Question 1 |
Strokes theorem connects
a line integral and a surface integral | |
a surface integral and a volume integral | |
a line integral and a volume integral | |
gradient of a function and its surface integral |
Question 1 Explanation:
A line integral and a surface integral is related by stroke's theorem
Question 2 |
A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is
0.0036 | |
0.1937 | |
0.2234 | |
0.3874 |
Question 2 Explanation:
Probability of defective item
P=0.1
Probability of non-defective item
Q=1-p=1-0.1=0.9
Probability that exactly 2 of the chosen items are defective
=^{10} C_{2}(P)^{2}(Q)^{8}
=^{10} C_{2}(0.1)^{2}(0.9)^{8}=0.1937
P=0.1
Probability of non-defective item
Q=1-p=1-0.1=0.9
Probability that exactly 2 of the chosen items are defective
=^{10} C_{2}(P)^{2}(Q)^{8}
=^{10} C_{2}(0.1)^{2}(0.9)^{8}=0.1937
Question 3 |
\int_{-a}^{a}(\sin ^{6} x + \sin ^{7} x)dx
is equal to
2\int_{0}^{a}(\sin ^{6} x)dx | |
2\int_{0}^{a}(\sin ^{7} x)dx | |
2\int_{0}^{a}(\sin ^{6} x + \sin ^{7} x)dx | |
zero |
Question 3 Explanation:
I=\int_{-a}^{a}\left(\sin ^{6} x+\sin ^{7} x \right) dx
= 2 \int_{0}^{a} \sin ^{6} x d x+0
( because \int_{0}^{a} \sin ^{7}x\cdot d x=0)
= 2 \int_{0}^{a} \sin ^{6} x d x+0
( because \int_{0}^{a} \sin ^{7}x\cdot d x=0)
Question 4 |
A is a 3 x 4 real matrix and Ax=b is an inconsistent system of equations. The highest possible rank of A is
1 | |
2 | |
3 | |
4 |
Question 4 Explanation:
C =[A: B]_{3 \times 5}
\therefore \rho\left[C_{3 \times 5}\right] \leq \min \{3,5\}
\because The system is inconsistent
\rho(A) \lt \rho(C)
\therefore \rho(A)\lt 3
Hence maximum possible rank of
A=2
\therefore \rho\left[C_{3 \times 5}\right] \leq \min \{3,5\}
\because The system is inconsistent
\rho(A) \lt \rho(C)
\therefore \rho(A)\lt 3
Hence maximum possible rank of
A=2
Question 5 |
Changing the order of the integration in the double integral I=\int_{0}^{8}\int_{\frac{x}{4}}^{2}f(x,y)dydx
leads to I=\int_{r}^{s}\int_{p}^{q}f(x,y)dxdy. What is q?
4y | |
16y^{2} | |
x | |
8 |
Question 5 Explanation:
\text { When } \quad I=\int_{0}^{8} \int_{x / 4}^{2} f(x \cdot y) dydx
I=\int_{0}^{2} \int_{0}^{4 y} f(x)dydx
I=\int_{0}^{2} \int_{0}^{4 y} f(x)dydx
There are 5 questions to complete.