Practice Test - Mathematics 14 for JEE & BITSAT Exams

Question 1

The line L₁ : y - x = 0 and L₂ : 2x + y = 0 intersect the line L₃ : y + 2 = 0 at P and Q respectively. The bisector of the acute angle between L₁ and L₂ intersects L₃ at R.
Statement-1: The ratio PR : RQ equals 2

Statement-2: In any triangle bisector of an angle divides the triangle into two similar triangles.

Question 2

If the mean deviation about the median of the numbers a, 2a, ... , 50a is 50, then |a| equals

Question 3

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after.

Question 4

A person is to count 4500 currency notes. Let a_n denote the number of notes he counts in the nth minute. If a₁ = a₂ = ... = a₁₀ = 150 and a₁₀, a₁₁, ... are in an AP with the common difference –2, then the time taken by him to count all notes is

Question 5

Consider 5 independent Bernoulli's trails each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32, then p lies in the interval.

Question 6

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

Question 7

Let A =

, a, b ∈N. Then

Question 8

Consider the following statements
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest
The negation of the statement Suman is brilliant and dishonest if and only if Suman is rich can be expressed as

Question 9

Directions: Assertion–Reason type questions. Each of these questions contains two statements: statement–1 (Assertion) and Statement–2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number". and r be the statement "x is a rational number iff y is a transcendental number".
Statement–1: r is equivalent to either q or p.
Statement–2: r is equivalent to ~ (p ↔ ~q).

Question 10

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