An electrician can be paid under two schemes:

I. ₹600 and ₹50 per hour

II. ₹170 per hour

If job takes $n$ hours, for which values of $n$ does scheme I give better wages

1

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

Topic: AMU MCA 2016

2

If $y=\sec(\tan^{-1}x)$, then $\frac{dy}{dx}$ at $x=1$ is

Topic: AMU MCA 2016

3

If $y = \tan^{-1}(\sqrt{1+x^2} - x)$, then $\frac{dy}{dx}$ equals

Topic: AMU MCA 2016

4

If $f(x)=\frac{x}{2}-1$, then on the interval $[0,\pi]$

Topic: AMU MCA 2016

5

If $\lim_{x\to 0} \frac{\log(3+x) - \log(3-x)}{x} = K$, then $K$ is

Topic: AMU MCA 2016

6

If $x^2 + y^2 = t - \frac{1}{t}$ and $x^4 + y^4 = t^2 + \frac{1}{t^2}$, then $x^3 y \frac{dy}{dx}$ equals

Topic: AMU MCA 2016

7

If $x^y = e^{x-y}$, then $\frac{dy}{dx}$ is equal to

Topic: AMU MCA 2016

8

The sum of $n$ terms of the series $1^2 + (1^2+2^2) + (1^2+2^2+3^2) + \dots$ is

Topic: AMU MCA 2016

9

The minimum value of $9^x + 9^{1-x}$, $x \in R$ is

Topic: AMU MCA 2016

10

Given that the points $P(3,2,-4)$, $Q(5,4,-6)$ and $R(9,8,-10)$ are collinear, the ratio in which $Q$ divides $PR$ exte…

Topic: AMU MCA 2016

1

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

Topic: AMU MCA 2016

2

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

3

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

4

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

Topic: AMU MCA 2016

5

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

6

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

7

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

8

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

9

An $n$-tuple $(x_1,x_2,\dots,x_n)$ which satisfies all the constraints of a linear programming problem and for which th…

Topic: AMU MCA 2016

10

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