Maths-
General
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Question

Assertion(A): Let A left parenthesis stack a with rightwards arrow on top right parenthesis comma B left parenthesis stack b with rightwards arrow on top right parenthesis and C left parenthesis stack c with rightwards arrow on top right parenthesis be three points such that stack a with rightwards arrow on top equals 2 stack i with hat on top plus stack j with hat on top plus stack k with hat on top comma stack b with rightwards arrow on top equals 3 stack i with hat on top minus stack j with hat on top plus 3 stack k with hat on top and stack c with rightwards arrow on top equals – stack i with hat on top plus 7 stack j with hat on top minus 5 stack k with hat on top then OABC is a tetrahedron.
Reason(R): Let A left parenthesis stack a with rightwards arrow on top right parenthesis comma B left parenthesis stack b with rightwards arrow on top right parenthesis andC left parenthesis stack c with rightwards arrow on top right parenthesis be three points such that stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top are non-coplanar, then OABC is a tetrahedron, where O is the origin.

  1. If both (A) and (R) are true, and (R) is the correct explanation of (A).  
  2. If both (A) and (R) are true but (R) is not the correct explanation of (A).  
  3. If (A) is true but (R) is false.  
  4. If (A) is false but (R) is true.  

The correct answer is: If (A) is false but (R) is true.


    Since stack a with rightwards arrow on top. left parenthesis stack b with rightwards arrow on top cross times stack c with rightwards arrow on top right parenthesis = 0
    stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on topare coplanar

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    Assertion: If stack a with ̄ on top× stack b with ̄ on top= stack c with ̄ on top× stack d with ̄ on top, and stack a with ̄ on top×stack c with ̄ on top= stack b with ̄ on top× stack d with ̄ on top then stack a with ̄ on topstack d with ̄ on top is perpendicular to stack b with ̄ on topstack c with ̄ on top.
    Reason: If stack r with ̄ on topis perpendicular tostack q with ̄ on topthen stack r with ̄ on top.stack q with ̄ on top= 0

    Assertion: If stack a with ̄ on top× stack b with ̄ on top= stack c with ̄ on top× stack d with ̄ on top, and stack a with ̄ on top×stack c with ̄ on top= stack b with ̄ on top× stack d with ̄ on top then stack a with ̄ on topstack d with ̄ on top is perpendicular to stack b with ̄ on topstack c with ̄ on top.
    Reason: If stack r with ̄ on topis perpendicular tostack q with ̄ on topthen stack r with ̄ on top.stack q with ̄ on top= 0

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    Assertion: 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–stack j with hat on top+stack k with hat on topand 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 .
    Reason: Three vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on topare coplanar if stack a with rightwards arrow on top.(stack b with rightwards arrow on top× stack c with rightwards arrow on top) = stack 0 with rightwards arrow on top.

    Assertion: 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–stack j with hat on top+stack k with hat on topand 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 .
    Reason: Three vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on topare coplanar if stack a with rightwards arrow on top.(stack b with rightwards arrow on top× stack c with rightwards arrow on top) = stack 0 with rightwards arrow on top.

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    Assertion (A): If vector stack a with rightwards arrow on top and stack b with rightwards arrow on topare linearly dependent, then vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top must be dependent.
    Reason (R): If vector stack a with rightwards arrow on top and stack b with rightwards arrow on top are linearly independent, then vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top must be linearly independent, where vector stack c with rightwards arrow on top is non-zero.

    Assertion (A): If vector stack a with rightwards arrow on top and stack b with rightwards arrow on topare linearly dependent, then vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top must be dependent.
    Reason (R): If vector stack a with rightwards arrow on top and stack b with rightwards arrow on top are linearly independent, then vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top must be linearly independent, where vector stack c with rightwards arrow on top is non-zero.

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    General
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    Assertion: If in a ABC ; Error converting from MathML to accessible text. = Error converting from MathML to accessible text.Error converting from MathML to accessible text. and Error converting from MathML to accessible text. = Error converting from MathML to accessible text. ; |Error converting from MathML to accessible text.|  |Error converting from MathML to accessible text.|, then the value of cos 2A + cos 2B + cos 2C is – 1.
    Reason: If in ABC, C = 90º, then cos 2A + cos 2B + cos 2C = – 1.

    Assertion: If in a ABC ; Error converting from MathML to accessible text. = Error converting from MathML to accessible text.Error converting from MathML to accessible text. and Error converting from MathML to accessible text. = Error converting from MathML to accessible text. ; |Error converting from MathML to accessible text.|  |Error converting from MathML to accessible text.|, then the value of cos 2A + cos 2B + cos 2C is – 1.
    Reason: If in ABC, C = 90º, then cos 2A + cos 2B + cos 2C = – 1.
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    If stack a with ̄ on top comma stack b with ̄ on top comma stack c with ̄ on top are noncoplanar vectors and stack r with rightwards arrow on top equals left parenthesis stack a with ̄ on top cross times stack b with ̄ on top right parenthesis cross times left parenthesis stack a with ̄ on top cross times stack c with ̄ on top right parenthesis.
    Assertion: stack r with ̄ on topand stack a with ̄ on top are linearly dependent
    Reason: stack r with rightwards arrow on topis r to each of three stack a with ̄ on top comma stack b with ̄ on top comma & stack c with ̄ on top.

    If stack a with ̄ on top comma stack b with ̄ on top comma stack c with ̄ on top are noncoplanar vectors and stack r with rightwards arrow on top equals left parenthesis stack a with ̄ on top cross times stack b with ̄ on top right parenthesis cross times left parenthesis stack a with ̄ on top cross times stack c with ̄ on top right parenthesis.
    Assertion: stack r with ̄ on topand stack a with ̄ on top are linearly dependent
    Reason: stack r with rightwards arrow on topis r to each of three stack a with ̄ on top comma stack b with ̄ on top comma & stack c with ̄ on top.

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    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

    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

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    Assertion(A) : Let A left parenthesis stack a with rightwards arrow on top right parenthesis comma B left parenthesis stack b with rightwards arrow on top right parenthesis and C left parenthesis stack c with rightwards arrow on top right parenthesis be three points such that stack a with rightwards arrow on top equals 2 stack i with hat on top plus stack j with hat on top plus stack k with hat on top comma stack b with rightwards arrow on top equals 3 stack i with hat on top minus stack j with hat on top plus 3 stack k with hat on top and stack c with rightwards arrow on top equals – stack i with hat on top plus 7 stack j with hat on top minus 5 stack k with hat on top then OABC is a tetrahedron.
    Reason(R) : Let A left parenthesis stack a with rightwards arrow on top right parenthesis comma B left parenthesis stack b with rightwards arrow on top right parenthesis andC left parenthesis stack c with rightwards arrow on top right parenthesis be three points such that stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top are non-coplanar, then OABC is a tetrahedron, where O is the origin.

    Assertion(A) : Let A left parenthesis stack a with rightwards arrow on top right parenthesis comma B left parenthesis stack b with rightwards arrow on top right parenthesis and C left parenthesis stack c with rightwards arrow on top right parenthesis be three points such that stack a with rightwards arrow on top equals 2 stack i with hat on top plus stack j with hat on top plus stack k with hat on top comma stack b with rightwards arrow on top equals 3 stack i with hat on top minus stack j with hat on top plus 3 stack k with hat on top and stack c with rightwards arrow on top equals – stack i with hat on top plus 7 stack j with hat on top minus 5 stack k with hat on top then OABC is a tetrahedron.
    Reason(R) : Let A left parenthesis stack a with rightwards arrow on top right parenthesis comma B left parenthesis stack b with rightwards arrow on top right parenthesis andC left parenthesis stack c with rightwards arrow on top right parenthesis be three points such that stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top are non-coplanar, then OABC is a tetrahedron, where O is the origin.

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    Assertion : If stack a with ̄ on top× stack b with ̄ on top= stack c with ̄ on top× stack d with ̄ on top, and stack a with ̄ on top×stack c with ̄ on top= stack b with ̄ on top× stack d with ̄ on top then stack a with ̄ on topstack d with ̄ on top is perpendicular to stack b with ̄ on topstack c with ̄ on top.
    Reason : If stack r with ̄ on topis perpendicular tostack q with ̄ on topthen stack r with ̄ on top.stack q with ̄ on top= 0

    Assertion : If stack a with ̄ on top× stack b with ̄ on top= stack c with ̄ on top× stack d with ̄ on top, and stack a with ̄ on top×stack c with ̄ on top= stack b with ̄ on top× stack d with ̄ on top then stack a with ̄ on topstack d with ̄ on top is perpendicular to stack b with ̄ on topstack c with ̄ on top.
    Reason : If stack r with ̄ on topis perpendicular tostack q with ̄ on topthen stack r with ̄ on top.stack q with ̄ on top= 0

    Maths-General
    parallel
    General
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    Assertion : 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–stack j with hat on top+stack k with hat on topand 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 .
    Reason : Three vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on topare coplanar if stack a with rightwards arrow on top.(stack b with rightwards arrow on top× stack c with rightwards arrow on top) = stack 0 with rightwards arrow on top.

    Assertion : 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–stack j with hat on top+stack k with hat on topand 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 .
    Reason : Three vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on topare coplanar if stack a with rightwards arrow on top.(stack b with rightwards arrow on top× stack c with rightwards arrow on top) = stack 0 with rightwards arrow on top.

    Maths-General
    General
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    Assertion (A) : If vector stack a with rightwards arrow on top and stack b with rightwards arrow on topare linearly dependent, then vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top must be dependent.
    Reason (R) : If vector stack a with rightwards arrow on top and stack b with rightwards arrow on top are linearly independent, then vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top must be linearly independent, where vector stack c with rightwards arrow on top is non-zero.

    Assertion (A) : If vector stack a with rightwards arrow on top and stack b with rightwards arrow on topare linearly dependent, then vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top must be dependent.
    Reason (R) : If vector stack a with rightwards arrow on top and stack b with rightwards arrow on top are linearly independent, then vectors stack a with rightwards arrow on top, stack b with rightwards arrow on top, stack c with rightwards arrow on top must be linearly independent, where vector stack c with rightwards arrow on top is non-zero.

    Maths-General
    General
    Maths-

    Assertion: If in a ABC ; Error converting from MathML to accessible text. = Error converting from MathML to accessible text.Error converting from MathML to accessible text. and Error converting from MathML to accessible text. = Error converting from MathML to accessible text. ; |Error converting from MathML to accessible text.|  |Error converting from MathML to accessible text.|, then the value of cos 2A + cos 2B + cos 2C is – 1.
    Reason: If in ABC, C = 90º, then cos 2A + cos 2B + cos 2C = – 1.

    Assertion: If in a ABC ; Error converting from MathML to accessible text. = Error converting from MathML to accessible text.Error converting from MathML to accessible text. and Error converting from MathML to accessible text. = Error converting from MathML to accessible text. ; |Error converting from MathML to accessible text.|  |Error converting from MathML to accessible text.|, then the value of cos 2A + cos 2B + cos 2C is – 1.
    Reason: If in ABC, C = 90º, then cos 2A + cos 2B + cos 2C = – 1.
    Maths-General

    parallel
    General
    Maths-

    If stack a with ̄ on top comma stack b with ̄ on top comma stack c with ̄ on top are noncoplanar vectors and stack r with rightwards arrow on top equals left parenthesis stack a with ̄ on top cross times stack b with ̄ on top right parenthesis cross times left parenthesis stack a with ̄ on top cross times stack c with ̄ on top right parenthesis.
    Assertion : stack r with ̄ on topand stack a with ̄ on top are linearly dependent
    Reason : stack r with rightwards arrow on topis r to each of three stack a with ̄ on top comma stack b with ̄ on top comma & stack c with ̄ on top.

    If stack a with ̄ on top comma stack b with ̄ on top comma stack c with ̄ on top are noncoplanar vectors and stack r with rightwards arrow on top equals left parenthesis stack a with ̄ on top cross times stack b with ̄ on top right parenthesis cross times left parenthesis stack a with ̄ on top cross times stack c with ̄ on top right parenthesis.
    Assertion : stack r with ̄ on topand stack a with ̄ on top are linearly dependent
    Reason : stack r with rightwards arrow on topis r to each of three stack a with ̄ on top comma stack b with ̄ on top comma & stack c with ̄ on top.

    Maths-General
    General
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    Let Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text. denote the sides of a regular hexagon.
    Assertion : Error converting from MathML to accessible text.× (Error converting from MathML to accessible text.+Error converting from MathML to accessible text.)  Error converting from MathML to accessible text.
    Reason : Error converting from MathML to accessible text.× Error converting from MathML to accessible text.=Error converting from MathML to accessible text. & Error converting from MathML to accessible text.×Error converting from MathML to accessible text.= Error converting from MathML to accessible text.

    Let Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text., Error converting from MathML to accessible text. denote the sides of a regular hexagon.
    Assertion : Error converting from MathML to accessible text.× (Error converting from MathML to accessible text.+Error converting from MathML to accessible text.)  Error converting from MathML to accessible text.
    Reason : Error converting from MathML to accessible text.× Error converting from MathML to accessible text.=Error converting from MathML to accessible text. & Error converting from MathML to accessible text.×Error converting from MathML to accessible text.= Error converting from MathML to accessible text.

    Maths-General
    General
    Maths-

    Assertion : Let stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top & stack d with rightwards arrow on top are position vectors of four points A, B, C & D and 3 stack a with rightwards arrow on top minus 2 stack b with rightwards arrow on top plus 5 stack c with rightwards arrow on top minus 6 stack d with rightwards arrow on top equals stack 0 with rightwards arrow on top then points A, B, C and D are coplanar.
    Reason : Three non-zero, linearly dependent co-initial vectors (Error converting from MathML to accessible text.¸Error converting from MathML to accessible text. & Error converting from MathML to accessible text.) are coplanar.

    Assertion : Let stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top & stack d with rightwards arrow on top are position vectors of four points A, B, C & D and 3 stack a with rightwards arrow on top minus 2 stack b with rightwards arrow on top plus 5 stack c with rightwards arrow on top minus 6 stack d with rightwards arrow on top equals stack 0 with rightwards arrow on top then points A, B, C and D are coplanar.
    Reason : Three non-zero, linearly dependent co-initial vectors (Error converting from MathML to accessible text.¸Error converting from MathML to accessible text. & Error converting from MathML to accessible text.) are coplanar.

    Maths-General
    parallel

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