Question

1 MARK HOTS.. solve all circled and explain in detail.. TOMORROW EXAM SO NO SPAM please​

Answer 1

...Answers with step by step explanation...

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3)

the sum of n natural numbers is given by n(n+1)/2

yes, it is true.....

explanation

we know Sn = n/2 (2a + (n-1)d) for sum of nth term in AP.

1,2,3,4,5....... n } are natural numbers having common difference of 1 and first term (a) = 1 between any 2 consecutive numbers.

Sn = n/2 (2a + (n-1)d) [put a = 1 and d = 1]

Sn = n/2 x (2 + n-1)

Sn = n(n+1)/2

hence proved

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7)

two friends were born in same year 2000.

2000 is a leap year consisting 366 days.

possible chances of birthday of same day = 1

probability of this event = 1/366

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10)

Sorry ratios is not complete in figure.

I think it can be 1:1

if ratio is 1:1 this implies that point is the mid point of given line segment.

so,

x of that point = (7+3)/2 = 10/2 = 5

y of that point = (-6+4)/2 = -2/2 = -1

(x,y) = (5,-1)

as we can see that here x is +ve and y is -ve.

in 4th quadrant x is +ve and y is -ve.

therefore this point also lies in 4th quadrant.

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11)

sin∅ + sin²∅ = 1

sin∅ = 1-sin²∅ ......(i)

to find cos²∅ + cos⁴∅ .....(ii)

cos²∅ = 1-sin²∅

cos⁴∅ = (cos²∅)² = (1-sin²∅)²

put these values in ...(ii)

we get

= 1 - sin²∅ + (1-sin²∅)²

= sin∅ + (sin∅)² (from ....(i))

= sin∅ + sin²∅

= 1

hence cos²∅ + cos⁴∅ = 1

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15)

there is only one possibilty to score 35 marks out of 50 marks.

so

its probability = 35/50 = 7/10

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Hope this will help you.

Hope this will help you.please mark me as brainliest

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