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Mitali Sabale 7 years, 4 months ago
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Posted by Sahil Mandavkar 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
In triangle ABC, we have
BP = BQ = 3cm
AP = AR = 4cm
(tangents drawn from an external point to the circle are equal).
So, RC = AC - AR
= 11 - 4
= 7 cm
Hence RC = CQ = 7 cm
Then, BC = BQ + QC
= 7 + 3
= 10 cm
Posted by Sunny Shing 7 years, 4 months ago
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Kushal Jain 7 years, 4 months ago
Posted by Rahul Yaduvanshi 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
Suppose the first and second number be x and y respectively.
According to the question,
{tex}2x + 3y = 92{/tex} .......(i)
{tex}4x - 7y = 2{/tex} .......(ii)
Multiplying equation (i) by 7 and (ii) by 3,
{tex}\Rightarrow 14x + 21y = 644{/tex} .......(iii)
{tex}12x - 21y = 6{/tex} .........(iv)
Adding equations (iii) and (iv),
{tex}\Rightarrow 26x = 650{/tex}
{tex}\Rightarrow x = \frac { 650 } { 26 } = 25{/tex}
Putting {tex}x = 25{/tex} in equation (i),
{tex}\Rightarrow 2 \times 25 + 3 y = 92{/tex}
{tex}\Rightarrow50 + 3y = 92{/tex}
{tex}\Rightarrow 3 y = 92 - 50{/tex}
{tex}y = \frac { 42 } { 3 } = 14{/tex}
y = 14
{tex}\therefore{/tex} the first number is 25 and second is 14
Posted by Ankush Garg 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
Side of square {tex}= 6\ units{/tex}
Since A and B are the mid-point of KL and LM,
{tex}KA = AL = LB =BM = 3 units{/tex}
{tex}\therefore{/tex}Area of square = {tex}6 \times 6 = 36\ sq. units{/tex}
Area of {tex}\triangle{/tex}AJB = area of square - area of {tex}\triangle{/tex}AKJ - area of {tex}\triangle{/tex}BMJ - Area of {tex}\triangle ALB{/tex}
=36 - {tex}\frac{1}{2}{/tex} {tex}\times{/tex} 6 {tex}\times{/tex} 3 - {tex}\frac{1}{2}{/tex} {tex}\times{/tex} 3 {tex}\times{/tex} 3 - {tex}\frac{1}{2}{/tex} {tex}\times{/tex}6 {tex}\times{/tex}3
={tex}36 - 9 - 4.5 - 9{/tex}
={tex}13.5\ square\ units{/tex}
Probability that the point will be chosen from the interior of {tex}\triangle{/tex}AJB {tex}= \frac { \text { Area } \Delta J A B } { \text { Area of square } }{/tex} = {tex}\frac{13.5}{36}{/tex} = {tex}\frac{135}{360}{/tex}= {tex}\frac{3}{8}{/tex}.
Posted by Abhishek Kumar 7 years, 4 months ago
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Check notes from here : <a href="https://mycbseguide.com/cbse-revision-notes.html">https://mycbseguide.com/cbse-revision-notes.html</a>
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Sia ? 6 years, 6 months ago
Let us suppose that 'a' be the first term and 'd' be the common difference of the A.P.
Now according to question it is given that
S9 = 162.
Using formula for sum to n terms of A.P, we have
{tex}\Rightarrow \frac{9}{2}\left[ {2a + (9 - 1)d} \right] = 162{/tex}
{tex} \Rightarrow \frac{9}{2}\left[ {2a + 8d} \right] = 162{/tex}
{tex}\Rightarrow{/tex} 9a + 36d = 162 ........................(i)
Let a6 and a13 be the 6th and 13th term of the A.P. respectively.
Therefore, using general form of nth term, we have,a6 = a + 5d and a13 = a + 12d
Since, {tex}\frac{{{a_6}}}{{{a_{13}}}} = \frac{1}{2}{/tex}
{tex} \Rightarrow \frac{{a + 5d}}{{a + 12d}} = \frac{1}{2}{/tex}
{tex}\Rightarrow{/tex} 2a + 10d = a + 12d
{tex}\Rightarrow{/tex} a = 2d
Now,substituting the value of a = 2d in equation (i), we get,
9(2d) + 36d = 162
{tex}\Rightarrow{/tex} 18d + 36d = 162
{tex}\Rightarrow{/tex} 54d = 162
{tex}\Rightarrow{/tex} d = 3
{tex}\Rightarrow{/tex} a = 2d = 2 {tex}\times{/tex} 3 = 6 = First term
Therefore, 15th term=a+14d=6+14(3)=48
Posted by Dablu Kumar 7 years, 4 months ago
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Sia ? 6 years, 6 months ago
Suppose that he invested ₹ x at the rate of 12% simple interest and ₹ y at the rate 10% simple interest.
Then, according to the question,{tex}\frac{12x}{{100}} + \frac{{10y}}{{100}} = 130{/tex}
{tex}\Rightarrow {/tex} 12x+10y=13000 ..........Dividing throughout by 2
{tex}\Rightarrow {/tex} 6x+5y=6500 .......(1)
and,{tex}\frac{{12y}}{{100}} + \frac{{10x}}{{100}} = 134 {/tex}
{tex}\Rightarrow {/tex} 12y+10x=13400
{tex}\Rightarrow {/tex} 6y+5x=6700 .............Dividing through by 2
{tex}\Rightarrow {/tex} 5x+6y=6700 ...........(2)
Multiplying equation (1) by 6 and equation (2) by 5, we get
36x+30y=39000 ...............(3)
25x+30y=33500 .......(4)
{tex}\Rightarrow {/tex}subtracting (3) and (4) we get x = 500
Substituting this value of x in equation (1), we get 6(500)+5y=6500
{tex}\Rightarrow {/tex} 3000+5y=6500
{tex}\Rightarrow {/tex} 5y=6500-3000
{tex}\Rightarrow {/tex} 5y=3500
{tex}\Rightarrow {/tex} {tex}y = \frac{{3500}}{5} = 700{/tex}
So, the solution of the equation (1) and (2) is x=500 and y=700
Hence, he invested ₹ 500 at the rate of 12% simple interest and ₹ 700 at the rate of 10% simple interest.
verification.Substituting x=500, y=700,
We find that both the equation (1) and (2) are satisfied as shown below:
6x + 5y=6(500)+5(700)=3000+3500=6500
5x+6y=5(500)+6(700)=2500+4200=6700
This verifies the solution.
Posted by Vineet Singh 7 years, 4 months ago
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Soham Deshpande 7 years, 4 months ago

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Sanjeet Yadav 7 years, 3 months ago
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