PGDBA 2017

Instructions

For the following questions answer them individually

Question 31

If

$$A_n = \frac{1.2.3 + 2.3.4 + 3.4.5 + .... upto n terms}{n(1.2 + 2.3 + 3.4 + .... upto n terms)}$$ 

then $$\lim_{n \rightarrow \infty} A_n$$ is

Question 32

The function $$f: R \rightarrow R$$, defined by $$f(x) = x^3 - 3x^2 + 6x - 5$$, is

Question 33

The number of distinct words that can be formed using all the letters except vowels of the word 'PROBABILITY' is


Question 34

The area enclosed between the curves $$y =2x^2$$ and $$y = 6$$ is

Question 35

The value of $$lim_{x \rightarrow 0} \frac{\sin(x^2)}{x \sin x}$$ is

Question 36

The value of $$\frac{30_{C_1}}{2} + \frac{30_{C_3}}{4} + \frac{30_{C_5}}{6} +...+ \frac{30_{C_{29}}}{30}$$ is


Question 37

In the quadrilateral $$ABCD$$ below, $$\angle DAB$$ = 90° and $$AB = 24$$cm , $$BC = 40$$cm, $$CD = 50$$cm and $$AD = 18$$cm(The diagram is not drawn to scale) Find the area of the quadrilateral 

Question 38

Let $$x = \frac{\pi}{4}$$. Then the value of  $$\cot x \cot 2x \cot 3x ....\cot 19x $$ is 

Question 39

Consider the function: $$f(x) = \mid {2 - \mid x - 1\mid}\mid$$ for all $$x \in R$$. Then the value of $$f'(-2) + f'(0) + f'(2) + f'(4)$$ is


Question 40

Let

$$P = \begin{bmatrix}a & b & 0\\-1 & 2 & 1\\2 & -3 & -2 \end{bmatrix}$$

with $$det(P) = -2$$. Then the minor $$M_{22}$$ of $$P$$ is

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