Question

1. The common difference of the A.P. -5, -1, 3, 7 ..... is -

3

4

-4

5

2. 9th term of the AP : 3, 8, 13, 18, ...... is -

43

40

45

44

3. The sum of the first 22 terms of the AP : 8, 3, -2, ........

979

797

967

-979

4. The distance of a point P(a,b) from the origin O(o,o) is -

√x²+y²

√a+b

√a²-b²

√a²+b²

5. The coordinates of a point lie on the x-axis are of the form -

(0,x)

(x,0)

(0,y)

(0,0)

6. The ratio in which the line segment joining the points (-3,10) and (6,-8) is divided by (-1,6) is -

7:2

2:7

3:7

7:3

7. If tangents PA and PB form a point P to a circle with centre O are inclined each other at angle of 100⁰, then ∠POA = .........

30⁰

50⁰

40⁰

60⁰

8. How many tangents can be drawn through a point lying outside the circle?

0

1

many

2

9. The sum of the first 500 positive integers is -

125,250

125,200

500,500

152,250

10. In an AP : if a = 10, a₁₀ = 30, then d = ...........

9/20

20/17

20/9

50/9​

Answer 1

Answer:

• ye Question hai

Answer 2

Answer:

1.AP:(-5),(-1),3,7

a1=(-5), a2=(-1), a3=3, a4=7

d=a2-a1=(-1)-(-5)=(-1)+5=4

Option 2

2.AP:3,8,13,18,...

a=3, d=8-3=5, n=9

An=a+(n-1)d

A9=3+(9-1)5

A9=3+(8)5

A9=3+40

A9=43

Option 1

3.AP:8,3,(-2),...

a=8, d=3-8=(-5), n=22

Sn=n/2[2a+(n-1)d]

S22=22/2[2(8)+(22-1)(-5)

S22=11[16+(21)(-5)]

S22=11(16+(-105)]

S22=11(16-105)

S22=11(-89)

S22=(-979)

Option 4

4.P=(a,b), O=(0,0)

Distance of point P from origin O=√a²+b²

Option 4

5.The coordinates of a point lie on the x-axis are of the form (x,0).

Option 2

6.Let B be the point which divides the line segment AC in the ratio k:1.

A=(-3,10), C=(6,-8), B=(-1,6)

x=(-1), x1=(-3), x2=6, y=6, y1=10, y2=(-8)

$x = \frac{m1x2 + m2x1}{m1 + m2}$

$( - 1) = \frac{k(6) + 1( - 3)}{k + 1}$

$( - 1)(k + 1) = k(6) + 1( - 3)$

$( - k) - 1 = 6k - 3$

$( - k) - 6k = ( - 3) +1$

$( - 7k) = ( - 2)$

$7k = 2$

$\frac{k}{1} = \frac{7}{2}$

k:1=7:2

The ratio is 7:2.

Option 2

7.When u draw the figure

<AOB=100°

<POA=½<AOB=½×100°=50°

Option 2

8. 2 tangents can be drawn through a point lying outside the circle.

Option 4

9.AP=1+2+3+....+500

a=1, d=2-1=1, n=500

Sn=n/2[2a+(n-1)d]

S500=500/2[2(1)+(500-1)1]

S500=250(2+499)

S500=250(501)

S500=125250

Option 1

10.a=10, a₁₀=30, n=10

An=a+(n-1)d

A₁₀=10+(10-1)d

30=10+9d

9d=30-10

9d=20

d=20/9

Option 3