Maths-
General
Easy

Question

Let x to the power of 2 end exponent plus 3 y to the power of 2 end exponent equals 3 be the equation of an ellipse in the xy-plane. A and B are two points whose position vectors are negative square root of 3 i text  and  end text minus square root of 3 i plus 2 stack k with hat on top then the position vector of a point P on the ellipse such that angle A P B equals pi divided by 4 is

  1. plus-or-minus j    
  2. plus-or-minus left parenthesis stack i with hat on top plus j right parenthesis    
  3. plus-or-minus i    
  4. plus-or-minus stack k with rightwards arrow on top    

The correct answer is: plus-or-minus j


    Let stack p with rightwards arrow on top equals x stack i with rightwards arrow on top plus y stack j with rightwards arrow on top lies on the ellipse Now from the diagram, according to given conditions, AP=AB
    text or  end text left parenthesis x plus square root of 3 right parenthesis to the power of 2 end exponent plus left parenthesis y minus 0 right parenthesis to the power of 2 end exponent equals 4 text  or  end text left parenthesis x plus square root of 3 right parenthesis to the power of 2 end exponent plus y to the power of 2 end exponent equals 4
    solving (i) and (ii) we get x =0 and y =plus-or-minus 1
    Hence point P has position vector plus-or-minus j

    Related Questions to study

    General
    maths-

    A man travelling east at 8km/h finds that the wind seems to blow directly from the north. On doubling the speed, he finds that it appears to come from the north-east. The velocity of the wind is

    A man travelling east at 8km/h finds that the wind seems to blow directly from the north. On doubling the speed, he finds that it appears to come from the north-east. The velocity of the wind is

    maths-General
    General
    physics-

    A disc of radius R = 2m moves as shown in the figure, with a velocity of translation of 6 v subscript 0 end subscript of its centre of mass and an angular velocity of fraction numerator 2 v subscript 0 end subscript over denominator R end fraction. The distance (in m) of instantaneous axis of rotation from its centre of mass is

    A disc of radius R = 2m moves as shown in the figure, with a velocity of translation of 6 v subscript 0 end subscript of its centre of mass and an angular velocity of fraction numerator 2 v subscript 0 end subscript over denominator R end fraction. The distance (in m) of instantaneous axis of rotation from its centre of mass is

    physics-General
    General
    biology

    A plant of type ‘H’ will produce seeds with the genotype identical to seeds produced by the plants of

    A plant of type ‘H’ will produce seeds with the genotype identical to seeds produced by the plants of

    biologyGeneral
    parallel
    General
    biology

    Female gametes In the Punnet square given above, the genotype of the female parents and male parents respectively.

    Female gametes In the Punnet square given above, the genotype of the female parents and male parents respectively.

    biologyGeneral
    General
    chemistry-

    Phenol  Name of the above reaction is

    Phenol  Name of the above reaction is

    chemistry-General
    General
    chemistry-

    The product ‘A’ in the following reaction is

    The product ‘A’ in the following reaction is

    chemistry-General
    parallel
    General
    chemistry-

    Which will undergo a Friedel-Craft's alkylation reaction

    Which will undergo a Friedel-Craft's alkylation reaction

    chemistry-General
    General
    chemistry-

    Sp. vol. of cylindrical virus particle is 6.02 cross times 10 to the power of negative 2 end exponent cc divided by gm . Whose radius and length are 7 text Å  end text straight & 10 text Å end text respectively. If straight N subscript straight A equals 6.02 cross times 10 to the power of 23. Find mol. wt. of uirus -

    Sp. vol. of cylindrical virus particle is 6.02 cross times 10 to the power of negative 2 end exponent cc divided by gm . Whose radius and length are 7 text Å  end text straight & 10 text Å end text respectively. If straight N subscript straight A equals 6.02 cross times 10 to the power of 23. Find mol. wt. of uirus -

    chemistry-General
    General
    chemistry-

    H O 

    H O 

    chemistry-General
    parallel
    General
    chemistry-

    Which of the following reaction is correctly represented

    Which of the following reaction is correctly represented

    chemistry-General
    General
    chemistry-

    A 0.200 M KOH solutions is electrolyzed for 1.5 h using a current of 8.00 A How many moles of O2 were produced at the anode?

    A 0.200 M KOH solutions is electrolyzed for 1.5 h using a current of 8.00 A How many moles of O2 were produced at the anode?

    chemistry-General
    General
    chemistry-

    Electrolysis involves electronation and de-electronation at the respective electrodes Anode of electrolytic cell is the electrode at which de-electronation takes place whereas at cathode electronation is noticed If two or more ions of same charge are to be electonated or de electronated, the ion having laser discharge potential is discharged Discharge potential of anion refers for E0OP of E0RP as the case may be The products formed at either electrode is given in terms of Faraday's laws of electrolysis i.e. w equals fraction numerator blank E i t blank over denominator 96500 end fraction During electrolysis of CuSO4(aq), the pH of solution becomes

    Electrolysis involves electronation and de-electronation at the respective electrodes Anode of electrolytic cell is the electrode at which de-electronation takes place whereas at cathode electronation is noticed If two or more ions of same charge are to be electonated or de electronated, the ion having laser discharge potential is discharged Discharge potential of anion refers for E0OP of E0RP as the case may be The products formed at either electrode is given in terms of Faraday's laws of electrolysis i.e. w equals fraction numerator blank E i t blank over denominator 96500 end fraction During electrolysis of CuSO4(aq), the pH of solution becomes

    chemistry-General
    parallel
    General
    chemistry-

    Conductors allow the passage of electric current through them Metallic and electrolytic are the two types of conductors Current carriers in metallic and electrolytic conductors are free electrons and free ions respectively Specific conductance of conductivity of the electrolyte solution is given by the following relation :
    logical and subscript m end subscript equals K x fraction numerator 1000 over denominator M end fraction logical and subscript e end subscript equals K x fraction numerator 1000 over denominator blank N end fraction where, M and N are the molarity and normality of the solution respectively. Molar conductance of storage electrolyte depends on concentration : logical and subscript m end subscript equals logical and subscript m end subscript superscript 0 end superscript minus b square root of c where, logical and subscript m end subscript superscript 0 end superscript equals molar conductance at infinite dilution
    c= concentration of the solution b= constant
    The degrees of dissociation of weak electrolytes are calculated as: alpha equals fraction numerator logical and subscript m end subscript over denominator logical and subscript m end subscript superscript 0 end superscript end fraction equals fraction numerator logical and subscript e end subscript over denominator logical and subscript e end subscript superscript 0 end superscript end fraction
    For which of the following electrolytic solution logical and subscript m and logical and subscript e are equal ?

    Conductors allow the passage of electric current through them Metallic and electrolytic are the two types of conductors Current carriers in metallic and electrolytic conductors are free electrons and free ions respectively Specific conductance of conductivity of the electrolyte solution is given by the following relation :
    logical and subscript m end subscript equals K x fraction numerator 1000 over denominator M end fraction logical and subscript e end subscript equals K x fraction numerator 1000 over denominator blank N end fraction where, M and N are the molarity and normality of the solution respectively. Molar conductance of storage electrolyte depends on concentration : logical and subscript m end subscript equals logical and subscript m end subscript superscript 0 end superscript minus b square root of c where, logical and subscript m end subscript superscript 0 end superscript equals molar conductance at infinite dilution
    c= concentration of the solution b= constant
    The degrees of dissociation of weak electrolytes are calculated as: alpha equals fraction numerator logical and subscript m end subscript over denominator logical and subscript m end subscript superscript 0 end superscript end fraction equals fraction numerator logical and subscript e end subscript over denominator logical and subscript e end subscript superscript 0 end superscript end fraction
    For which of the following electrolytic solution logical and subscript m and logical and subscript e are equal ?

    chemistry-General
    General
    chemistry-

     A Galvanic cell consists of three compartments as shown in figure The first compartment contains ZnSO4 (1M) and III compartment contains CuSO4 (1M) The mid compartment contain NaNO3(M) Each compartment contains 1L solution:E subscript Z n to the power of 2 plus end exponent divided by Z n end subscript superscript o end superscript equals negative 0.76 semicolon E subscript C u to the power of 2 plus end exponent divided by C u end subscript superscript o end superscript equals plus 0.34
    The concentration of S O subscript 4 end subscript superscript 2 minus end superscript ion in III compartment after discharge of 0.1 F charge will be :

     A Galvanic cell consists of three compartments as shown in figure The first compartment contains ZnSO4 (1M) and III compartment contains CuSO4 (1M) The mid compartment contain NaNO3(M) Each compartment contains 1L solution:E subscript Z n to the power of 2 plus end exponent divided by Z n end subscript superscript o end superscript equals negative 0.76 semicolon E subscript C u to the power of 2 plus end exponent divided by C u end subscript superscript o end superscript equals plus 0.34
    The concentration of S O subscript 4 end subscript superscript 2 minus end superscript ion in III compartment after discharge of 0.1 F charge will be :

    chemistry-General
    General
    chemistry-

     A Galvanic cell consists of three compartments as shown in figure The first compartment contains ZnSO4 (1M) and III compartment contains CuSO4 (1M) The mid compartment contain NaNO3(M) Each compartment contains 1L solution:E subscript Z n to the power of 2 plus end exponent divided by Z n end subscript superscript o end superscript equals negative 0.76 semicolon E subscript C u to the power of 2 plus end exponent divided by C u end subscript superscript o end superscript equals plus 0.34
    The concentration of N O subscript 3 end subscript superscript minus end superscript in mid compartment after discharge of 0.1F of charge will be:

     A Galvanic cell consists of three compartments as shown in figure The first compartment contains ZnSO4 (1M) and III compartment contains CuSO4 (1M) The mid compartment contain NaNO3(M) Each compartment contains 1L solution:E subscript Z n to the power of 2 plus end exponent divided by Z n end subscript superscript o end superscript equals negative 0.76 semicolon E subscript C u to the power of 2 plus end exponent divided by C u end subscript superscript o end superscript equals plus 0.34
    The concentration of N O subscript 3 end subscript superscript minus end superscript in mid compartment after discharge of 0.1F of charge will be:

    chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.