Question

answer for all questions

Answer 1

Answer:

Step-by-step explanation:

Total outcomes=105

Favourable outcome= (outcome for no.1+ that of 3+ that of 5)=72

P(E) = favourable outcome÷total outcome

i.e. 72÷105= 0.48

Answer 2

I guess the answer of 1st one is => x = -2

2. here we have to check whether x - y + 3 = 0 or not
x = 0 and y = -3
verification :-
=> 0 - (-3) + 3
=> 0 + 3 + 3
=> 6
hence, (0,-3) is not a solution of x - y + 3 = 0

4. given the edge of a solid cube = 6cm
we have to find how many solid cubes of edge 6cm can be formed from this cube.
no more cubes can be formed. only one.
let's prove..
volume of the cube = side³
= 6 × 6 × 6
= 36 × 6
= 216cm³
now volume of the second cube = side³
= 6 × 6 × 6
= 216cm³
therefore no. of cubes of edge 6cm can be formed from the cube if edge 6cm = 216/216
= 1
only one cube.

5. given the CSA (curved surface area) of the right circular cylinder = 957cm²
height = 21cm
we have to find it's diameter
the formula for the CSA of a right circular cylinder is 2πrh
therefore 2πrh = 957cm²
=> 2 × 22/7 × r × 21 = 957cm²
=> 44 × r × 3 = 957cm²
=> 132 × r = 957cm²
=> r = 957/132
=> r = 7.25
the radius of the cylinder is 7.25cm
we know that the diameter is double of the radius.
therefore it's diameter = 7.25 × 2 = 14.5cm

6. given the side of the cube = 8cm
therefore the diameter of the largest sphere that can be carved from the cube = 8cm
radius is half of the cube.
therefore radius of the largest cube that can be carved from the cube of side 8cm.
= 8/2 = 4cm
radius of 4cm can be carved.

7. given BA = AC, angle ABC = 50°
angle BCA = 50° (since BA = AC)
therefore angle BAC = 180° - (50° + 50°) (angle sum property)
= 180° - 100°
= 80°
=> angle BOC = 80° × 2 = 160° (by theorem that angle subtended by the same arc on the center is double of the angle subtended on the circle)
now angle BDC = 180 - 80 = 100° (since all the points A,B,D and C are lying on the same circle i.e it's a cyclic quadrilateral and the sum of opposite angles of a cyclic quadrilateral is 180°)

9. given:-
height of the cone = 8.4cm
radius of the base of the cone = 2.1cm
volume of the cone = 1/3πr²h
= 1/3 × 22/7 × 2.1 × 2.1 × 8.4
= 97.02/7 × 2.8
= 97.02 × 0.4
= 38.808cm³
ATQ, volume of the cone = volume of the sphere
therefore volume of the sphere = 38.808cm³
formula for the volume of a sphere is 4/3πr³
=> 4/3 × 22/7 × r³ = 38.808cm³
=> 88/21 × r³ = 38.808cm³
=> r³ = 38.808/1 × 21/88
=> r³ = 814.968/88
=> r³ = 9.261
=> r = ³√9.261
=> r = ³√(2.1×2.1×2.1)
=> r = 2.1cm
hence, the radius of the sphere is 2.1cm

sorry I don't know probability so I can't solve 10th question.

answer of 3rd and 8th question is in the attachment.

for 8th question,

1.draw a ray, say YX.
2. taking Y as center, draw an arc cutting the ray YZ. name the point O
3. keeping the same width, from O draw another arc cutting the previous arc at P.
4. taking the point P, with the same width (radius) draw another arc cutting the same arc drawn in the step 2. name M
5. now draw two arcs from P and M. name the point N.
6. connect Y and N with a straight line. now it's a 90° angle.
7. the point where 90° bisects the first arc drawn in step 2, name it Q.
8. keeping same width, draw an arc from Q and M.
9. name the point X where both arcs intersect.
10. join X and Y with a straight line and u get 105° angle.