The system of equations 4x + 6y = 5, 6x + 9y = 7 has _______.

(a)

a unique solution

(b)

no solution

(c)

infinitely many solutions

(d)

none of these

Cramer’s rule is applicable only to get an unique solution when _______.

(a)

\({ \triangle }_{ z }\neq 0\)

(b)

\({ \triangle }_{ x }\neq 0\)

(c)

\({ \triangle } \neq 0\)

(d)

\({ \triangle }_{ y }\neq 0\)

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 given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.

(a)

40

(b)

\(\frac{41}{2}\)

(c)

\(\frac{40}{3}\)

(d)

\(\frac{41}{5}\)

The area bounded by the parabola y² = 4x bounded by its latus rectum is ________.

(a)

\(\frac { 16 }{ 3 } \) sq.units

(b)

\(\frac { 8 }{ 3 } \) sq.units

(c)

\(\frac { 72 }{ 3 } \) sq.units

(d)

\(\frac { 1 }{ 3 } \) sq.units

The particular integral of the differential equation is \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx } \) + 16y = 2e^4x ______.

(a)

\(\frac { { x }^{ 2 }{ e }^{ 4x } }{ 2! } \)

(b)

\(\frac { { e }^{ 4x } }{ 2! } \)

(c)

x²e^4x

(d)

xe^4x

If c is a constant, then Δc.f(x) ______________

(a)

0

(b)

c.f(Δx)

(c)

c.Δf(x)

(d)

f(Δcx)

A listing of all the outcomes of an experiment and the probability associated with each outcome is called ________.

(a)

probability distribution

(b)

probability density function

(c)

attributes

(d)

distribution function

Given E(X + c) = 8 and E(X - c) = 12, then the value of c is ___________

(a)

-2

(b)

4

(c)

-4

(d)

2

If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to ________.

(a)

(2/3)⁶

(b)

(2/3)⁵(1/3)

(c)

(1/3)⁶

(d)

4(2/3)⁶