TCS NQT Questions on Geometry with Answers Quiz 1

1dm=0.1m
Thus 19m2.5dm=19.25 & 12m5dm=12.5m
Area of path with overlapping = (19.25m X 2m) + (12.50m X 2m) = 63.5 m^{2}
Since area of path is overlapped which is shaded in below figure. So, subtract 2m x 2m =4 m^{2}
Hence, the actual area of path = (63.5 m^{2} – 4 m^{2}) = 59.5 m^{2}(Answer)

 





Video solution:

We know, s = \frac{(a + b + c)}{2}
Here a=6cm, b=8cm, c=12cm
So, s = \frac{(6 + 8 + 12)}{2} = 13cm
Are of triangle = \sqrt {s(s-a)(s-b)(s-c)}
= \sqrt {13(13-6)(13-8)(13-12)}
= \sqrt{13\times 7\times 5\times 1}
=21.33 cm^{2}(Answer)
Note: Here s stands for semi perimeter.



Video Explanation:

Perimeter = 2(a + b) = 18 cm
i.e., a + b = 9 cm
Diagonal = a^{2} + b^{2} = (\sqrt{41})^{2}
i.e., a^{2} + b^{2} = 41
we know, (a + b)^{2} =a^{2} + b^{2} + 2ab
= >9^{2} = 41 + 2ab
= > \frac{(81 – 41)}{2} = ab
ab = 20cm^{2}(Answer)



Video Explanation:

Formula for rombus area is \frac{1}{2}\times diagonal 1 \times diagonal 2 = 40 cm^{2}

\frac{1}{2}\times 8 \times 10 = 40 cm^{2}



Video Explanation:

we know daigonal = side \sqrt{2}

Then side = 18 cm

Area of square = 18^{2} =324 cm square



Video Explanation:

Volume of a sphere = \frac{4}{3} \pi r^{3} --(1) ( here r =3cm)
Volume of circular plate of thickness 1 cm is = \pi \times r^{2} \times h -- (2)
( here h=1cm that is thickness )
Equating (1) and (2)
r=6cm



Video Explanation:

Number of diagonal in a polygon = \frac{n\times (n-3)}{2}, where n is number of sides

Thus, \frac{n\times (n-3)}{2}= 77

= > n^{2} – 3n = 154

= > n^{2} – 3n – 154 = 0

= > n^{2} -14n + 11n – 154 = 0

= > n(n-14) + 11(n-14) = 0

= > (n-14) (n+11) = 0

n = 14 & n = -11

Since, the side can’t be negative. So, n = -11 is rejected.

Hence the number of sides of the polygon is 14



Video Explanation:

Solution:

let a is side of square field then a^{2} =31684 meter square
a=178 m
perimeter= 4 x a = 712 m
5% more than perimeter = 712 + 5% of 712 = 712 + 35.6 = 747.6 m
Because we enclose four times so 4 x  747.6 = 2990.4 m



Video Explanation:

Volume of a hollow cylinder=\pi h(R^{2}-r^{2})
=\frac{22}{7}\times 21m\times (36-25)m^{2}

=66\times 11 m^{3}
= 726 m^{3}



Video Explanation:

Area of the path = (112 x 78) – (107  x 73) = 925 m^{2}



Video Explanation: