# Algebra Part 1: Advance math questions series 2000

Algebra Part 1: Advance math questions series 2000

Q481. If x 47 + 1/x 47  = 2 then x 48  –  1/ x 48 = ?

(a) 1

(b) 0

(c) 2

(d) None of these

Q482. If point A is in third quadrant and 3 tan A – 4 = 0 then the value of 5 sin 2A + 3 sin A + 4 cos A = ?

(a) 0

(b) – 24/5

(c)  24/5

(d) 48/5

Q483. If α and β  are the roots of equation x² + px + q = 0 then what will be the equation whose roots are α2+ αβ and β2+ αβ?

(a) x2 + p2x + p2q = 0

(b) x2 – q2x + p2q = 0

(c) x2 + q2x + p2q = 0

(d) x2 – p2x + p2q = 0

Q484. The value of expression

(a) (x2 – y2)(y2 – z2)(z2 – x2)

(b)3(x – y)(8y – z)(z – x)

(c) (x + y)(y + z)(z + x)

(d) 3(x + y)(y + z)(z + x)

Q485.  If a2 + b2 + c2 = ab + bc + ca, then the value of a2 + b2 + c2 is

(a) 3abc

(b) 3a2b2c2

(c) 3(abc)3

(d) None of these

Q486.  If a4  + 1/a4 = 119 then the value of a3 – 1 /a3   is

(a) 27

(b) 36

(c) 45

(d) 54

Q487. If a3b = abc = 180, a, b, c, are positive integers, then the value of c is

(a) 110

(b) 1

(c) 4

(d) 25

Q488. If a 1/3 + b 1/3 + c 1/3 = 0, then a relation among a, b, c is

(a) a +b +c = 0

(b) (a+ b+ c)3 = 27 abc

(c) a+ b+ c = 3 abc

(d) a3+b3+c3  = 0

Q489. If a + b = 1, c + d = 1 and a – b = d/c , then the value of  c2 – d2 is

(a)  a/b

(b)  b/a

(c) 1

(d) -1

Q490. If x = b + c – 2a, y = c + a – 2b, z = a + b – 2c, then the value of x2 + y2 – z2 + 2xy is

(a) 0

(b) a + b + c

(c) a – b + c

(d) a + b – c

Q491. If x + 9/x = 6, then the value of (x2 + 9/x2 ) is

(a) 8

(b) 9

(c) 10

(d) 12

Q492. If x = 5 – √21 , then the value of  is

(a)

(b)

(c)

(d)

Q493. If x – y = x+y/7 = xy/4 ,the numerical value of xy is

(a)  4/3

(b)  3/4

(c)  1/4

(d) 4/1

Q494.  Let a = √6 – √5, b = √5 – 2 ,  c = 2 – √3 then point out the correct alternative among the four alternatives given below.

(a) b< a < c

(b) a < c < b

(c) b < c < a

(c) a < b < c

Q495. If x is real, then the minimum value of (x2-x+1) is

(a) 3/4

(b) 0

(c) 1

(d) 1/4

Q496.If a ≠ b, then which of the following statements is true?

(a)

(b)

(c)

(d) All of the above

Q497. If x= , then the value of 5x2-5x-1 is

(a) 0

(b) 3

(c) 10

(d) 5

Q498. If ab= a+ b+ ab, then 34 – 2*3 is equal to :

(a) 6

(b) 8

(c) 10

(d) 12

Q499.  If    = a+b√6, then the values of a and b are respectively

(a) 9/15 , – 4/15

(b) 3/11 , 4/11

(c) 9/10 , 2/5

(d) 3/5 , 4/15

Q500. The value of the expression X4 – 17x3 + 17x2 – 17x + 17  at x= 16 is

(a) 0

(b) 1

(c) 2

(d) 3

Q501. If   , then    is equal to

(a) 1

(b) 2/√3

(c)2-√3

(d) 2

Q502.  If x =  , the value of     is

(a) 1

(b) 2

(c) √3

(d) √5

Q503.   If x = 5 + 2√6, then the value of (√x+1/√x ) is,

(a) 2√2

(b) 3√2

(c) 2√3

(d) 3√3

Q504.   If  a + b + c = 0, then the value of  is

(a) 0

(b) 1

(3) 2

(d) 3

Q505. If  a2 + b2 + 4c2 = 2a + 2b – 4c – 3 and a, b, c are real, then the value of (a2 + b2 + c2) is

(a) 3

(b) 3 ¼

(c) 2

(d) 2 ¼

Q506.  If x + 1/x = 4 then the value of x4 + 1/ x4

(a) 196

(b) 194

(c) 192

(d) 190

Q507.  If x + 1/x = 1 then x12 + x9 + x6 + x3 + 1   = ?

(a)  – 1

(b) – 2

(c) 1

(d) 2

Q508. If p : q = r : s = t : u = 2 : 3, then (mp + nr + ot) : (mq + ns + ou) equals :

(a) 3 : 2

(b) 2 : 3

(c) 11 : 3

(d) 1 : 2

Q509.  If  and x + y + z ≠ 0, then each ration is

(a)

(b)

(c)

(d)

Q510. If a3 + b3 = 9 and a + b = 3, then the value of  1/a + 1/b  is

(a) 1/2

(b) 3/2

(c) 5/2

(d) -1

Q511. If a = 4.965, b = 2.343 and c = 2.622, then the value of  a3 – b3 – c3 – 3abc is :

(a) -2

(b) -1

(c) 0

(d) 9.93

Q512.  If  x3 +3/x =  4(a3 + b3) and 3x + 1/x= 4(a– b3), then a2 – b2 is equal  to

(a) 4

(b) 0

(c) 1

(d) 2

Q513. If (x +  1/x) 2 = 3, then the value of x206+x200+x90+x84+x18+x12+x6+1 is

(a) 0

(b) 1

(c) 84

(d) 206

Q514. If x + 1/x = 3, then the value of  is

(a) 322

(b) 126

(c) 123

(d) 113

Q515. If , then the value of  is

(a) 22

(b) 33

(c) 40

(d) 45

Q516.  If p= 101, then the value of   is

(a) 100

(b) 101

(c) 102

(d) 1000

Q517. If ab + bc + ca = 0, then the value of    is

(a) 2

(b) -1

(c) 0

(d) -2

Q518. if    then the value of is

(a) – 2

(b) 0

(c) 2

(d) 4

Q519. If 2x = 3y = 6-z, then the value of

(a) 0

(b) 1

(c) 3/2

(d) – 1/2

Q520.If x = then the value of

(a) 0

(b) 3

(c) 4

(d) 5