ANSWER : 7000

Explanation : : Given x=332 ;Y=333 ; z=335 =x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx) =(x+y+z)1/2[(x-y)²+(y-z)²+(z-x)²] =1/2[332+333+335] =7000

ANSWER : (i) and (iii)

Explanation : : (√6+√2)²=(√6)²+(√2)²+2(√6)(√2) =8+2√12 (√5+√3)²=(√5)²+(√3)²+2(√5)(√3) =8+2√15 (√6+√12)<(√5+√3) is a correct relation options (i) and (iii) are incorrect relations

ANSWER : k=4

Explanation : : Given 2x-ky+7=0 6x-12y + 15=0 These two equations has no solution if 2/6=-k/-12 =>k=4

ANSWER : 5

Explanation : The values of 1/√7-√6 - 1/√6-√5 + 1/√5-2 - 1/√8-√7 + 1/3-√8 is opt1:0 opt2:1 opt3:5 opt4:7 ans: 5 Exp: 1/√7-√6 x √7+√6/√7-√6 =√7 + √6 / 7-6= √7 + √6 / 1 similarly, 1/√6-√5 =(√6 + √5) 1/√5-2= √5+2 / (√5-2)(√5 + 2) = √5+2/ 5-4 =√5+2 1/√8-√7=(√8+√7) and 1/3-√8 x 3+√8 / 3+√8 = 3+ √8 / 9-8=( 3+√8) 1/√7-√6 - 1/√6-√5 + 1/√5-2 - 1/√8-√7 + 1/3-√8 =√7+√6-(√6+√5) + √5 + 2-(√8+√7)+(3+√8) =2+3=5

ANSWER : 16 years

Explanation : : Rate of interest = 6 1/4 % (or) 6.25 % Let the principle =p No.of years =n Since it is doubled, we have S.I=P P=P x n x 6.25/100 => n = 100/6.25 =10000/625 =16 years