question_answer1) Evaluate the determinant
View Answer play_arrowquestion_answer4) Evaluate \[\int_{0}^{2}{{{e}^{x-[x]}}dx.}\]
View Answer play_arrowquestion_answer10) Find the approximate value of \[\sqrt{25.2.}\]
View Answer play_arrowquestion_answer11) Evaluate \[\int_{-1}^{2}{(|x+1|+|x|+|x-1|)}\,dx\]
View Answer play_arrowquestion_answer12) Find the binomial distribution for which the mean is 4 and variance 3.
View Answer play_arrowquestion_answer14) For what value of k, is the function Continuous at x = 0?
View Answer play_arrowquestion_answer18) Evaluate \[\int{\frac{dx}{{{\sin }^{4}}x+{{\cos }^{4}}x}.}\]
View Answer play_arrowquestion_answer19) Evaluate \[\int_{0}^{\pi }{\frac{dx}{3+2\sin x+\cos x}.}\]
View Answer play_arrowFind the vector equation of the plane passing through the point \[(2,\,\,0,\,\,-\,1)\] and perpendicular to the line joining the points (1, 2, 3) and \[(3,\,\,-1,\,\,6).\] |
OR |
Find the equation of the line passing through the point (2, 1, 3) and perpendicular to the lines |
\[\frac{x-1}{1}=\frac{y+1}{2}=\frac{z-2}{3}\] |
and \[\frac{x-4}{-\,3}=\frac{y+1}{2}=\frac{z-1}{5}.\] |
A binary operation \['*'\] is defined on the set |
\[X=R-\{-\,1\}\] by \[x*y=x+y+xy,\] \[\forall x,\] \[y\in X.\] Check whether \['*'\] is commutative and associative. Find its identity element and also find the inverse of each element of X. |
OR |
If N denotes the set of all natural numbers and R be the relation on \[N\times N\] defined by (a, b)R |
(c, d), if \[ad(b+c)=bc(a+d).\]Show that R is an equivalence relation. |
Using integration, find the area of the triangular region whose vertices are |
P (1, 0), Q (2, 2) and R (3, 1). |
OR |
Using integration find the area of the following region. |
\[\{(x,\,\,y):|x-1|\,\,\le y\le \sqrt{5-{{x}^{2}}}\}\] |
Find the vector equation of the plane passing through the three points with position vectors \[\hat{i}+\hat{j}-2\hat{k},\] \[2\hat{i}-\hat{j}+\hat{k}\] and \[\hat{i}+2\hat{j}+\hat{k}.\] Also, find the coordinates of the point of intersection of this plane and the line \[\vec{r}=(3\hat{i}-\hat{j}-\hat{k})+\lambda (2\hat{i}-2\hat{j}+\hat{k}).\] |
OR |
Find the vector equation of the plane through the points \[(2,\,\,1,\,\,-\,1)\] and \[(-\,1,\,\,3,\,\,4)\] and perpendicular to the plane \[x-2y+4z=10.\] |
question_answer29) If a, b and c are all distinct and Show that \[abc(ab+bc+ca)=a+~b+c.\]
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