93) the average score of boys in the examination of a school is 71 and that of the girls is 73. the average score of the school in the examination is 71.8. find the ratio of number of boys to the number of girls who appeared in the examination.

81) a box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. ramesh, a shopkeeper will buy only those shirts which are good but ‘kewal’ another shopkeeper will not buy shirts with major defects. a shirt is taken out of the box at random. what is the probability that
i) ramesh will buy the selected shirt ?
ii)‘kewal’ will buy the selected shirt ?

79) two different dice are thrown together. find the probability of :
getting a number greater than 3 on each die
getting a total of 6 or 7 of the numbers on two dice

76) the angles of depression of the top and bottom of a 50m high building from the top of a tower are 45° and 60° respectively. find the height of the tower and the horizontal distance between the tower and the building (use √3 = 1.73)

75) the sum of the radius of base and height of a solid right circular cylinder is 37cm. if the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. (use π = 22/7)

74) a well of diameter 4m is dug 21m deep. the earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3m to form an embankment. find the height of the embankment.

71) in fig. , are shown two arcs paq and pbq. arc paq is a part of circle with centre o and radius op while arc pbq is a semi-circle drawn on pq as diameter with centre m. if op = pq = 10 cm show that area of shaded region is 25 (√3 - "π" /6) cm2

70) in fig., abc is a triangle, coordinates of whose vertex a are (0, – 1). d and e respectively are the mid-points of the sides ab and ac and their coordinates are (1, 0) and (0, 1) respectively. if f is the mid-point of bc, find the areas of Δabc and Δdef.

In fig., is a decorative block, made up of two solids – a cube and a hemisphere. the base of the block is a cube of side 6 cm and the hemisphere fixed on the top has a diameter of 3.5 cm. find the total surface area of the block. (use π = 22/7)
explained by: brijesh sharma

Question taken in this video:
in the given fig. , abcd is a square of side 14 cm. semi-circles are drawn with each side of square as diameter. find the area of the shaded region. (use π = 22/7)
explained by: brijesh sharma

Question taken in this video:
67)
the sums of first n terms of three arithmetic progressions are s1, s2 and s3 respectively. the first term of each a.p. is 1 and their common differences are 1, 2 and 3 respectively. prove that s1 + s3 = 2s2.
explained by: brijesh sharma

Question taken in this video:
66)
three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. find the numbers.
explained by: brijesh sharma

Question taken in this video:
65)
there are 100 cards in a bag on which numbers from 1 to 100 are written. a card is taken out from the bag at random. find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square, (ii) is a prime number greater than 80
explained by: brijesh sharma

Question taken in this video:
64)
from a pack of 52 playing cards, jacks, queens and kings of red colour are removed. from the remaining, a card is drawn at random. find the probability that drawn card is :
i) a black king, (ii) a card of red colour, (iii) a card of black colour.
explained by: brijesh sharma

Question taken in this video:
63)
if the roots of the quadratic equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal, prove that 2a = b + c.
explained by: brijesh sharma

Question taken in this video:
62)
the digits of a positive number of three digits are in a.p. and their sum is 15. the number obtained by reversing the digits is 594 less than the original number. find the number.
explained by: brijesh sharma

Question taken in this video:
61)
three different coins are tossed together. find the probability of getting (i) exactly two heads,
(ii) at least two heads (iii) at least two tails.
explained by: brijesh sharma

Question taken in this video:
60)
a sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. if the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 𝟑𝟐/𝟗 cm. find the diameter of the cylindrical vessel.
explained by: brijesh sharma

Question taken in this video:
59)
a conical vessel, with base radius 5 cm and height 24 cm, is full of water. this water is emptied into a cylindrical vessel of base radius 10 cm. find the height to which the water will rise in the cylindrical vessel. (use π = 22/7)
explained by: brijesh sharma

Question taken in this video:
57)
if the ratio of the sum of first n terms of two a.p' s is (7n + 1) : (4n + 27), find the ratio of their mth terms.
explained by: brijesh sharma