SSC CGL 20201)What is the area of a sector of a circle of radius 14 cm and central angle 45 degree? take \(\pi = {22 \over 7} \)
77 sqcm
Area of Sector = \(x = \pi r^2 .{\theta \over 360 } = 77 cm^2\)
SSC CGL 20202)A wheel covers a distance of 1,100 cm in one round. The radius of the wheel is :
175 cm
A wheel covers a distance of 1,100 cm in one round so,
Perimeter of wheel = 1100 cm;
\(2\pi r\) = 1100;
r = \(550\times\frac{7}{22}\) = 175 cm;
Diameter = 2r = 2 175 = 350 cm
SSC CGL 20203)The perimeter of a square plot is the same as that of a rectangular plot with sides 35 m and 15 m. The side of the square plot is:
25 metre
The perimeter of a rectangular plot = 2(length + breadth) = 2(35 + 15) = 100 m;
The perimeter of a square plot = perimeter of a rectangular plot;
The perimeter of a square plot = 100 m;
100 = 4 side;
side = 100/4 = 25 m
SSC CGL 20204)What is the area of a triangle whose sides are 3 cm, 5 cm and 4 cm?
\(6\) \(cm^2\)
By triplet 3-4-5, the triangle will be right angle triangle so,
5 will be hypotenuse.
Area of triangle = \({1\over2}\times base\times height\) = \({1\over2}\times3\times4 = 6 \) \(cm^2\)
SSC CGL 20205)Find the area and circumference of a circle if the radius is 14 cm.(Take \(\pi= {22\over7}\))
Area = \(616 \)\(cm^2\); circumference = 88 cm
Radius of circle = 14 cm. ;
Area of circle = \(\pi r^2={22\over7}\times{(14)^2}= 616 cm^2\);;
Circumference of circle = \(2\pi r = 2\times{22\over7}\times 14 = 88 cm\)
SSC CGL 20206)If the perimeter of a certain rectangle is 50 units and its area is 150 sq. units, then how many units is the length of its shorter side?
10
Let, the length of rectangle= x units; Its width = y units; According to the question, 2(x+y) = 50;
x + y = 25 ---(1) ; and, xy = 150___(2); \((x-y)^2=(x+y)^2-4xy\) \(=(25)^2-4\times150=25\); ⇒ \(x-y=\sqrt{25} =5\)____(3);
By equation (1) - (3) we have; x + y - x + y = 25 - 5 = 20; So y = 10 units
SSC CGL 20207)The perimeter of an isosceles triangle is 50 cm.If the base is 18 cm, then find the length of the equal sides.
16 cm
Let Each equal side of isosceles triangle = x cm.
According to the question, x + x + 18 = 50; ⇒ x = 16 cm.
SSC CGL 20208)The area of the four walls of a room having length 6 m, breadth 4 m and height 4 m, is:
80 sq. metre
l = 6m, b = 4m, h = 4m ; Area of four walls of a room = \(2\times h(l+b)=2\times4(6+4)\) = 80 sq. metre
SSC CGL 20209)Two circles of radii 8 cm and 6 cm touch each other externally. The length of the direct common tangent is:
13.86 cm
The length of the direct common tangent = \(2\sqrt{r1.r2}\);
r1 = 8 cm;
r2 = 6 cm;
The length of the direct common tangent = \( 2\sqrt{8 \times 6} = 2\sqrt{48} = 2 \times 6.93 = 13.86 cm\)
SSC CGL 202010)The inner and outer radius of a circular track are 29 m and 23 m respectively. The cost of leveling the track at Rs. 7 per sq. metre is :
Rs. 6,864
Radius of outer circle = 29 m;
Radius of inner circle = 23 m;
Area of the circular track = \(\pi (R^2-r^2)\);
Total cost of leveling the track = \({22\over7}(29^2-23^2)\times7\) = Rs. 6864