Q1 What is the equation of a circle of radius 6 units centered at (3, 2)?
A. x² + y² + 6x - 4y = 23
B. x² + y² - 6x - 4y = 23
C. x² + y² - 6x + 4y = 23
D. x² + y² + 6x + 4y = 23
x² + y² - 6x - 4y = 23
Q2 Find k, if the line 2x - 3y = 11 is perpendicular to the line 3x + ky = -4?
A. -1
B. 2
C. -2
D. 1
None
Q3 In which quadrant does the point (4, - 6) lies?
A. First
B. Second
C. Third
D. Fourth
The point (4,-6) lies in 4th quadrant
Q4 The separation of the point p (8, - 6) from the beginning is:
A. 2 units
B. 14 units
C. 10 units
D. 20 units
Op = √ (8-0)2+ (-6-0)2 = √64+ 36 = √100 =10 unit
Q5 P is a point on x-hub at a separation of 3 units from y-pivot on its right side. The co-ordinates of P are:
A. (3, 0)
B. (0, 3)
C. (3, 3)
D. (- 3, 3)
the co-ordinates of P are P (3, 0).
Q6 The vertices of a quadrilateral ABCD are A(0,0) ,B(4,4) ,C(4,8) and D(0,4).Then ABCD is a
A. Square
B. Rhombus
C. Rectangle
D. Paralleogram
AB2= (4-0) 2+ (4-0) 2= 32 BC2= (4-4) 2+ (8-4) 2= 0+16= 16 CD2= (0-4) 2+ (4-8) 2= (16+16) = 32 AB= CD= √32 = 4√2, BC= AD =√16 = 4 AC2= (4-0) 2+ (8-0) 2= (16+64) = 80 BD2= (0-4) 2+ (4-4) 2= 16+0= 16 ∴ Diag = AC≠Diag BD. ∴ ABCD is a parallelogram.
Q7 The end purposes of the distance across of a circle are A (4,- 1) and B(- 2,- 5). The co-ordinates of its middle are:
A. (1, - 3)
B. (2, - 4)
C. (- 1, 2)
D. (- 2, 3)
Co-ordinates of the center are [4+ (-2)/2, -1+ (-5)/2], i.e. (1,-3)
Q8 The lines x+2y-9 =0 and 3x+6y+8 =0 are commonly.
A. Parallel
B. Opposite
C. Equal
D. Not Equal
x+2y-9 =0 ⇒ 2y = -x+9 ⇒ y= -x/2+9/2 3x+6y+8 =0 ⇒ 6y= -3x-8 ⇒ y=-x/2 -4/3 ∴ m₁: m₂ = -1/2 Hence, the given lines are parallel.
Q9 On the off chance that the slant of a line joining the focuses A(x,- 3) and B(2,5) is 135⁰ then x=?
A. 5
B. -5
C. 8
D. 10
Slop of AB = (5+3)/(2-x) =8/2-x ∴ 8/2-x = tan135⁰ = tan (180⁰- 45⁰) = -tan 45⁰ =-1 8/2-x = -1 ⇒8 = x-2 ⇒ x= 10
Q10 A line goes through the focuses A (- 2, 3) and B (- 6, 5). The slop of line AB is
A. -1/2
B. 1/2
C. 3/4
D. -1
Slop = (y₁ ?y₂)/( x₁-x₂) = (5-3)/(-6+2) = 2/-4 =-1/2