Mathematics - Online Test
Q1. is equal to
Answer : Option B
Explaination / Solution:
Q2. 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.
Q3. 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.
Q4. If then the value of is
Answer : Option B
Explaination / Solution:
Q5. is equal to
Answer : Option B
Explaination / Solution:
limx→π2[sinx]=0[sinceπ2−h≤x≤π2+h]
Q6. limx→01−cosxx2 is equal to
Answer : Option A
Explaination / Solution:
(UsingL’hospital Rule ).
Q7. is divisible by ( x - y ) for
Answer : Option A
Explaination / Solution:
Replacing n by 1,2,3... we get the expression with the factor ( x - y ).Hence it is divisible by ( x - y ).
Q8. Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is
Answer : Option A
Explaination / Solution:
circumcentre of a right angled triangle ABC right angled at A is as circumcentre of right angled triangle lies on the mid pont of the hypotenuse.
so mid point of BC=(,) i.e.(3,2)
Q9. The number of arrangements of n different things taken r at a time which include a particular thing is
Answer : Option D
Explaination / Solution:
The number of arrangements of n different things taken r at a time which include a particular thing is r n-1Pr-1 = rP(n-1,r-1)
Q10. The degree of the equationis
Answer : Option B
Explaination / Solution:
the power of the highest order derivative i.e . is 2.hence the degree 2
