vitamin | Litre of milk | Kg of beaf | Doze of eggs | Minimum daily requirements |
A | 1 | 1 | 10 | 1 mg |
B | 100 | 10 | 10 | 50 mg |
C | 10 | 100 | 10 | 10 mg |
Cost | Rs. 1.00 | Rs. 1.10 | Rs. 0.50 |
Evaluate \[\int_{0}^{\pi /2}{\frac{{{\sin }^{4/5}}x}{{{\cos }^{4/5}}x+{{\sin }^{4/5}}x}\,dx.}\] |
OR |
Evaluate integrals as a limit of sum \[\int_{2}^{4}{{{2}^{x}}\,dx.}\] |
The probabilities of two students A and B coming to the school in time are \[\frac{3}{7}\] and \[\frac{5}{7},\] respectively. Assuming that the events, ?A coming in time' and 'B coming in time' are independent, find the probability, of only one of them coming to the school in time |
OR |
Find the probability that in 10 throws of a fair die, a score which is a multiple of 3 will be obtained in at least 8 of the throws. |
Brand P | Brand Q | |
Nitrogen | 3 | 3.5 |
Phosphoric acid | 1 | 2 |
Potash | 3 | 1.5 |
Chlorine | 1.5 | 2 |
Find the equation of the plane passing through the intersection of the planes |
\[\vec{r}\cdot (\hat{i}+3\hat{j})-6=0\] and \[\vec{r}\cdot (3\hat{i}-\hat{j}-4\hat{k})=0,\] whose perpendicular distance from origin is unity. |
OR |
If \[\vec{a}\cdot \vec{b}=\vec{a}\cdot \vec{c},\,\,\vec{a}\times \vec{b}=\vec{a}\times \vec{c}\] and \[\vec{a}\ne \vec{0},\] then prove that \[\vec{b}=\vec{c}.\] |
Let A = {1, 2, 3,..., 9} and R be the relation in \[A\times A\] defined by (a, b)R(c, d), if \[a+d=b+c\]for (a, b), (c, d) in \[A\times A.\] Prove that R is an equivalence relation and also obtain the equivalent class [(2, 5)]. |
OR |
Prove that the relation R in set A = {1, 2, 3, 4, 5} given by \[R=\{(a,\,b):|a-b|\]is even}is even} is an equivalence relation. |
Find the equation of tangents to the curve\[y=\cos (x+y),\] \[-\,2\pi \le x\le 2\pi ,\] that are parallel to the line \[x+2y=0.\] |
OR |
Find the radius of the smallest circle with centre on Y-axis and passing through the point (7, 3). |
Solve the following initial value problem. |
\[2xy+{{y}^{2}}-2{{x}^{2}}\frac{dy}{dx}=0,\] \[y(1)=2\] |
OR |
Solve the following differential equation. |
\[(1+y+{{x}^{2}}y)\,dx+(x+{{x}^{3}})dy=0\] |
You need to login to perform this action.
You will be redirected in
3 sec