If \(\rho (A)\) = r  then which of the following is correct?

(a)

all the minors of order r which does not vanish

(b)

A has at least one minor of order r which does not vanish

(c)

A has at least one (r+1) order minor which vanishes

(d)

all (r+1) and higher order minors should not vanish

If f (x) is a continuous function and a < c < b, then \(\int_{a}^{c} f(x) d x+\int_{c}^{b} f(x) d x\) is _______.

(a)

\(\int_{a}^{b} f(x) d x-\int_{a}^{c} f(x) d x\)

(b)

\(\int_{a}^{c} f(x) d x-\int_{a}^{b} f(x) d x\)

(c)

\(\int_{a}^{b} f(x) d x\)

(d)

0

The value of \(\int _{ -3 }^{ 2 }{ |x+1| } dx\) is______.

(a)

4

(b)

\(\frac{1}{4}\)

(c)

8

(d)

2

The complementary function of \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } -\frac { dy }{ dx } \) = 0 is ______.

(a)

A + Be^x

(b)

(A + B) e^x

(c)

(Ax + B) e^x

(d)

Ae^x + B

The solution of \(\frac { dy }{ dx } \) = e^x-y is _____________

(a)

e^ye^x = c

(b)

y=log ce^x

(c)

y=log(e^x+c)

(d)

e^x+y = c

The value of Δ e^x is ______________

(a)

e^ax (e^h - 1)

(b)

e^x (1- e^h)

(c)

e^x (e^h - 1)

(d)

e^ax (1 - h)

If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to ________.

(a)

\(\sum { f(x) } \)

(b)

\(\sum[x+f(x)]\)

(c)

\(\sum { f(x)+x } \)

(d)

\(\sum { xp(x) } \)

If F(x) is the probability distribution function, then F(∞) is ________.

(a)

1

(b)

2

(c)

∞

(d)

0

The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are ________.

(a)

0.5443

(b)

0.4543

(c)

0.5543

(d)

0.4573

In a binomial distribution, n = 4, p(X = 0) = \(\frac{16}{81}\), then p(X = 4) is ___________

(a)

\(\frac{1}{16}\)

(b)

\(\frac{1}{81}\)

(c)

\(\frac{1}{27}\)

(d)

\(\frac{1}{8}\)