Mathematics - Online Test
Q1. All the terms in A.P., whose first term is a and common difference d are squared. A different series is thus formed. This series is a
Answer : Option B
Explaination / Solution:
the series obtained will not follow rules of AP, GP and HP
Q2. The two lines of regression are x + 4y = 3 and 3x +y = 15 . value of x for y = 3 is
Answer : Option D
Explaination / Solution:
we have x + 4y = 3 and 3x + y = 15 as the lines of regression of y on x and x on y respectively.
therfore, for y = 3 the required line is x on y
so put y= 3 in 3x + y = 15
we get, x = 4
Q3. Which of the following is not an equivalence relation on I, the set of integers ; x, y
Answer : Option B
Explaination / Solution:
f R is a relation defined by xRy:ifx⩽y, then R is reflexive and transitive .But , it is not symmetric. Hence , R is not an equivalence relation.
Q4. Projection (the foot of perpendicular) from ( x , y ) on the x – axis is
Answer : Option D
Explaination / Solution:
Let L be the foot of the perpendicular from the X axis. Therefore its y coocrdinate is zero
Therefore the coordiantes of the point L is (x,0)
Q5. Let p and q be two prepositions given by p : I take only bread and butter in breakfast. q : I do not take anything in breakfast. Then , the compound proposition “ I take only bread and butter in breakfast or I do not take anything “ is represented by
Answer : Option D
Explaination / Solution:
and is replaced by ∧
or is replaced by ∨
Q6. is equal to
Answer : Option B
Explaination / Solution:
Q7. If l, m and n are direction cosines of the position vector OP the coordinates of P are
Answer : Option A
Explaination / Solution:
If l , m and n are the direction cosines of vector denoted by , then , the coordinates of point P are given by : lr ,mr and nr respectively.
Q8. An instructor has a question bank consisting of 300 easy True / False questions,200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Answer : Option E
Explaination / Solution:
| True/False | MCQ |
Easy | 300 | 500
|
Difficult | 200 | 400 |
Total = 1400, therefore n(S) = 1400 Let A = event of getting easy question B = event of getting multiple choice question.
Q9. If then the value of is
Answer : Option B
Explaination / Solution:
Q10. is equal to
Answer : Option B
Explaination / Solution:
limx→π2[sinx]=0[sinceπ2−h≤x≤π2+h]
