Maths-
General
Easy

Question

If the four faces of a tetrahedron are represented by the equations r with minus on top left parenthesis alpha i with minus on top plus beta j with minus on top right parenthesis equals 0 comma r with minus on top left parenthesis beta j with rightwards arrow on top plus gamma k with minus on top right parenthesis equals 0 comma r with minus on top left parenthesis gamma k with minus on top plus alpha i with rightwards arrow on top right parenthesis equals 0 and r with minus on top times left parenthesis alpha i with rightwards arrow on top plus beta j with minus on top plus gamma k with minus on top right parenthesis equals P then volume of the tetrahedron (in cubic units) is

  1. open vertical bar fraction numerator P to the power of 3 end exponent over denominator 6 alpha beta gamma end fraction close vertical bar    
  2. open vertical bar fraction numerator 4 P to the power of 3 end exponent over denominator 6 alpha beta gamma end fraction close vertical bar    
  3. open vertical bar fraction numerator 3 P to the power of 3 end exponent over denominator 6 alpha beta gamma end fraction close vertical bar    
  4. none of these    

The correct answer is: open vertical bar fraction numerator P to the power of 3 end exponent over denominator 6 alpha beta gamma end fraction close vertical bar

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If z subscript 1 comma z subscript 2 comma z subscript 3 are distinct non-zero complex numbers and a comma b comma c element of R to the power of plus end exponentsuch that fraction numerator a over denominator open vertical bar z subscript 1 end subscript minus z subscript 2 end subscript close vertical bar end fraction equals fraction numerator b over denominator open vertical bar z subscript 2 end subscript minus z subscript 3 end subscript close vertical bar end fraction equals fraction numerator c over denominator open vertical bar z subscript 3 end subscript minus z subscript 1 end subscript close vertical bar end fraction then fraction numerator a squared over denominator z subscript 1 minus z subscript 2 end fraction plus fraction numerator b squared over denominator z subscript 2 minus z subscript 3 end fraction plus fraction numerator c squared over denominator z subscript 3 minus z subscript 1 end fraction is always equal to

If z subscript 1 comma z subscript 2 comma z subscript 3 are distinct non-zero complex numbers and a comma b comma c element of R to the power of plus end exponentsuch that fraction numerator a over denominator open vertical bar z subscript 1 end subscript minus z subscript 2 end subscript close vertical bar end fraction equals fraction numerator b over denominator open vertical bar z subscript 2 end subscript minus z subscript 3 end subscript close vertical bar end fraction equals fraction numerator c over denominator open vertical bar z subscript 3 end subscript minus z subscript 1 end subscript close vertical bar end fraction then fraction numerator a squared over denominator z subscript 1 minus z subscript 2 end fraction plus fraction numerator b squared over denominator z subscript 2 minus z subscript 3 end fraction plus fraction numerator c squared over denominator z subscript 3 minus z subscript 1 end fraction is always equal to

Maths-General
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Chemistry-

6 CO subscript 2 plus 12 straight H subscript 2 straight O not stretchy ⟶ with text  Sun light  end text on top straight C subscript 6 straight H subscript 12 straight O subscript 6 plus 6 straight O subscript 2 plus 6 straight H subscript 2 straight O Equivalent weights of  and straight C subscript 6 straight H subscript 12 straight O subscript 6
respectively are

6 CO subscript 2 plus 12 straight H subscript 2 straight O not stretchy ⟶ with text  Sun light  end text on top straight C subscript 6 straight H subscript 12 straight O subscript 6 plus 6 straight O subscript 2 plus 6 straight H subscript 2 straight O Equivalent weights of  and straight C subscript 6 straight H subscript 12 straight O subscript 6
respectively are

Chemistry-General
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Maths-

Let a with minus on top equals i with minus on top plus j with minus on top plus k with minus on top comma b with minus on top equals negative i with minus on top plus j with minus on top plus k with minus on top comma c with minus on top equals i with minus on top minus j with minus on top plus k with minus on top and d with minus on top equals i with minus on top plus j with minus on top minus k with minus on top. Then, the line of intersection of planes one determined by stack a with ‾ on top comma stack b with ‾ on top and other determined by stack c with ‾ on top comma stack d with ‾ on top is perpendicular to

Let a with minus on top equals i with minus on top plus j with minus on top plus k with minus on top comma b with minus on top equals negative i with minus on top plus j with minus on top plus k with minus on top comma c with minus on top equals i with minus on top minus j with minus on top plus k with minus on top and d with minus on top equals i with minus on top plus j with minus on top minus k with minus on top. Then, the line of intersection of planes one determined by stack a with ‾ on top comma stack b with ‾ on top and other determined by stack c with ‾ on top comma stack d with ‾ on top is perpendicular to

Maths-General
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General
Maths-

A non - zero vector stack a with rightwards arrow on top is parallel to the line of intersection of the plane P subscript 1 end subscript determined by i with ˆ on top plus j with ˆ on top and i plus 2 j with ˆ on top and plane P subscript 2 end subscript determined by vector 2 i with ˆ on top minus j with ˆ on top and 3 i with ˆ on top plus 2 k with ˆ on top, then angle between stack a with rightwards arrow on top and vector i with ˆ on top minus 2 j with ˆ on top plus 2 k with ˆ on top is

A non - zero vector stack a with rightwards arrow on top is parallel to the line of intersection of the plane P subscript 1 end subscript determined by i with ˆ on top plus j with ˆ on top and i plus 2 j with ˆ on top and plane P subscript 2 end subscript determined by vector 2 i with ˆ on top minus j with ˆ on top and 3 i with ˆ on top plus 2 k with ˆ on top, then angle between stack a with rightwards arrow on top and vector i with ˆ on top minus 2 j with ˆ on top plus 2 k with ˆ on top is

Maths-General
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Let a,b,c be distinct non - negative numbers and the vectors a i with ˆ on top blank 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 comma i with ˆ on top plus j with ˆ on top plus b k with ˆ on top comma lie in a plane, then the quadratic equation a x to the power of 2 end exponent plus 2 c x plus b equals 0 has

Let a,b,c be distinct non - negative numbers and the vectors a i with ˆ on top blank 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 comma i with ˆ on top plus j with ˆ on top plus b k with ˆ on top comma lie in a plane, then the quadratic equation a x to the power of 2 end exponent plus 2 c x plus b equals 0 has

Maths-General
General
Maths-

If stack a with rightwards arrow on top comma stack b with rightwards arrow on top and stack c with rightwards arrow on top are anythree vectors forming a linearly independent system then for all theta element of R open square brackets stack a with minus on top c o s invisible function application theta plus stack b with rightwards arrow on top s i n invisible function application theta plus stack c blank with rightwards arrow on top c o s invisible function application 2 theta comma stack a with minus on top c o s invisible function application open parentheses fraction numerator 2 pi over denominator 3 end fraction plus theta close parentheses plus stack b with minus on top s i n invisible function application open parentheses fraction numerator 2 pi over denominator 3 end fraction plus theta close parentheses plus stack c with rightwards arrow on top c o s invisible function application 2 open parentheses fraction numerator 2 pi over denominator 3 end fraction plus theta close parentheses close open stack a with ‾ on top c o s invisible function application open parentheses theta minus fraction numerator 2 pi over denominator 3 end fraction close parentheses plus stack b with ‾ on top s i n invisible function application open parentheses theta minus fraction numerator 2 pi over denominator 3 end fraction close parentheses plus stack c with rightwards arrow on top c o s invisible function application 2 open parentheses theta minus fraction numerator 2 pi over denominator 3 end fraction close parentheses close square brackets equals

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Maths-General
parallel
General
Chemistry-

Select the correct statement

Select the correct statement

Chemistry-General
General
Chemistry-

Roasting of concentrated zinc sulphide ore is completed at the temperature of 1200 K to _______

Roasting of concentrated zinc sulphide ore is completed at the temperature of 1200 K to _______

Chemistry-General
General
Chemistry-

The final product (C) in the following reactions is:

The final product (C) in the following reactions is:

Chemistry-General
parallel
General
Chemistry-

How many structures of Fis possible?

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Chemistry-General
General
Chemistry-

Reactivity of M e M g B r with the following in the decreasing order is:
i)
ii)
iii)
iv) 

Reactivity of M e M g B r with the following in the decreasing order is:
i)
ii)
iii)
iv) 

Chemistry-General
General
Chemistry-

When is treated with C subscript 2 end subscript H subscript 5 end subscriptMgBr,followed by hydrolysis, the product is:

When is treated with C subscript 2 end subscript H subscript 5 end subscriptMgBr,followed by hydrolysis, the product is:

Chemistry-General
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General
Chemistry-

Consider the following halogen-containing compounds;
I) C H C l subscript 3 end subscript
II) C C l subscript 4 end subscript
III) C H subscript 2 end subscript C l subscript 2 end subscript
IV) C H subscript 3 end subscript C l
V)

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I) C H C l subscript 3 end subscript
II) C C l subscript 4 end subscript
III) C H subscript 2 end subscript C l subscript 2 end subscript
IV) C H subscript 3 end subscript C l
V)

Chemistry-General
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Which of the following mentioned positions in the given compound is more reactive towards electrophilic substitutions?

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Maths-General
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