\(\int_{-1}^{1} e^{|x|}\,dx =\)

The solution of the differential equation \(x\,dy - y\,dx = 0\) represents a family of

For two events \(A, B\): \(P(A\cup B) = \frac{7}{12}\), \(P(A) = \frac{5}{12}\), \(P(B) = \frac{3}{12}\). Then \(P(A\cap B) =\)

If \(a\) and \(b\) are the order and degree of the differential equation \(y'' + (y)^2 + 2y = 0\), then the value of \(2a+6b\) is:

The probability distribution of X is x | 0 | 1 | 2 | 3 | 4 P(X = x) | 0.1 | 2k | k | k | 2k Then \(\text{Var}(X) =\)

\(\int_{-1}^{1}(|x-2|+|x|)\,dx =\)

The maximum value of \(z = 4x+2y\) subject to the constraints \(2x+3y\le28\), \(x+y\le10\), \(x,y\ge0\) is:

\(\int \frac{dx}{x(x^5+3)}\) is equal to

Match List - I with List - II List - I | List - II A. R = {(x, y) : x and y are students of the same school} | I. Symmetric B. R = {(L1, L2) : L1 ⊥ L2, where L is a set of all lines} | II. One-one C. A function f : R → R defined by f(x) = 2 − 3x is | III. Bijective D. A function…