objective Ques (21 results)
SSC CGL 202011)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 202012)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
SSC CGL 202013)A circular disc of area \(0.64\pi\space m^2\) rolls down a length of 1.408 km. The number of revolutions it makes is: (Take \(\pi ={22\over7}\))
280
Area = \(\pi r^2\);
\(\pi r^2= 0.64\pi\space m^2\);
r = 0.8 m;
Circumference of disc = \(2 \pi r = 2 \times (22/7) \times 0.8 = 5.02\) ;
Length = 1.408 km = 1408 m;
The number of revolutions = 1408/5.02 = 280
SSC CGL 202014)A metallic sphere of diameter 40 cm is melted into smaller spheres of radius 0.5 cm each. How many such small balls can be made?
64,000
Number of smaller balls = \({Volume \space of\space bigger \space ball\over Volume\space of \space a\space smaller\space ball}\) = \({{4\over3}\pi R^3\over {4\over3}\pi r^3}=({20\over0.5})^3= 64000\)
SSC CGL 202015)The perimeter of a square is 64 cm. Its area will be:
256 \(cm^2\)
Perimeter of square = 64 cm ; ⇒ 4 x Side = 64; ⇒ Side = 16 cm; Area of square = \((Side)^2=(16)^2 = 256 \space cm^2\)
SSC CGL 202016)The diagonal of a square A is (a + b) units. What is the area (in square units) of the square drawn on the diagonal of square B whose area is twice the area of A?
\(2(a+b)^2\)
Area of square A = \( \frac{(diagonal)^2}{2} = \frac{(a + b)^2}{2}\) ;
Area of square B = \(2 \times area \space of \space square A = 2\times \frac{(a + b)^2}{2} = (a + b)^2\) ;
Side of B = a + b ;
Diagonal of B = \(\sqrt{2} side = \sqrt{2}(a+b)\) ;
Area (in square units) of the square drawn on the diagonal of square B = \((side)^2 = (\sqrt{2}(a+b))^2 = 2(a + b)^2\)
SSC CHSL 202117)One diagonal of a rhombus is 8√3 cm. If the other diagonal is equal to its side, then the area (in \(cm^2\) ) of the rhombus is:
32√3
SSC CHSL 202118)Find the area (in cm2) and the diameter (in cm), respectively, of a circle whose circumference is 40π cm?
400 π and 40
SSC CHSL 202119)The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:
840
SSC CHSL 202120)What is the perimeter of a right-angled triangle whose sides (making 90°) are 20√3 cm and 15√3 cm?
60√3 cm
