An $n$-tuple $(x_1,x_2,\dots,x_n)$ which satisfies all the constraints of a linear programming problem and for which the objective function is maximum is called

1

If $f(x)=x^\alpha \log x$ and $f(0)=0$, then the value of $\alpha$ for which Rolle’s theorem can be applied in $[0,1]$ …

Topic: AMU MCA 2016

2

Let $R$ be a reflexive relation on a finite set $A$ having $n$ elements and let there be $m$ ordered pairs in $R$, then

Topic: AMU MCA 2016

3

A root of the equation $17x^2 + 17x \tan\left(2\tan^{-1}\frac{1}{5} - \frac{\pi}{4}\right) - 10 = 0$ is

Topic: AMU MCA 2016

4

A root of the equation $17x^2 + 17x \tan\left(2\tan^{-1}\frac{1}{5} - \frac{\pi}{4}\right) - 10 = 0$ is

Topic: AMU MCA 2016

5

The solution set of the equation $\sin^{-1} x = 2\tan^{-1} x$ is

Topic: AMU MCA 2016

6

The value of the expression $1 - \frac{\sin^2 y}{1+\cos y} + \frac{1+\cos y}{\sin y} - \frac{\sin y}{1-\cos y}$ is equ…

Topic: AMU MCA 2016

7

The value of $\frac{\sin^3 3\theta}{\sin^2 \theta} - \frac{\cos^2 3\theta}{\cos^2 \theta}$ is equal to

Topic: AMU MCA 2016

8

If $X = {4^n - 3n - 1 \mid n \in N}$ and $Y = {9(n-1) \mid n \in N}$, then

Topic: AMU MCA 2016

9

An electrician can be paid under two schemes:I. ₹600 and ₹50 per hourII. ₹170 per hourIf job takes $n$ hours, for which…

Topic: AMU MCA 2016

10

The value of $\sum_{n=1}^{13}(i^n + i^{n+1})$, where $i=\sqrt{-1}$ equals

Topic: AMU MCA 2016

1

Given the LPP:Minimize $f = 2x_1 - x_2$$x_1 \ge 0,\ x_2 \ge 0$$x_1 + x_2 \ge 5$$-x_1 + x_2 \le 1$$5x_1 + 4x_2 \le 40$Th…

Topic: AMU MCA 2016

2

If $49^n + 16n + \lambda$ is divisible by $64$ for all $n \in N$, then the least negative integral value of $\lambda$ is

Topic: AMU MCA 2016

3

A polygon has $44$ diagonals. The number of its sides are

Topic: AMU MCA 2016

4

The greatest value of the term independent of $x$, as $\alpha$ varies over $R$, in the expansion of $\left(x\cos\alpha…

Topic: AMU MCA 2016

5

The value of $\left(\frac{1+i}{1-i}\right)^{100}$ is equal to

Topic: AMU MCA 2016