# WBJEE 2014 Solved Mathematics Question Paper Part-8

Mar 24, 2017 18:31 IST

Find WBJEE 2015 Solved Mathematics Question Paper – Part 8 in this article. This paper consists of 5 questions (#36 to #40) 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.

36. Let f(x) = x + 1/2, then the number of real values of x for which the three unequal terms f(x), f(2x), f(4x) are in H.P. is

(A) 1

(B) 0

(C) 3

(D) 2

Ans: (A)

Sol.

37. The function f(x)= x2 + bx + c, where b and c real constants, describes

(A) one-to-one mapping

(B) onto mapping

(C) not one-to-one but onto mapping

(D) neither one-to-one nor onto mapping

Ans: (D)

Sol.

Upward parabola f(x) has a minimum value. So, it is not onto, also symmetric about its axis which is a straight line parallel to y-axis, so it is not one-to-one.

38. Suppose that the equation f(x) = x2+bx+c = 0 has two distinct real roots α and β. The angle between the tangent to the curve y = f(x) at the point , ((α + β)/2, f((α + β)/2))and the positive direction of the x-axis is

(A) 0°

(B) 30°

(C) 60°

(D) 90°

Ans: (A)

Sol.

As α and β are the roots of the equation f(x) = x2+bx+c = 0. So, it represents upward parabola which cuts x-axis at α and β. As the graph is symmetric, so, tangent at  ((α + β)/2, f((α + β)/2)) parallel to x-axis.

Hence the angle between the tangent to the curve at the given point and positive direction of x axis is 0o.

Ans: (C)

Sol.

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