(D) a – b = 0

Ans : (C)

Sol: x

f(x) = a sin|x| + be|x|

f(x) = a sinx + bex       x ≥ 0                 …(1)

Also,

f(x) = –a sinx + be–x    x < 0             …(2)

Differentiating equation (1) with respect to x

f′(x) = acosx + bex       x ≥ 0          …(3)

Differentiating equation (2) with respect to x

f′(x) = –acosx – be–x                x < 0             …(4)

From (3) and (4) at x = 0,

a + b = –a – b

a + b = 0

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