Maths-
General
Easy

Question

Assertion (A): Let a with rightwards arrow on top equals 3 i with ˆ on top minus j with ˆ on top comma b with rightwards arrow on top equals 2 i with ˆ on top plus j with ˆ on top minus 3 k with ˆ on top. If stack b with rightwards arrow on top equals stack b with rightwards arrow on top subscript 1 end subscript plus stack b with rightwards arrow on top subscript 2 end subscript such that stack b with rightwards arrow on top subscript 1 end subscript is collinear with stack a with rightwards arrow on top and stack b with rightwards arrow on top subscript 2 end subscript is perpendicular to stack a with rightwards arrow on top is possible, then b with rightwards arrow on top subscript 2 equals i with ˆ on top plus 3 j with ˆ on top minus 3 k with ˆ on top.
Reason (R): If stack a with rightwards arrow on top and stack b with rightwards arrow on top are non-zero, non-collinear vectors, then stack b with rightwards arrow on top can be expressed as stack b with rightwards arrow on top equals stack b with rightwards arrow on top subscript 1 end subscript plus stack b with rightwards arrow on top subscript 2 end subscript where stack b with rightwards arrow on top subscript 1 end subscript is collinear with stack a with rightwards arrow on top and stack b with rightwards arrow on top subscript 2 end subscript is perpendicular to stack a with rightwards arrow on top

  1. Statement negative 1 is true, statement - 2 is true; statement negative 2 is a correct explanation for statement negative 1    
  2. Statement negative 1 is true, statement negative 2 is true statement negative 2 is not a correct explanation for statement negative 1    
  3. Statement - 1 is true, statement negative 2 is false    
  4. statement negative 1 is false, statement negative 2 is true    

The correct answer is: statement negative 1 is false, statement negative 2 is true

Related Questions to study

General
Maths-

Statement negative 1 colon If a comma b comma c are distinct non-negative numbers and the vectors â plus a j with ˆ on top plus c k with ˆ on top comma i with ˆ on top plus k with ˆ on top and c i with ˆ on top plus c j with ˆ on top plus b k with ˆ on top are coplanar then c is arithmetic mean of a and b.
Statement -2: Parallel vectors have proportional direction ratios.

Statement negative 1 colon If a comma b comma c are distinct non-negative numbers and the vectors â plus a j with ˆ on top plus c k with ˆ on top comma i with ˆ on top plus k with ˆ on top and c i with ˆ on top plus c j with ˆ on top plus b k with ˆ on top are coplanar then c is arithmetic mean of a and b.
Statement -2: Parallel vectors have proportional direction ratios.

Maths-General
General
Maths-

If a with ‾ on top equals i plus j minus k comma b with ‾ on top equals 2 i plus j minus 3 k and stack r with ‾ on top is a vector satisfying 2 stack r with ‾ on top plus stack r with ‾ on top cross times stack a with ‾ on top equals stack b with ‾ on top.
Assertion left parenthesis A right parenthesis colon stack r with ‾ on top can be expressed in terms of stack a with ‾ on top comma stack b with ‾ on top and stack a with ‾ on top cross times stack b with ‾ on top.
Reason left parenthesis R right parenthesis colon r with ‾ on top equals 1 over 7 left parenthesis 7 i plus 5 j minus 9 k plus a with ‾ on top cross times b with ‾ on top right parenthesis

If a with ‾ on top equals i plus j minus k comma b with ‾ on top equals 2 i plus j minus 3 k and stack r with ‾ on top is a vector satisfying 2 stack r with ‾ on top plus stack r with ‾ on top cross times stack a with ‾ on top equals stack b with ‾ on top.
Assertion left parenthesis A right parenthesis colon stack r with ‾ on top can be expressed in terms of stack a with ‾ on top comma stack b with ‾ on top and stack a with ‾ on top cross times stack b with ‾ on top.
Reason left parenthesis R right parenthesis colon r with ‾ on top equals 1 over 7 left parenthesis 7 i plus 5 j minus 9 k plus a with ‾ on top cross times b with ‾ on top right parenthesis

Maths-General
General
Maths-

If stack a with minus on top comma stack b with minus on top are non-zero vectors such that vertical line stack a with minus on top plus stack b with minus on top vertical line equals vertical line stack a with minus on top minus 2 stack b with minus on top vertical line then
Assertion left parenthesis A right parenthesis : Least value of stack a with ‾ on top times stack b with ‾ on top plus fraction numerator 4 over denominator vertical line stack b with ‾ on top vertical line to the power of 2 end exponent plus 2 end fraction is 2 square root of 2 minus 1
Reason (R): The expression stack a with minus on top times stack b with minus on top plus fraction numerator 4 over denominator vertical line stack b with minus on top vertical line to the power of 2 end exponent plus 2 end fraction is least when magnitude of stack b with minus on top is square root of 2 t a n invisible function application open parentheses fraction numerator pi over denominator 8 end fraction close parentheses end root

If stack a with minus on top comma stack b with minus on top are non-zero vectors such that vertical line stack a with minus on top plus stack b with minus on top vertical line equals vertical line stack a with minus on top minus 2 stack b with minus on top vertical line then
Assertion left parenthesis A right parenthesis : Least value of stack a with ‾ on top times stack b with ‾ on top plus fraction numerator 4 over denominator vertical line stack b with ‾ on top vertical line to the power of 2 end exponent plus 2 end fraction is 2 square root of 2 minus 1
Reason (R): The expression stack a with minus on top times stack b with minus on top plus fraction numerator 4 over denominator vertical line stack b with minus on top vertical line to the power of 2 end exponent plus 2 end fraction is least when magnitude of stack b with minus on top is square root of 2 t a n invisible function application open parentheses fraction numerator pi over denominator 8 end fraction close parentheses end root

Maths-General
parallel
General
Maths-

Statement- 1: If a with rightwards arrow on top equals 3 i with ˆ on top minus 3 j with ˆ on top plus k with ˆ on top comma b with rightwards arrow on top equals negative i with ˆ on top plus 2 j with ˆ on top plus k with ˆ on top and c with rightwards arrow on top equals i with ˆ on top plus j with ˆ on top plus k with ˆ on top and d with rightwards arrow on top equals 2 i with ˆ on top minus j with ˆ on top, then there exist real numbers alpha comma beta, gamma such that stack a with rightwards arrow on top equals alpha stack b with rightwards arrow on top plus beta stack c with rightwards arrow on top plus gamma d
Statement- 2: stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top comma stack d with rightwards arrow on top are four vectors in a 3 - dimensional space. If stack b with rightwards arrow on top comma stack c with rightwards arrow on top comma stack d with rightwards arrow on top are non-coplanar, then there exist real numbers alpha comma beta comma gamma such that stack a with rightwards arrow on top equals alpha stack b with rightwards arrow on top plus beta stack c with rightwards arrow on top plus gamma stack d with rightwards arrow on top

Statement- 1: If a with rightwards arrow on top equals 3 i with ˆ on top minus 3 j with ˆ on top plus k with ˆ on top comma b with rightwards arrow on top equals negative i with ˆ on top plus 2 j with ˆ on top plus k with ˆ on top and c with rightwards arrow on top equals i with ˆ on top plus j with ˆ on top plus k with ˆ on top and d with rightwards arrow on top equals 2 i with ˆ on top minus j with ˆ on top, then there exist real numbers alpha comma beta, gamma such that stack a with rightwards arrow on top equals alpha stack b with rightwards arrow on top plus beta stack c with rightwards arrow on top plus gamma d
Statement- 2: stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top comma stack d with rightwards arrow on top are four vectors in a 3 - dimensional space. If stack b with rightwards arrow on top comma stack c with rightwards arrow on top comma stack d with rightwards arrow on top are non-coplanar, then there exist real numbers alpha comma beta comma gamma such that stack a with rightwards arrow on top equals alpha stack b with rightwards arrow on top plus beta stack c with rightwards arrow on top plus gamma stack d with rightwards arrow on top

Maths-General
General
Maths-

Statement- 1 open parentheses S subscript 1 end subscript close parentheses:If A open parentheses x subscript 1 end subscript comma y subscript 1 end subscript close parentheses comma B open parentheses x subscript 2 end subscript comma y subscript 2 end subscript close parentheses comma C open parentheses x subscript 3 end subscript comma y subscript 3 end subscript close parentheses are non-collinear points. Then every point left parenthesis x comma y right parenthesis in the plane of capital delta to the power of text le  end text end exponent A B C, can be expressed in the form open parentheses fraction numerator k x subscript 1 end subscript plus l x subscript 2 end subscript plus m x subscript 3 end subscript over denominator k plus l plus m end fraction comma fraction numerator k y subscript 1 end subscript plus l y subscript 2 end subscript plus m y subscript 3 end subscript over denominator k plus l plus m end fraction close parentheses
Statement- 2 open parentheses S subscript 2 end subscript close parentheses:The condition for coplanarity of four points A left parenthesis stack a with ‾ on top right parenthesis comma B left parenthesis stack b with ‾ on top right parenthesis comma C left parenthesis stack c with ‾ on top right parenthesis comma D left parenthesis stack d with ‾ on top right parenthesis is that there exists scalars 1 comma m comma n comma p not all zeros such that  l a with ‾ on top plus m b with ‾ on top plus n c with ‾ on top plus p d with ‾ on top equals 0 with minus on top where l plus m plus n plus p equals 0.

Statement- 1 open parentheses S subscript 1 end subscript close parentheses:If A open parentheses x subscript 1 end subscript comma y subscript 1 end subscript close parentheses comma B open parentheses x subscript 2 end subscript comma y subscript 2 end subscript close parentheses comma C open parentheses x subscript 3 end subscript comma y subscript 3 end subscript close parentheses are non-collinear points. Then every point left parenthesis x comma y right parenthesis in the plane of capital delta to the power of text le  end text end exponent A B C, can be expressed in the form open parentheses fraction numerator k x subscript 1 end subscript plus l x subscript 2 end subscript plus m x subscript 3 end subscript over denominator k plus l plus m end fraction comma fraction numerator k y subscript 1 end subscript plus l y subscript 2 end subscript plus m y subscript 3 end subscript over denominator k plus l plus m end fraction close parentheses
Statement- 2 open parentheses S subscript 2 end subscript close parentheses:The condition for coplanarity of four points A left parenthesis stack a with ‾ on top right parenthesis comma B left parenthesis stack b with ‾ on top right parenthesis comma C left parenthesis stack c with ‾ on top right parenthesis comma D left parenthesis stack d with ‾ on top right parenthesis is that there exists scalars 1 comma m comma n comma p not all zeros such that  l a with ‾ on top plus m b with ‾ on top plus n c with ‾ on top plus p d with ‾ on top equals 0 with minus on top where l plus m plus n plus p equals 0.

Maths-General
General
Maths-

Assertion (A): The number of vectors of unit length and perpendicular to both the vectors. i with ˆ on top plus j with ˆ on top and j with ˆ on top plus k with ˆ on top is zero Reason
(R): stack a with ‾ on top and stack b with ‾ on top are two non-zero and non-parallel vectors it is true that stack a with ‾ on top cross times stack b with ‾ on top is perpendicular to the plane containing stack a with ‾ on top and stack b with ‾ on top

Assertion (A): The number of vectors of unit length and perpendicular to both the vectors. i with ˆ on top plus j with ˆ on top and j with ˆ on top plus k with ˆ on top is zero Reason
(R): stack a with ‾ on top and stack b with ‾ on top are two non-zero and non-parallel vectors it is true that stack a with ‾ on top cross times stack b with ‾ on top is perpendicular to the plane containing stack a with ‾ on top and stack b with ‾ on top

Maths-General
parallel
General
Maths-

The value of p for which the straight lines r with rightwards arrow on top equals left parenthesis 2 i with ˆ on top plus 9 j with ˆ on top plus 13 k with ˆ on top right parenthesis plus t left parenthesis i with ˆ on top plus 2 j with ˆ on top plus 3 k with ˆ on top right parenthesis and r with rightwards arrow on top equals left parenthesis negative 3 i with ˆ on top plus 7 j with ˆ on top plus p k with ˆ on top right parenthesis plus s left parenthesis negative i with ˆ on top plus 2 j with ˆ on top minus 3 k with ˆ on top right parenthesis are coplanar is

For such questions, we should know the condition for two lines to be coplanar. We should also know about the scalar triple product.

The value of p for which the straight lines r with rightwards arrow on top equals left parenthesis 2 i with ˆ on top plus 9 j with ˆ on top plus 13 k with ˆ on top right parenthesis plus t left parenthesis i with ˆ on top plus 2 j with ˆ on top plus 3 k with ˆ on top right parenthesis and r with rightwards arrow on top equals left parenthesis negative 3 i with ˆ on top plus 7 j with ˆ on top plus p k with ˆ on top right parenthesis plus s left parenthesis negative i with ˆ on top plus 2 j with ˆ on top minus 3 k with ˆ on top right parenthesis are coplanar is

Maths-General

For such questions, we should know the condition for two lines to be coplanar. We should also know about the scalar triple product.

General
Maths-

The position vector of the centre of the circle vertical line r with rightwards arrow on top vertical line equals 5 comma r with rightwards arrow on top times left parenthesis i with ˆ on top plus j with ˆ on top plus k with ˆ on top right parenthesis equals 3 square root of 3

The position vector of the centre of the circle vertical line r with rightwards arrow on top vertical line equals 5 comma r with rightwards arrow on top times left parenthesis i with ˆ on top plus j with ˆ on top plus k with ˆ on top right parenthesis equals 3 square root of 3

Maths-General
General
Maths-

Let stack r with rightwards arrow on top equals left parenthesis stack a with rightwards arrow on top cross times stack b with rightwards arrow on top right parenthesis s i n invisible function application x plus left parenthesis stack b with rightwards arrow on top cross times stack c with rightwards arrow on top right parenthesis c o s invisible function application y plus 2 left parenthesis stack c with rightwards arrow on top cross times stack a with rightwards arrow on top right parenthesis where stack a with rightwards arrow on top stack c with rightwards arrow on top are three noncoplanar vectors. If stack r with rightwards arrow on top is perpendicular to stack a with rightwards arrow on top plus stack b with rightwards arrow on top plus stack v with rightwards arrow on top, then minimum value of x squared plus y squared

Let stack r with rightwards arrow on top equals left parenthesis stack a with rightwards arrow on top cross times stack b with rightwards arrow on top right parenthesis s i n invisible function application x plus left parenthesis stack b with rightwards arrow on top cross times stack c with rightwards arrow on top right parenthesis c o s invisible function application y plus 2 left parenthesis stack c with rightwards arrow on top cross times stack a with rightwards arrow on top right parenthesis where stack a with rightwards arrow on top stack c with rightwards arrow on top are three noncoplanar vectors. If stack r with rightwards arrow on top is perpendicular to stack a with rightwards arrow on top plus stack b with rightwards arrow on top plus stack v with rightwards arrow on top, then minimum value of x squared plus y squared

Maths-General
parallel
General
Chemistry-

Which of the following represents Westrosol?

Which of the following represents Westrosol?

Chemistry-General
General
Chemistry-

Which of the following sequences would yield -nitro chlorobenzene (Z) from benzene?

Which of the following sequences would yield -nitro chlorobenzene (Z) from benzene?

Chemistry-General
General
Chemistry-

For the preparation of chloroethane

For the preparation of chloroethane

Chemistry-General
parallel
General
Chemistry-

 Which of the following statements is wrong about the reaction?

 Which of the following statements is wrong about the reaction?

Chemistry-General
General
Chemistry-

In the following reaction, the final product can be prepared by two paths (I) and (II).
Which of the following statements is correct?

In the following reaction, the final product can be prepared by two paths (I) and (II).
Which of the following statements is correct?

Chemistry-General
General
Chemistry-

The final product (X) in the following reaction is:

The final product (X) in the following reaction is:

Chemistry-General
parallel

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