Mathematics & Statistics Part 1
Chapters
Top questions
See all →- The shortest distance between the lines \(\vec r=(\hat i+2\hat j+\hat k)+\lambda(\hat i-\hat j+\hat k)\) and \(\vec r=(2\hat i-\hat j-\hat k)+\mu(2\hat i+\hat j+2\hat k)\) is Answer: D. 3/sqrt2 vec b₁×vec b₂=-3hat i+3hat k (magnitude 3sqrt2 ); vec a₂-vec a₁=hat i-3hat j-2hat k ; d=|-3-6|/3sqrt2=3/sqrt2 . 1
- The angle between the line \(\frac{x-1}{2}=\frac{y+2}{1}=\frac{z}{2}\) and the plane \(2x-y+2z=5\) is Answer: C. sin⁻¹(7/9) sinθ=|vec b·vec n|/|vec b||vec n|=|4-1+4|/3·3=7/9 . 1
- The distance of the point \((2,1,-1)\) from the plane \(x-2y+4z=9\) is Answer: C. 13/√(21) d=|2-2-4-9|/√(1+4+16)=13/√(21) . 1
- The maximum value of \(z=3x+2y\) subject to \(x+y\le4,\ x+3y\le6,\ x\ge0,\ y\ge0\) is Answer: C. 12 Corner points: (0,0)→0, (4,0)→12, (3,1)→11, (0,2)→4. Maximum =12 . 1
- The minimum value of \(z=2x+5y\) subject to \(x+y\ge4,\ x+3y\ge6,\ x,y\ge0\) is Answer: C. 11 Corner points of the (unbounded) region: (6,0)→12, (3,1)→11, (0,4)→20. Since both coefficients are positive, the minimum is 11... 1
- The negation of \(p\rightarrow q\) is Answer: B. pwedgesim q p→ qequivsim pvee q ; its negation is pwedgesim q . 1