Mathematics Test 167

Result

Mathematics Test 167

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Question 1
4 / -1

or the following relation

R = {(0, 0), (0, 1), (1, 1), (2, 1), (2, 2), (2, 0), (1, 0), (0, 2), (0, 1)}

A
domain = {0, 1}

B
range = {0, 1, 2}

C
both correct

D
None of these

Solution

We have domain of R = the set of first components of the ordered pairs in R = {0, 0, 1, 2, 2, 2, 1, 0, 0} = {0, 1, 2} range of R = the set of second components of the ordered pairs in R

= {0, 1, 1, 1, 2, 0, 0, 2, 1} = {0, 1, 2}
Question 2
4 / -1

A

B

C

D

Solution
Question 3
4 / -1

Let Then the smallest positive integer for which P(n) is true is

A
1

B
2

C
3

D
4

Solution
Question 4
4 / -1

A
1

B
2

C
3

D
4

Solution
Question 5
4 / -1

A

B

C

D

Solution
Question 6
4 / -1

If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fiftieth word is

A
NAAGI

B
NAGAI

C
NAAIG

D
NAIAG

Solution

Starting with the letter A, and arranging the other four letters, there are 4! = 24 words. These are the first 24 words. Then starting with G, and arranging A, A, I, and N in different ways, there are
Question 7
4 / -1

A
x = y

B
x < y

C
x > y

D
None of these

Solution
Question 8
4 / -1

A
(i) and (ii) both correct

B
(i) and (ii) both incorrect

C
(i) correct (ii) incorrect

D
(i) incorrect (ii) correct

Solution
Question 9
4 / -1

If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square, then the equation of second diagonal is

A
x + 3y = 21

B
2x – 3y = 7

C
x + 7y = 31

D
2x + 3y = 21

Solution
Question 10
4 / -1

If from any point P, tangents PT, PT' are drawn to two given circles with centres A and B respectively; and if PN is the perpendicular from P on their radical axis, then

A
PN. AB

B
2PN. AB

C
4PN. AB

D
None of these

Solution