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20, 191\4, 181\2

Posted by Kunal Saini 7 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Kunal Saini 7 years, 5 months ago

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(kx)2 + kx + 1 = (-4x)2 - x

Posted by Anurag Khobragade 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We have,
{tex}kx^2 + kx + 1 = -4x^2 - x{/tex}
{tex}\Rightarrow{/tex} {tex}kx^2 + 4x^2 + kx + x + 1 = 0{/tex}
{tex}\Rightarrow{/tex}{tex} (k + 4)x^2 + (k + 1)x + 1 = 0{/tex}
Here, a = k + 4, b = k + 1 and c = 1
{tex}\therefore{/tex} {tex}D = b^2 - 4ac{/tex}
= (k + 1)² - 4 {tex}\times{/tex} (k + 4) {tex}\times{/tex} (1)
{tex}= k^2 + 1 + 2k - 4k - 16{/tex}
{tex}= k^2 - 2k - 15{/tex}
{tex}\Rightarrow{/tex} {tex}D = k^2 - 2k - 15{/tex}
The given equation will have real and equal roots, if
D = 0
{tex}\Rightarrow{/tex} {tex}k^2 - 2k - 15 = 0{/tex}
{tex}\Rightarrow{/tex}{tex} k^2 - 5k + 3k - 15 = 0{/tex}
{tex}\Rightarrow{/tex} k(k - 5) + 3(k - 5) = 0
{tex}\Rightarrow{/tex} (k - 5)(k + 3) = 0
{tex}\Rightarrow{/tex} k - 5 = 0 or k + 3 = 0
{tex}\Rightarrow{/tex} k = 5 or k = -3

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Form an equation. A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. The ages of D and C differ by 40 years . Find the ages of A and B.

Posted by Varsha Yadav 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let the ages of A and B be x and y years respectively.
Then, age difference of A and B is 2 years.
{tex}\Rightarrow{/tex}x - y = {tex}\pm{/tex}2
A's father D is twice as old as A and B is twice as old as his sister C.
Then, D's age =2x years. and, C's age {tex}= \frac { y } { 2 }{/tex}years.
Clearly, D is older than C
The age of D and C differ by 40 years.
{tex}\therefore{/tex} {tex}2 x - \frac { y } { 2 } = 40 {/tex}
{tex}\Rightarrow 4 x - y = 80{/tex}
Thus, we have the following two systems of linear equations
x - y =2 ...............(i)
and, 4x - y =80 ...........(ii)
x - y = -2 ............(iii)
and, 4x - y=80 ..................(iv)
Subtracting equation (i) from equation (ii), we get
(x - y) - (4x - y)= 2 - 80
⇒ x - y - 4x + y = -78
⇒ - 3x = - 78
⇒ 3x =78
⇒x =26
Putting x =26 in equation (i), we get
x - y =2
⇒ 26 - y = 2
⇒ y =24
Subtracting equation (iv) from equation (iii), we get
{tex}- 3 x = - 82 {/tex}
{tex}\Rightarrow x = \frac { 82 } { 3 } = 27 \frac { 1 } { 3 }{/tex}
Putting {tex}x = \frac { 82 } { 3 }{/tex}in equation (iii), we get
{tex}y = \frac { 82 } { 3 } + 2 = \frac { 88 } { 3 } = 29 \frac { 1 } { 3 }{/tex}
Hence, A's age =26 years and B's age =24 years
or,
A's age {tex}= 27 \frac { 1 } { 3 }{/tex}Years and B's age {tex}29 \frac { 1 } { 3 }{/tex}years.

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Form an external point p, two tangent pT and PS are drawn to a circle with center o and radius r. If op =2r,show that ots =ost =30

Posted by Dodoya Shlok 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given,

In {tex}\triangle{/tex}OTS,
{tex}OT =OS {/tex}
{tex}\Rightarrow \quad \angle O T S = \angle O S T{/tex} ...(i)
In right {tex}\triangle OTP,{/tex}
{tex}\frac { \mathrm { OT } } { \mathrm { OP } } = \sin \angle \mathrm { TPO }{/tex}
{tex}\Rightarrow \frac { r } { 2 r } = \sin \angle \mathrm { TPO }{/tex}
{tex}\sin \angle \mathrm { TPO } = \frac { 1 } { 2 } \Rightarrow \angle \mathrm { TPO } = 30 ^ { \circ }{/tex}
Similarly {tex}\angle \mathrm { OPS } = 30 ^ { \circ }{/tex}
{tex}\Rightarrow \angle T P S = 30 ^ { \circ } + 30 ^ { \circ } = 60 ^ { \circ }{/tex}
Also {tex}\angle \mathrm { TPS } + \angle \mathrm { SOT } = 180 ^ { \circ }{/tex}
{tex}\Rightarrow \quad \angle \mathrm { SOT } = 120 ^ { \circ }{/tex}
In {tex}\triangle{/tex}SOT,
{tex}\angle \mathrm { SOT } + \angle \mathrm { OTS } + \angle \mathrm { OST } = 180 ^ { \circ }{/tex}
{tex}\Rightarrow 120 ^ { \circ } + 2 \angle \mathrm { OTS } = 180 ^ { \circ }{/tex}
{tex}\Rightarrow \angle \mathrm { OTS } = 30 ^ { \circ }{/tex} ...(ii)
From (i) and (ii)
{tex}\angle \mathrm { OTS } = \angle \mathrm { OST } = 30 ^ { \circ }{/tex}

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Solve the quadratic equations by completing the squares x2-10x+16

Posted by Abhijith Praseed 7 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Ramanujan Mondal 7 years, 5 months ago

x2-10x+16=x2-(8+2)x +16=x2-8x-2x+16=x(x-8)-2(x-8)=(x-8)(x-2)

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Agar hamare pass study hours kam ho to kya tution karna jaroori hain

Posted by Akash Choudhary 7 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Suraj Kumar 7 years, 5 months ago

Yes you can take the help of tution to cover your sulibus

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Kunal Singh 7 years, 5 months ago

If u think that in school u can cover subject such as sst English. Hindi so u can think about taking tuition of maths n science else if u think that u are good enough to study by ur own than self study at home?

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Which term of the A.P. :21,18,15..............is zero?

Posted by Om Khobragade 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

The given AP is
21,18,15......................,0
Here a=21 and d=18-21= -3 and a_n=0,n=?
{tex}\Rightarrow{/tex} a_n = a + (n - 1)d
{tex}\Rightarrow{/tex} 0 = a + (n - 1)d

Now on substitution of value of a and d we get
0 = 21 + (n - 1) (-3)

-21 =(n-1)(-3)
n - 1 = {tex}\frac{{ - 21}}{{ - 3}}{/tex}
n - 1 = 7
Hence n = 8.

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Find the greatest number of 6 digits exactly divisible by 24,15 and 36?

Posted by Deepthi J Gowda 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

The greater number of 6 digits is 999999.
LCM of 24, 15, and 36 is 360.
{tex}999999 = 360 \times 2777 + 279{/tex}
Required number is = 999999 - 279 = 999720

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Corresponding angle kya ha samajo

Posted by Prerika Lamba 7 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Om Khobragade 7 years, 5 months ago

The angles which occupy the same relative position at each intersection where a straight line crossess two others. If two lines are parallel, the corresponding angles are equal. Welcome

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Give the linear equation 2x + 3y _ 8 = 0, write another linear eqution in two variables such that the geometrical of the pair so formed is 1,intersecting 2, parllel lines 3, coincident lines

Posted by Adiya Alexander 7 years, 5 months ago

CBSE > Class 10 > Mathematics