Maths-

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Question

If the system of equations $x plus y plus z equals 6 comma$ $x plus 2 y plus lambda z equals 0 comma$ $x plus 2 y plus 3 z equals 10$ has no solution, then $lambda equals$

2
3
4
5

hint Hint:

Systems of linear equations do not have a solution when the graphs of their equations are parallel

The correct answer is: 3

$x plus y plus z equals 6 x plus 2 y plus lambda z equals 0 x plus 2 y plus 3 z equals 10 H e r e comma D equals open vertical bar table row 1 1 1 row 1 2 lambda row 1 2 3 end table close vertical bar equals 0 R subscript 2 rightwards arrow R subscript 3 open vertical bar table row 1 1 1 row 1 2 lambda row 0 0 cell 3 minus lambda end cell end table close vertical bar equals 0 1 open square brackets 2 open parentheses 3 minus lambda close parentheses minus 0 close square brackets minus 1 open square brackets 3 minus lambda minus 0 close square brackets equals 0 6 minus 2 lambda minus 3 plus lambda equals 0 3 minus lambda equals 0 therefore lambda equals 3$

In Cramer's rule, when the value of $D = 0$ and $D_{x}, D_{y}$ and $D_{z}$ are not all zero, then the system is inconsistent and there is no solution.

Two bars of thermal conductivities $K$ and $3 K$ and lengths $1 c m$ and $2 c m$ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $0 ℃$ and $100 ℃$ respectively (see figure), then the temperature $ϕ$ of the interface is

physics-General

General

Maths-

If $A equals open curly brackets table attributes columnalign left end attributes row i 0 row 0 cell negative i end cell end table close curly brackets$ then A² $equals$

Maths-General

General

maths-

The perimeter of a $straight triangle$ is 6 times the A.M of the sines of its angles if the side $text 'a' end text$ is , then the angle A is

maths-General

General

Maths-

If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

Maths-General

General

Maths-

The angles of a triangle are in the ratio 3:5:10.Then ratio of smallest to greatest side is

Maths-General

General

Maths-

$text If end text f left parenthesis 9 right parenthesis equals 9 comma f to the power of apostrophe left parenthesis 9 right parenthesis equals 4 comma text then end text fraction numerator L t over denominator x not stretchy rightwards arrow t end fraction fraction numerator square root of f left parenthesis x right parenthesis end root minus 3 over denominator square root of x minus 3 end fraction text equals end text$

Maths-General

General

Maths-

The sides of a triangle are $sin invisible function application alpha comma cos invisible function application alpha text and end text square root of 1 plus sin invisible function application alpha cos invisible function application alpha end root text for some end text 0 less than alpha less than pi over 2$ Then the greatest angle of the triangle is [AIEEE 2014]

Maths-General

General

Maths-

$L t subscript x not stretchy rightwards arrow negative straight infinity end subscript open square brackets fraction numerator x to the power of 4 sin invisible function application open parentheses 1 over x close parentheses plus x squared over denominator open parentheses 1 plus vertical line x vertical line cubed close parentheses end fraction close square brackets equals$

Maths-General

General

Maths-

If the sides of a triangle are in the ratio $x colon y colon square root of x squared plus x y plus y squared end root$ then greatest angle is

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x$ where are real and non-zero=

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x squared plus 5 x plus 3 over denominator x squared plus x plus 2 end fraction close parentheses to the power of x equals$

Maths-General

General

Maths-

In $straight triangle A B C text , if end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c text then end text 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals$

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of x plus 4 end exponent equals$

Maths-General

General

Maths-

If tan $A plus tan invisible function application B plus tan invisible function application C equals 3 square root of 3$ then the $straight capital delta to the power of k$ is

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 3 end exponent equals$

Maths-General

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If the system of equations has no solution, then

2 3 4 5

Systems of linear equations do not have a solution when the graphs of their equations are parallel

The correct answer is: 3

Related Questions to study

Two bars of thermal conductivities and and lengths and respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is and respectively (see figure), then the temperature of the interface is

Two bars of thermal conductivities and and lengths and respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is and respectively (see figure), then the temperature of the interface is

If then A2

If then A2

The perimeter of a is 6 times the A.M of the sines of its angles if the side is , then the angle A is

The perimeter of a is 6 times the A.M of the sines of its angles if the side is , then the angle A is

If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

The angles of a triangle are in the ratio 3:5:10.Then ratio of smallest to greatest side is

The angles of a triangle are in the ratio 3:5:10.Then ratio of smallest to greatest side is

The sides of a triangle are Then the greatest angle of the triangle is [AIEEE 2014]

The sides of a triangle are Then the greatest angle of the triangle is [AIEEE 2014]

If the sides of a triangle are in the ratio then greatest angle is

If the sides of a triangle are in the ratio then greatest angle is

where are real and non-zero=

where are real and non-zero=

In

In

If tan then the is

If tan then the is

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If the system of equations $x plus y plus z equals 6 comma$ $x plus 2 y plus lambda z equals 0 comma$ $x plus 2 y plus 3 z equals 10$ has no solution, then $lambda equals$

2
3
4
5

If $A equals open curly brackets table attributes columnalign left end attributes row i 0 row 0 cell negative i end cell end table close curly brackets$ then A² $equals$

If $A equals open curly brackets table attributes columnalign left end attributes row i 0 row 0 cell negative i end cell end table close curly brackets$ then A² $equals$

The perimeter of a $straight triangle$ is 6 times the A.M of the sines of its angles if the side $text 'a' end text$ is , then the angle A is

The perimeter of a $straight triangle$ is 6 times the A.M of the sines of its angles if the side $text 'a' end text$ is , then the angle A is

If the sides of a triangle are in the ratio $x colon y colon square root of x squared plus x y plus y squared end root$ then greatest angle is

If the sides of a triangle are in the ratio $x colon y colon square root of x squared plus x y plus y squared end root$ then greatest angle is

In $straight triangle A B C text , if end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c text then end text 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals$

In $straight triangle A B C text , if end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c text then end text 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals$

If tan $A plus tan invisible function application B plus tan invisible function application C equals 3 square root of 3$ then the $straight capital delta to the power of k$ is

If tan $A plus tan invisible function application B plus tan invisible function application C equals 3 square root of 3$ then the $straight capital delta to the power of k$ is