# Algebra Part 2: Advance math questions series 2000

Algebra Part 2: Advance math questions series 2000

Q521. If 3(x – y) = 27 and 3(x + y) = 243, then the value of x is

(a) 0

(b) 2

(c) 4

(d) 6

Q522. If 8a – b2 = 24, 8b + b2 = 56 then a + b = ?

(a) 3

(b) 7

(c) 10

(d) 80

Q523. If x47 + 1/x47  =2 then x48 – 1/x48 = ?

(a) 1

(b) 0

(c) 2

(d) None of these

Q524. 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

Q525. If  α and β are the root of equation x2 + px + q = 0 then the value of

(a)

(b)

(c)

(c)

Q526. If y + 1/z = 1 and x + 1/y = 1 , then the value of xyz is

(a) 1

(b) – 1

(c) 0

(d) 1/2

Q527. Which of the following statement is true?

(a) 960 < 2735

(b) 960 ≤ 2735

(c) 960 > 2735

(d) 960 ≥ 2735

Q528. If ab + bc + ca = 0 then the value of  is

(a) 0

(b) 1

(c) 3

(d) a + b + c

Q529. 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

Q530. If  α and β are the roots of equation x2 + bx + c = 0 then the value of αβ2 + α2β + αβ is

(a) c(1 – b)

(b) 0

(c) – bc

(d) None of these

Q531. The graph of the equation 4x – 5y = 20 intersects the x – axis at the point

(a) (2,0)

(b) (5,0)

(c) (4,5)

(d) (0,5)

Q532. Area of the triangle formed by the graph of the straight line x – y = 0, x + y = 2 and the x – axis is

(a) 1sq unit

(b) 2 sq units

(c) 4 sq units

(d) None of these

Q533. The area in sq. unit. Of the triangle formed by the graphs of x = 4, y = 3 and 3x + 4y = 12 is

(a) 12

(b) 8

(c) 10

(d) 6

Q534. The graphs of x = a and y = b intersect at

(a) (a,b)

(b) (b,a)

(c) (-a,b)

(d) (a,-b)

Q535. Equation of the straight line parallel to x – axis and also 3 units below x – axis is :

(a) x = – 3

(b) y = 3

(c) y = – 3

(d) x = 3

Q536. The x –  intercept on the graph of 7x – 3y = 2 is

(a) 3/4

(b) 3/7

(c) 2/5

(d) 2/7

Q537. If 2x + y = 6 and x = 2 are two linear equations, then graph of two equations meet at a point :

(a) (2,0)

(b) (0,2)

(c) (2,2)

(d) (1,2)

Q538. The linear equation such that each point on its graph has an ordinate four times its abscissa is :

(a) y+4x=0

(b) y=4x

(c) x=4y

(d)  x+4y=0

Q539. The graph of the equation 2x-3y = 6 intersects the y-axis at the point

(a) (-2,0)

(b) (0,-2)

(c)  (2,3)

(d) (2,-3)

Q540. An equation of the form ax + by + c = 0 where a  0, b  0, b  represents a straight line which             Through

(a) (0,0)

(b) (3,2)

(c) (2,4)

(d) None of these

Q541.The length of the intercept of the graph of the equation 9x – 12y = 108 between the two axes is

(a) 15 units

(b) 9 units

(c) 12 units

(d) 18 units

Q542. If a linear equation is of the form x = k where k is a constant, then graph of the equation will be

(a) a line parallel to x- axis

(b) a line cutting both the axes

(c) a line making positive acute angle with x – axis

(d) a line parallel to y – axis

Q543. An equation whose graph passes through the origin, out of the origin, out of the given equations 2x + 3y = 2, 2x – 3y = 3, -2x +3y = 5 and 2x + 3y = 0 is :

(a) 2x-3y = 3

(b) -2x +3y=5

(c) 2x+3y=0

(d) 2x+3y=2

Q544. If (2x)(2y) = 8 and (9x)(3y) = 81, then (x, y) is :

(a) (1,2)

(b) (2,1)

(c) (1,1)

(d) (2,2)

Q545. The lines 2x + y = 5 and x +2y = 4 intersect at the point :

(a) (1,2)

(b) (2,1)

(c) ( ,0)

(d) (0,2)

Q546. The graph of the linear equation 3x + 4y = 24 is a straight line intersecting x – axis and y – axis at the points A and B respectively. P(2,0) and Q (0 , 3/2) are two points on the sides OA and OB respectively of ΔOAB, where O is the origin of the co-ordinate system.  Given that AB = 10 cm, then PQ =

(a) 20 cm

(b) 2.5 cm

(c) 40 cm

(d) 5 cm

Q547. The graph of the equations 25x + 75y = 225 and x = 9 meet at the point

(a) (0,9)

(b) (9,0)

(c) (3,0)

(d) (0,3)

Q548. The area bounded by the lines x = 0, y = 0, x+y = 1, 2x + 3y = 6 (in square units ) is

(a) 2

(b) 2 1/3

(c) 2 1/2

(d) 3

Q549. The graph of 2x + 1 = 0 and 3y – 9 = 0 intersect at the point

(a) (- 1/2 , -3)

(b) (- 1/2 , 3)

(c) ( 1/2 , -3)

(d) None of these

Q550. If the graph of the equations 3x + 2y = 18 and 3y – 2x = 1 intersect at the point (p,q), then the value of p + q is

(a) 7

(b) 6

(c) 5

(d) 4

Q551. if the graph of the equations x + y = 0 and 5y +7x = 24 intersect at (m,n), then the value of m + n is

(a) 2

(b) 1

(c) 0

(d) -1

Q552. The area of the triangle formed by the graph of 3x + 4y = 12, x – axis and y – axis (in sq. units) is

(a) 4

(b) 12

(c) 6

(d) 8

Q553. The straight line 2x + 3y = 12 passes through :

(a) 1st, 2nd and 3rd quadrant

(b) 1st, 2nd and 4th quadrant

(c) 2nd, 3rd and 4th quadrant

(d) 1st, 3rd and 4th quadrant

Q554. The equations 3x + 4y = 10, – x + 2y = 0 have the solution (a,b), the value of a + b is

(a) 1

(b) 2

(c) 3

(d) 4

Q555. If   then two value of x are

(a) 1,2

(b) 2, – 1/2

(c) 0,1

(d) 1/2 , 1

Q556. Which of the following will be the solution of linear equation   ?

(a) x positive and y negative

(b) y positive and x negative

(c) both x and y are positive

(d) both x and y are negative

Q557. 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)

Q558. In the given figure, there is a square having side 3 cm. If another square having side 5 cm and In Δ BCE ∠c is 90º . Then the length of the CN is

(a)    √56 cm

(b)    √57 cm

(c)    √58 cm

(d)    √59 cm

Q559. In the given figure ABCD is a parallelogram whose sides are AD = a unit, DC = 2a unit and DE: EC = 1 : 2, CEFG is a rectangle whose side EF = 3AE. What will be the ratio of area of parallelogram to the area of rectangle?

(a) 1 : 1

(b) 1 : 2

(c) a2/5

(d) 2 : 1

Q560. If x = 12 and y = 4 then the value of (x + y)x/y is

(a) 4096

(b) 3066

(c) 3616

(d) 4226

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