Related InterviewSolutions

• If `veca+vecb+vecc=vec0, |veca| = 3, |vecb| = 5, |vecc| = 7`, then angle between `veca` and `vecb` isA. ` ( pi ) /( 2 ) `B. ` ( pi ) /( 3 ) `C. ` ( pi ) /( 4 ) `D. ` ( pi ) /( 6 ) `
• If the position vectors of the vertices A, B and C are 6i, 6j and k respectively w.r.t origin O, then the volume of the tetrahedron OABC isA. ` 6 `B. ` 3 `C. ` ( 1 )/( 6 ) `D. ` (1 )/( 3 ) `
• `i(jxx k ) + j ( k xx i) + k (j xx i) ` is equal toA. ` 3 `B. ` 2 `C. `1`D. `0`
• The value of `int_0^oox/((1+x)(x^2+1))dx` isA. ` 2pi `B. ` ( pi ) /( 4 ) `C. ` ( pi ) /( 16 ) `D. ` ( pi ) /( 32 ) `
• The value of `int (dx)/(x(x^(n)+1))`A. ` ( 1 ) /( n ) log (( x^ n ) /( x ^n + 1 )) + C `B. `log (( x ^n + 1 ) /( x^n )) + C `C. ` ( 1 )/( n ) log (( x^n + 1 ) /( x^n )) + C `D. `log (( x^n ) /( x^n + 1 )) + C `
• Find a vector of magnitude 9, which is perpendicular to both vectors `4 hat i- hat j+3 hat ka n d-2 hat i+ hat j-2 hat k`.A. `3i + 6j - 6 k `B. ` 3i - 6j + 6k `C. `-3i + 6j + 6k `D. None of the above
• `int_0^pilog(1+cosx)dx` .A. ` - ( pi ) /( 2 ) log 2 `B. ` pi log "" ( 1 ) /( 2 ) `C. ` pi log 2 `D. ` ( pi ) /( 2 ) log 2 `
• The value of `int (dx)/(x(x^(n)+1))`A. ` ( 1 ) /( n ) log (( x^ n ) /( x ^n + 1 )) + C `B. `log (( x ^n + 1 ) /( x^n )) + C `C. ` ( 1 )/( n ) log (( x^n + 1 ) /( x^n )) + C `D. `log (( x^n ) /( x^n + 1 )) + C `
• The value of ` int ( ( x ^ 2 + 1 )) /( x ^ 4 + x ^ 2 + 1 ) dx ` isA. ` (1 ) /( sqrt 3 ) tan ^( - 1 ) { ( x - 1// x ) /( sqrt 3)} + C `B. ` ( 1 ) /( 2sqrt 3 ) log { ( ( x- 1 // x) - sqrt 3) /( (x - 1 // x ) + sqrt 3 } + C `C. ` tan ^( - 1 ) (( x + 1// x ) /(sqrt 3) ) + C `D. `tan^( - 1 ) (( x - 1//x )/ (sqrt 3 )) + C `
• `int sin(2x)/(sin^4x+cos^4x) dx`A. ` tan ^( - 1 ) (cot ^ 2 x ) + C `B. ` - tan ^( - 1 ) ( cos 2x ) + C `C. ` tan ^( - 1 ) ( sin 2x ) + C `D. ` tan ^( -1 ) ( tan ^ 2 x) +C `