CSIR NET 2017 Mathematical Science Question Paper (17-Dec-2017)

Question 1

A boy holds one end of a rope of length $l$ and the other end is fixed to a thin pole of radius $r$ ($r \ll l$). Keeping the rope taut, the boy goes around the pole causing the rope to get wound around the pole. Each round takes $10	ext{ s}$. What is the speed (in units of $	ext{s}^{-1}$) with which the boy approaches the pole?

Accepted Answer

$\frac{\pi r}{5}$

Answer

$\frac{\pi l}{5}$

Answer

$2\pi(r + l)$

Answer

$\frac{2\pi(l - r)}{5}$

Question 2

The smallest square floor which can be completely paved with tiles of size $8 	imes 6$, without breaking any tile, needs $n$ tiles. Find $n$.

Accepted Answer

$12$

Answer

$56$

Answer

$24$

Answer

$48$

Question 3

A $2	ext{ m}$ long ladder is to reach a wall of height $1.75	ext{ m}$. The largest possible horizontal distance of the ladder from the wall could be

Accepted Answer

slightly less than $1	ext{ m}$

Answer

slightly more than $1	ext{ m}$

Answer

$1	ext{ m}$

Answer

$1.2	ext{ m}$

Question 4

A rectangular flask of length $11	ext{ cm}$, width $8	ext{ cm}$ and height $20	ext{ cm}$ has water filled up to height $5	ext{ cm}$. If $21$ spherical marbles of radius $1	ext{ cm}$ each are dropped in the flask, what would be the rise in water level?

Accepted Answer

$1	ext{ cm}$

Answer

$8.8	ext{ cm}$

Answer

$10	ext{ cm}$

Answer

$0	ext{ cm}$

Question 5

Contours in the bivariate (weight, height) graph connect regions of approximately equal popula-tions. Which of the following interpretations is correct?

Accepted Answer

Taller and lighter individuals are more in number than taller and heavier individuals

Answer

There is no correlation between height and weight of the population

Answer

Heavier individuals are likely to be taller than lighter individuals

Answer

There are no individuals of medium weight and medium height

CSIR NET 2017 Mathematical Science Question Paper (17-Dec-2017)

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