IIT JEE , AIEEE Forum - Mathematics , Algebra

shajikoshy

Q 1. A square is drawn by joining the mid points of the sides of the given square. A third square is drawn inside the second square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas of all the squares.

Q2. Which is the correct order for a given number "k" in increasing order (Roorkee scr 93)

(A) log₂k, log₃ k, log_e k_,log₁₀ k

(B) log₁₀k, log₃ k, log_e k_,log₂ k

(C) log₁₀k, log_e k, log₂ k_,log₃ k

(D) log₃k, log_e k, log₂ k_,log₁₀ k

Q3. Find the total number of terms in the expansion of

(X +Y + Z +W)ⁿ where N belongs to the set of Natural number. (IIT JEE)

divalli_oct07

Q3. Find the total number of terms in the expansion of

(X +Y + Z +W)ⁿ where N belongs to the set of Natural number.

Soln:- The no. of terms in the expn (x+y+z+w)ⁿ can be

found out using the formula ^n+r-1C_r-1

where r = no.of terms (x,y,z,w )

here r=4 so, total terms = ⁿ⁺³C₃

Greatdreams

1.) 1st square is 4 cm in length

Now if we draw the diagram and calculate the side of the 2 nd square,

we get its side to be 2

2 cm

Similarly on finding the 3 rd side we get it as 2 cm

So sum of areas of the squares are ....

4*4 + 2

2* 2

2 + 2 *2..........

= 16 + 8 + 4+ ................

So we get an infinite G.P series hence the sum = a / 1- r

Here a = 16 and r = 1/2

So area = 32 sq cm.

raulrag009

Q.2 IS THE ANSWER

B.

madman

Q2. greater the base for a number k smaller is the logarithm
hence B

Greatdreams

Sorry for the late reply as there was a power cut

10 > 3 > e > 2

Taking k > 1

log _k 10 > log_k 3 > log _k e > log _k 2

Now take reciprocal and change sign of inequality,

we have log ₁₀ k < log ₃ k < log_ek < log₂ k

So option is b

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