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Find the remainder when 7^103 is divided by 24 Solution) we know by the concept of mod that..... 49 is congruent to 1 mod 24(means if 1 is subtracted fom 49 u get 48 which is divisible by 24) so 7^2congruent to 1 mod 24 so 7^102congruent to 1 mod 24(raising to the power 51) hence the remainder when 7^102 is divided by 24 is 1 i.e. 7^102=24m+1 so multipling by 7 both sides we have....7^103=24.7m+ 7hence 7^103=24n + 7so remainder is 7 (ans)
A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.
Calculate the area and perimeter of a square: Calculate the area and perimeter of a square with w = 5´ and l = 6´. Be sure to involved units in your answer. Solution:
Evaluate following integrals. (a) ∫ 3e x + 5 cos x -10 sec 2 x dx (b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy Solution (a) ∫ 3e x + 5 cos x -10 sec 2 x
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if a,b,c are in HP
It is not the first time that we've looked this topic. We also considered linear independence and linear dependence back while we were looking at second order differential equation
HOW MATHEMATICAL IDEAS GROW : In this section we shall consider three aspects of the nature of mathematical ideas, namely, that they progress from concrete to abstract, from part
What is a review technique? What are its advantages and disadvantages?
compare: 643,251: 633,512: 633,893. The answer is 633,512.
The diagram below shows the cross section of a pipe 1/2 inch thick that has an inside diameter of 3 inches. Determine the area of the shaded region in terms of π. a. 8.75π i
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