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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

System of equations x + y = 2, 2x + 2y = 3 has ______ - Mathematics and Statistics

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प्रश्न

System of equations x + y = 2, 2x + 2y = 3 has ______

पर्याय

  • no solution

  • only one solution

  • many finite solutions.

  • infinite solutions.

MCQ
रिकाम्या जागा भरा

उत्तर

no solution

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पाठ 1.2: Matrics - MCQ

संबंधित प्रश्‍न

Solve system of linear equations, using matrix method.

2x + y + z = 1

x – 2y – z =` 3/2`

3y – 5z = 9


Solve the system of the following equations:

`2/x+3/y+10/z = 4`

`4/x-6/y + 5/z = 1`

`6/x + 9/y - 20/x = 2`


Evaluate the following determinant:

\[\begin{vmatrix}\cos 15^\circ & \sin 15^\circ \\ \sin 75^\circ & \cos 75^\circ\end{vmatrix}\]


For what value of x the matrix A is singular? 
\[ A = \begin{bmatrix}1 + x & 7 \\ 3 - x & 8\end{bmatrix}\]


Without expanding, show that the value of the following determinant is zero:

\[\begin{vmatrix}49 & 1 & 6 \\ 39 & 7 & 4 \\ 26 & 2 & 3\end{vmatrix}\]


Without expanding, show that the value of the following determinant is zero:

\[\begin{vmatrix}\sin\alpha & \cos\alpha & \cos(\alpha + \delta) \\ \sin\beta & \cos\beta & \cos(\beta + \delta) \\ \sin\gamma & \cos\gamma & \cos(\gamma + \delta)\end{vmatrix}\]


Evaluate :

\[\begin{vmatrix}x + \lambda & x & x \\ x & x + \lambda & x \\ x & x & x + \lambda\end{vmatrix}\]


Evaluate the following:

\[\begin{vmatrix}a + x & y & z \\ x & a + y & z \\ x & y & a + z\end{vmatrix}\]


\[\begin{vmatrix}1 + a & 1 & 1 \\ 1 & 1 + a & a \\ 1 & 1 & 1 + a\end{vmatrix} = a^3 + 3 a^2\]


Prove the following identity:

\[\begin{vmatrix}2y & y - z - x & 2y \\ 2z & 2z & z - x - y \\ x - y - z & 2x & 2x\end{vmatrix} = \left( x + y + z \right)^3\]


Without expanding, prove that

\[\begin{vmatrix}a & b & c \\ x & y & z \\ p & q & r\end{vmatrix} = \begin{vmatrix}x & y & z \\ p & q & r \\ a & b & c\end{vmatrix} = \begin{vmatrix}y & b & q \\ x & a & p \\ z & c & r\end{vmatrix}\]


\[If \begin{vmatrix}p & b & c \\ a & q & c \\ a & b & r\end{vmatrix} = 0,\text{ find the value of }\frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c}, p \neq a, q \neq b, r \neq c .\]

 


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\[\begin{vmatrix}x + 1 & 3 & 5 \\ 2 & x + 2 & 5 \\ 2 & 3 & x + 4\end{vmatrix} = 0\]

 


​Solve the following determinant equation:

\[\begin{vmatrix}1 & 1 & x \\ p + 1 & p + 1 & p + x \\ 3 & x + 1 & x + 2\end{vmatrix} = 0\]

Find the area of the triangle with vertice at the point:

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Find the value of \[\lambda\]  so that the points (1, −5), (−4, 5) and \[\lambda\]  are collinear.


x − 2y = 4
−3x + 5y = −7


Prove that :

\[\begin{vmatrix}a + b & b + c & c + a \\ b + c & c + a & a + b \\ c + a & a + b & b + c\end{vmatrix} = 2\begin{vmatrix}a & b & c \\ b & c & a \\ c & a & b\end{vmatrix}\]

 


\[\begin{vmatrix}a + b + c & - c & - b \\ - c & a + b + c & - a \\ - b & - a & a + b + c\end{vmatrix} = 2\left( a + b \right) \left( b + c \right) \left( c + a \right)\]

3x + y = 19
3x − y = 23


3x + y + z = 2
2x − 4y + 3z = − 1
4x + y − 3z = − 11


5x − 7y + z = 11
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3x + 2y − 6z = 7


2x − 3y − 4z = 29
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3x − y + 5z = − 11


x + 2y = 5
3x + 6y = 15


If A = [aij] is a 3 × 3 scalar matrix such that a11 = 2, then write the value of |A|.

 

If the matrix \[\begin{bmatrix}5x & 2 \\ - 10 & 1\end{bmatrix}\]  is singular, find the value of x.


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Solve the following system of equations by matrix method:
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x − y + 2z = 7
3x + 4y − 5z = −5
2x − y + 3z = 12


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6x + 9y = 15


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4x + 4y − z = 2
6x + 6y + 2z = 3


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x + y − 6z = 0
x − y + 2z = 0
−3x + y + 2z = 0


Let \[X = \begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}, A = \begin{bmatrix}1 & - 1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1\end{bmatrix}\text{ and }B = \begin{bmatrix}3 \\ 1 \\ 4\end{bmatrix}\] . If AX = B, then X is equal to

 


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cos2θx + sin2θy + (1 + 4sin3θ)z = 0

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 ______.


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