SAT (Stage-1) Mock Test

Result

SAT (Stage-1) Mock Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

If the sum of the first 5 terms of an AP is 160 and its first term is 6, find the common difference.

A
11

B
12

C
13

D
16

Solution

Here, a = 6, n = 5 and S_n = 160
Therefore, 160 = 5/2[2×6+(5 - 1)d]
160×2/5 = 12 + 4d
64 – 12 = 4d
52/4 = d
d = 13
Question 2
1 / -0

The probability that a leap year selected at random will contain 53 Sundays is

A
1/7

B
2/7

C
7/366

D
26/183

Solution

A leap year has 366 days.
366/7 = 52, remainder = 2
⇒ There are 52 weeks.
⇒ 52 Sundays, 2 days extra;
For 53 Sundays, either one of these should be a Sunday.
So, P (53 Sundays) = P (1^st day is Sunday) + P (2^nd day is Sunday)
= (1/7) + (1/7) = 2/7
Question 3
1 / -0

If α, β are the roots of the equation 2x² - 7x + 5 = 0, then α³ + β³is equal to

A
273/8

B
7

C
133/8

D
None of these

Solution

α + β = 7/2, αβ = 5/2 (Sum and Product of roots)
So, α² + β² = (α + β)² - 2αβ = (7/2)² -2 x 5/2
= 49/4 - 5 = 29/4
α³+ β³= (α + β) (α² + β² - αβ)
= 7/2×(29/4 –5/2)
= 133/8
Question 4
1 / -0

Work efficiency of two persons is in the ratio 2 : 3. Work assigned to them is in the ratio 4 : 5. Find the ratio of the time taken by them, if they start at the same time.

A
4 : 5

B
6 : 5

C
5 : 6

D
2 : 3

Solution

According to the given condition,
Let work efficiency of A be 2x and that of B be 3x.
Work done by A is 4y and that by B be 5y.
Ratio of time taken by them is:
4y/2x : 5y/3x = 2 : 5/3 = 6 : 5