Maths-
General
Easy

Question

In a triangle ABC,fraction numerator a cos invisible function application A plus b cos invisible function application B plus c cos invisible function application C over denominator a plus b plus c end fraction is equal to -

  1. fraction numerator r over denominator R end fraction  
  2. fraction numerator R over denominator r end fraction  
  3. fraction numerator 2 r over denominator R end fraction  
  4. fraction numerator R over denominator 2 r end fraction  

The correct answer is: fraction numerator r over denominator R end fraction

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Statement-1 (A) : If stack a with rightwards arrow on top,stack b with rightwards arrow on top,stack c with rightwards arrow on topare unit coplanar vectors then [2stack a with rightwards arrow on topstack b with rightwards arrow on top 2stack b with rightwards arrow on topstack c with rightwards arrow on topstack a with rightwards arrow on top] = 0
Statement-2 (R) : [stack a with rightwards arrow on top,stack b with rightwards arrow on top, stack c with rightwards arrow on top] = 0

Statement-1 (A) : If stack a with rightwards arrow on top,stack b with rightwards arrow on top,stack c with rightwards arrow on topare unit coplanar vectors then [2stack a with rightwards arrow on topstack b with rightwards arrow on top 2stack b with rightwards arrow on topstack c with rightwards arrow on topstack a with rightwards arrow on top] = 0
Statement-2 (R) : [stack a with rightwards arrow on top,stack b with rightwards arrow on top, stack c with rightwards arrow on top] = 0

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Statement-1 (A) : If stack a with rightwards arrow on top,stack b with rightwards arrow on top,stack c with rightwards arrow on top are non coplanar vectors then vectors 2stack a with rightwards arrow on topstack b with rightwards arrow on top+3stack c with rightwards arrow on top,stack a with rightwards arrow on top+stack b with rightwards arrow on top–2stack c with rightwards arrow on top, stack a with rightwards arrow on top+stack b with rightwards arrow on top– 3stack c with rightwards arrow on top are also non coplanar.
Statement-2 (R) : Three vector Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text. are non coplanar then [Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text.]  0

Statement-1 (A) : If stack a with rightwards arrow on top,stack b with rightwards arrow on top,stack c with rightwards arrow on top are non coplanar vectors then vectors 2stack a with rightwards arrow on topstack b with rightwards arrow on top+3stack c with rightwards arrow on top,stack a with rightwards arrow on top+stack b with rightwards arrow on top–2stack c with rightwards arrow on top, stack a with rightwards arrow on top+stack b with rightwards arrow on top– 3stack c with rightwards arrow on top are also non coplanar.
Statement-2 (R) : Three vector Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text. are non coplanar then [Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text.]  0

Maths-General
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Statement-1 (A) : Three vectorstack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top are non coplanar then stack a with rightwards arrow on top+stack b with rightwards arrow on top, stack b with rightwards arrow on top+stack c with rightwards arrow on top,stack c with rightwards arrow on top + stack a with rightwards arrow on top are also non coplanar.
Statement-2 (R) :[stack a with rightwards arrow on top+stack b with rightwards arrow on top,stack b with rightwards arrow on top+stack c with rightwards arrow on top,stack c with rightwards arrow on top+stack a with rightwards arrow on top]=[stack a with rightwards arrow on top,stack b with rightwards arrow on top, stack c with rightwards arrow on top]

Statement-1 (A) : Three vectorstack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top are non coplanar then stack a with rightwards arrow on top+stack b with rightwards arrow on top, stack b with rightwards arrow on top+stack c with rightwards arrow on top,stack c with rightwards arrow on top + stack a with rightwards arrow on top are also non coplanar.
Statement-2 (R) :[stack a with rightwards arrow on top+stack b with rightwards arrow on top,stack b with rightwards arrow on top+stack c with rightwards arrow on top,stack c with rightwards arrow on top+stack a with rightwards arrow on top]=[stack a with rightwards arrow on top,stack b with rightwards arrow on top, stack c with rightwards arrow on top]

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Statement-1 (A) :Vectors –2stack i with hat on top+stack j with hat on top+stack k with hat on top, stack i with hat on top–2stack j with hat on top+stack k with hat on top &stack i with hat on top+stack j with hat on top–2stack k with hat on top are coplanar for only two values of .
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Statement-1 (A) :Vectors –2stack i with hat on top+stack j with hat on top+stack k with hat on top, stack i with hat on top–2stack j with hat on top+stack k with hat on top &stack i with hat on top+stack j with hat on top–2stack k with hat on top are coplanar for only two values of .
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A vector has components P and 1 with respect to a rectangular Cartesian system. If the axes are rotated through an angle  about the origin in the anticlockwise sense.
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Statement I : If three points P, Q, R have position vectorsstack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on toprespectively and2 stack a with rightwards arrow on top plus 3 stack b with rightwards arrow on top – 5 stack c with rightwards arrow on top equals 0, then the points P, Q, R must be collinear.
Statement II : If for three points A, B, C, ; Error converting from MathML to accessible text., then the points A, B, C must be collinear.

Statement I : If three points P, Q, R have position vectorsstack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on toprespectively and2 stack a with rightwards arrow on top plus 3 stack b with rightwards arrow on top – 5 stack c with rightwards arrow on top equals 0, then the points P, Q, R must be collinear.
Statement II : If for three points A, B, C, ; Error converting from MathML to accessible text., then the points A, B, C must be collinear.

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A vector has components p and 1 with respect to a rectangular Cartesian system. If the axes are rotated through an angle  about the origin in the anticlockwise sense.
Statement I : If the vector has component p + 2 and 1 with respect to the new system then p = –1
Statement II : Magnitude of vector with original
and new system remains same

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Statement I : If the vector has component p + 2 and 1 with respect to the new system then p = –1
Statement II : Magnitude of vector with original
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Let P, Q and R are points on sides AB, AC and AD of the parallelogram ABCD such that Error converting from MathML to accessible text.and Error converting from MathML to accessible text., where k1, k2 and k3 are non-zero positive scalars
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Reason(R): If stack r with rightwards arrow on top equals x stack i with hat on top plus y stack j with hat on top plus z stack k with hat on top, then equation stack r with rightwards arrow on top cross times left parenthesis stack i with hat on top plus 2 stack j with hat on top minus 3 stack k with hat on top right parenthesis equals 2 stack i with hat on top minus stack j with hat on top represent a straight line

Assertion(A): If stack r with rightwards arrow on top equals x stack i with hat on top plus y stack j with hat on top plus z stack k with hat on top then equation stack r with rightwards arrow on top cross times left parenthesis 2 stack i with hat on top minus stack j with hat on top plus 3 stack k with hat on top right parenthesis equals 3 stack i with hat on top plus stack k with hat on top represent a straight line.
Reason(R): If stack r with rightwards arrow on top equals x stack i with hat on top plus y stack j with hat on top plus z stack k with hat on top, then equation stack r with rightwards arrow on top cross times left parenthesis stack i with hat on top plus 2 stack j with hat on top minus 3 stack k with hat on top right parenthesis equals 2 stack i with hat on top minus stack j with hat on top represent a straight line

Maths-General
parallel

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