MTH103
1. Find the component of \(2i+3j+k\) in the direction of \(3i-j.\)
\(\frac{\sqrt{10}}{10}\)
\(\frac{3\sqrt{10}}{10}\)
\({3\sqrt{10}}\)
\(\frac{3}{10}\)
2. Evaluate \((2i-3j)\cdot {(i+j-k)\times (3i-k)}\)
2
4
1
\(0\)
3. Find the equation of the straight line which passes through (-3, 5) and parallel to the line \(3y-5x+2=0\)
\(3y-5x-30=0\)
\(3y-5x+30=0\)
\(3y+5x+30=0\)
\(3y+5x-30=0\)
4. The general equation of a parabola is given as:
\(y^2=4ax\)
\(y=4ax^2\)
\(y=2ax^2\)
\(y=ax^2\)
5. If \(a=3i+4j-5k\) and \(b=-i+2j+6k\), then calculate the vector difference \(a-b.\)
\(4i-2j+11k\)
\(4i+2j+11k\)
\(4i-2j-11k\)
\(4i+2j-11k\)
6. Write the equation of this ellipse \( 25x^2+4y^2-50x-16y-59=0\) in the canonical form.
\(\frac{(x-1)^2}{4}+\frac{(y+2)^2}{25}=1\)
\(\frac{(x+1)^2}{4}+\frac{(y-2)^2}{25}=1\)
\(\frac{(x-1)^2}{4}-\frac{(y-2)^2}{25}=1\)
\(\frac{(x-1)^2}{4}+\frac{(y-2)^2}{25}=1\)
7. Weight and momentum are examples of which of the following
Vectors
Scalars
Magnitude
Direction
8. Find the gradient of the line joining (3, 2) and (7, 10).
1
2
-1
-2
9. Find the distance between the following pairs of points A(-3, -2) and B(1,-4).
\(2\sqrt{3}\)
\(3\sqrt{2}\)
\(5\sqrt{2}\)
\(2\sqrt{5}\)
10. Find the equation of the circle centre (3, -2), radius 2 units.
\(x^2+y^2-6x+4y-9=0\)
\(x^2+y^2-6x-4y-9=0\)
\(x^2+y^2-6x+4y+9=0\)
\(x^2+y^2-6x-4y+9=0\)
JOIN OUR TELEGRAM ON VIP NOUN UPDATES – FOR FREE PAST QUESTIONS AND EXAMS SUMMARIES
