Find **WBJEE 2015 Solved Mathematics Question Paper – Part 8** in this article. This paper consists of 5 questions (#71 to #75) from WBJEE 2015 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.

**About WBJEE Exam**

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 WBJEE engineering entrance exam has two sections – Mathematics, Physics and Chemistry. The Mathematics section of WBJEE 2015 engineering entrance exam consists of 80 questions.

**71.** Which of the following is/are always false?

(A) A quadratic equation with rational coefficients has zero or two irrational roots

(B) A quadratic equation with real coefficients has zero or two non-real roots

(C) A quadratic equation with irrational coefficients has zero or two rational roots

(D) A quadratic equation with integer coefficients has zero or two irrational roots

**Ans : (C)**

**Sol.**

A quadratic equation with rational coefficient has zero, rational or irrational roots but the quadratic equation with irrational coefficient has only zero or irrational coefficient.

**72.** If the straight line (*a* – 1)*x* – *by* + 4 = 0 is normal to the hyperbola xy = 1 then which of the followings does not hold?

(A) *a* > 1, *b* > 0

(B) *a* > 1, *b* < 0

(C) *a* < 1, *b* < 0

(D) *a* < 1, *b* > 0

**Ans : (A, C)**

**Sol.**

We have the equation of hyperbola,

xy = 1

The slope of hyperbola is given by *dy*/*dx*

**WBJEE 2016 Solved Physics and Chemistry Question Paper**

**73.** Suppose a machine produces metal parts that contain some defective parts with probability 0.05. How many parts should be produced in order that probability of at least one part being defective is 1/2 or more? (Given log_{10}95 = 1.977and log_{10}2= 0.3)

(A) 11

(B) 12

(C) 15

(D) 14

**Ans: (A, B)**

**Sol.**

Probability of at least one part being defective= 1 – probability of no part defective

Probability of no part defective = 1 – 0.05 = 0.95

Let *n* be the required parts to be produced

**Sol.**