number systems Model Questions & Answers, Practice Test for ssc mts paper 1

Answer: (a)

When a ball is dropped from a height = 36 m

$1^{st}$ bounce back = $2/3$ × 36 = 24 m

$2^{nd}$ bounce back = $2/3$ × 24 = 16 m

$3^{rd}$ bounce back $2/3 × 16 = 32/3 = 10{2}/3$ m.

Answer: (a)

∵ 7056 = $2^4 × 3^2 × 7^2$

∴ Number of factors/divisors of 7056

Product of factors = $(7056)^{45/2} = (84)^{45}$

Hence (c) is the correct option.

Answer: (b)

Total numbers between 6000 to 6999 = 1000.

Now, when all the digits are different, then thousands place is always to be filled by 6, next place by any of the remaining 9 digits and the remaining two places by any of the 8 and 7 digits respectively.

So, total no. of numbers, when all digits are different = 9 × 8 × 7 = 504.

Hence, total no. of numbers, where all digits are same total numbers — numbers where digits are different = 1000 – 504 = 496

Answer: (d)

Number of pieces = $455.8/{8.6}$ = 53

Answer: (b)

Units digit in $(7^4) = 1$. Therefore, units digit in $(7^4)^8$

i..e. $7^{32}$ will be 1. Hence, units digit in

$(7)^{35} = 1 × 7 × 7 × 7 = 3$

Again, units digit in $(3)^4 = 1$

Therefore, units digit in the expansion of

$(3^4)^{17} = (3)^{68} = 1$

⇒ Units digit in the expansion of

$(3^71) = 1 × 3 × 3 × 3 = 7$

and units digit in the expansion of $(11^{35}) = 1$

Hence, units digit in the expansion of

$7^{35} × 3^{71} × 11^{55} = 3 × 7 × 1 = 1$