Algebra Test

Result

Algebra Test - 1

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Question 1
1 / -0.25

A
± √2

B

C
± √3

D

Solution
Question 2
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Six years ago, Mohan was 3 times as old as Shyam. At present Mohan is 1.5 times as old as Shyam. Find the present age of Mohan.

A
12 years

B
11 years

C
60 years

D
48 years

Solution

Let the present age of Mohan be ‘x’ years and the present age of Shyam be ‘y’ years.

So (x – 6) = 3 × (y – 6)

⇒ x – 6 = 3y – 18
Question 3
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Find the value of ‘y’ in the folowing system of equations 2x + 4y = 6 and 3x + 15y = 25.

A
4/3

B
16/9

C
5/6

D
6/5

Solution
Question 4
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A
±7

B
±8

C
±9

D
±10

Solution
Question 5
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A
100

B
50

C
49

D
98

Solution
Question 6
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If (x – 5) is a factor of 2x² + 2px – 2p = 0, then the value of ‘p’ is:

A
–4

B

C
36/8

D
+ 4

Solution

If x – 5 is a factor of the given equation then 5 is the root of the equation (Remainder theorem).

So 2x² + 2px – 2p = 0
Question 7
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If x4 + 2x³ – 3x² + x – 1 is divided by x – 2, then the remainder is:

A
12

B
14

C
16

D
21

Solution

Putting x = 2 in the expression, we get
Question 8
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The sum of the series 101 + 104 + 107 + … + 161 is:

A
2300

B
2751

C
2851

D
2900

Solution

In the series 101 + 104 + … + 161

a = 101 and d = 3

a_n = a + (n – 1) d

161 = 101 + (n – 1)3

161 = 101 + 3n – 3

161 – 98 = 3n

3n = 63

n = 21
Question 9
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4 log 2 + log 6 = ?

A
log 22

B
log 96

C
log 3

D
log 10

Solution

4 log 2 + log 6 = log 2⁴ + log 6 [m log n = log n^m]

= log(16 × 6) = log 96 [log m + log n = log(m × n)]
Question 10
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log 5 + log 4 + log 30 – log 6 = ?

A
1

B
2

C
3

D
2.5

Solution

log 5 + log 4 + log 30 – log 6

log(5 × 4 × 30) – log 6 = log 600 – log 6

log 600/6 = log 100 = 2