Maths-
General
Easy

Question

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

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

The correct answer is: Statement - 1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement negative 1

Related Questions to study

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
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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
General
Chemistry-

Ethylmercaptan is prepared by the reaction of the following, followed by hydrolysis

Ethylmercaptan is prepared by the reaction of the following, followed by hydrolysis

Chemistry-General
General
Maths-

Two adjacent sides of a parallelogram A B C D are given by stack A B with minus on top equals 2 i with ‾ on top plus 10 j with ‾ on top plus 11 k with ‾ on top and stack A D with minus on top equals negative i with ‾ on top plus 2 j with ‾ on top plus 2 k with ‾ on top. The side A D is rotated by an acute angle alpha in the plane of parallelogram so that A D becomes AD’. If A D makes a right angle with the side AB then the cosine of angle alpha is given by

Two adjacent sides of a parallelogram A B C D are given by stack A B with minus on top equals 2 i with ‾ on top plus 10 j with ‾ on top plus 11 k with ‾ on top and stack A D with minus on top equals negative i with ‾ on top plus 2 j with ‾ on top plus 2 k with ‾ on top. The side A D is rotated by an acute angle alpha in the plane of parallelogram so that A D becomes AD’. If A D makes a right angle with the side AB then the cosine of angle alpha is given by

Maths-General
General
Maths-

If a with ‾ on top equals 2 i with ‾ on top plus 3 j with ‾ on top plus k with ‾ on top comma a with ‾ on top cross times b with ‾ on top equals 7 i with ‾ on top minus 3 j with ‾ on top minus 5 k with ‾ on top comma a with ‾ on top times b with ‾ on top equals 1 then stack b with ‾ on top equals

If a with ‾ on top equals 2 i with ‾ on top plus 3 j with ‾ on top plus k with ‾ on top comma a with ‾ on top cross times b with ‾ on top equals 7 i with ‾ on top minus 3 j with ‾ on top minus 5 k with ‾ on top comma a with ‾ on top times b with ‾ on top equals 1 then stack b with ‾ on top equals

Maths-General
parallel

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