Home
Class 12
MATHS
Let a,b,c,d,e,f,g,h be distinct elements...

Let `a,b,c,d,e,f,g,h` be distinct elements in the set `{-7,-5,-3,-2,2,4,6,13}`. The minimum value of `(a+b+c+d)^2 + (e+ f + g + h)^2` is:(1) 30 (2) 32 ( 3) 34 ( 4) 40

A

30

B

32

C

34

D

40

Text Solution

Verified by Experts

The correct Answer is:
B
`a+b+c+d+e+f+g+h=g`
Let `a+b+c+d=x`
`therefore e+f+g+h=8-x`
Let `y=x^(2)+(8-x)^(2)`
`therefore y=2x^(2)-16x+64`
`=2[x^(2)-8x+32]`
`=2[(x-4)^(2)+16]`
`therefore y_("min")=32 " when "x=4`
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|10 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked comprehension Type|2 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

Similar Questions

Explore conceptually related problems

The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 (d) 0

If U = { a, b, c, d, e, f, g, h} , find the complements of the following sets : A = {a, b, c}

From the sets given below, select equal sets : A = { 2, 4, 8, 12}, B = { 1, 2, 3, 4}, C = { 4, 8, 12, 14}, D = { 3, 1, 4, 2} E = {–1, 1}, F = { 0, a}, G = {1, –1}, H = { 0, 1}

Let A = {1,2,3}, B = {3,4} , C = {4,5,6} Then A cup (B cap C) is

If a ,b ,c ,d ,e , and f are in G.P. then the value of |((a^2),(d^2),x),((b^2),(e^2),y),((c^2),(f^2),z)| depends on (A) x and y (B) x and z (C) y and z (D) independent of x ,y ,and z

Let h(x)=|k x+5| ,then domainof f(x) be [-5,7], the domain of f(h(x)) be [-6,1] ,and the range of h(x) be the same as the domain of f(x). Then the value of k is. (a)1 (b) 2 (c) 3 (d) 4

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2A is equal to (a)2 (b) 3 (c) 4 (d) 5.

If a ,b and c are in A.P. and b-a ,c-b and a are in G.P., then a : b : c is (a). 1:2:3 (b). 1:3:5 (c). 2:3:4 (d). 1:2:4