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What Are the 4 Types of Entrepreneurship?

The four types of entrepreneurship are: Small businesses entrepreneurship Scalable start-up entrepreneurship Large companies or big business entrepreneurship Social entrepreneurship... View Article

12 July 2021: PIB Summary & Analysis

July 12th, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. Ashadhi Bij 2. Rath Yatra 3. National Bank For... View Article

If lim_x→-3 [3x² + ax + a – 7] / (x² + 2x – 3), exists, then a =

1) 10 2) 15 3) -15 4) -10 Solution: (1) 10 \(\begin{array}{l}\lim _{x \rightarrow-3} \frac{3 x^{2}+a x+a-7}{x^{2}+2 x-3} exist\\ x^{2}+2... View Article

If lim_n→∞ rⁿ = 0, then r =

1) 4/5 2) 5/4 3) 2 4) 1 Solution: (1) ⅘ \(\begin{array}{l}\lim _{n \rightarrow \infty} r^{n}=0\\ r^{\infty}=0\\ \therefore \text {... View Article

lim_x→1 (log ex)^1/logx =

1) e-1 2) e 3) 2 4) 0 Solution: (2) e \(\begin{array}{l}\begin{array}{l} \left.\lim _{x \rightarrow 1}(\log e x)^{1 / \log... View Article

lim_n→∞ [1² + 2² + ….. + n²] / (n³) =

1) 1/2 2) 2/3 3) 1/3 4) 1/6 Solution: (3) ⅓ \(\begin{array}{l}\begin{array}{l} \lim _{n \rightarrow \infty} \frac{1^{2}+2^{2}+3^{2}+\cdots+n^{2}}{n^{3}} \\ \Rightarrow \lim... View Article

If f : R → r is a differentiable function such that f(3) = 3, f'(3) = 1/2. Then the value of lim_x→3 [∫₃^{f (x)} 2t³ dt] / (x – 3) is

1) 25 2) 26 3) 27 4) None of these Solution: (3) 27 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 3} \frac{\int_{3}^{f(x)} 2... View Article

lim_n→∞ {1 / (1 – n²) + 2 / (1 – n²) + ……. + n / (1 – n²) =

1) 0 2) – 1 / 2 3) 1 / 2 4) none of these Solution: (2) – 1 /... View Article

If lim_x→0 [log (x + a) – log a] / x + K lim_x→e [log x – 1] / (x – e) = 1, then the value of K is

1) 1 – 1/a 2) e(1 – a) 3) e(1- 1/a) 4) e(1 + a) Solution: (3) e(1- 1/a) \(\begin{array}{l}\begin{array}{l}... View Article

If f (x) = (ax +b) / (x + 1), lim_x→∞ f (x) = 1 and lim_x→0 f (x) = 2, then f (- 2) =

1) 0 2) 1 3) 2 4) 3 Solution: (1) 0 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow \infty} \frac{a x+b}{x+1}=1\\ \text {... View Article

lim_x→2 [√1 + √2 + x – √3] / (x – 2) =

1) 1/8√3 2) 1/√3 3) 8√3 4) √3 Solution: (1) 1/8√3 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 2} \frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}\\ \text { Apply... View Article

If f(5) = 7 and f'(5) = 7, then lim_x→5 [x f (5) – 5 f (x)] / (x – 5) =

1) 35 2) -35 3) 28 4) -28 Solution: (4) -28 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5}\\ \text... View Article

lim_x→0 [(x / √1 + x – √1 – x)] =

1) 0 2) 1 3) 2 4) -1 5) -2 Solution: (2) 1 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 0}\left(\frac{x}{\sqrt{1+x}-\sqrt{1-x}}\right) \\ \text... View Article

lim_x→∞ [(x³ / (3x² – 4)) – (x² / (3x + 2))] =

1) – (1/4) 2) – (1/2) 3) 0 4) 2/9 Solution: (4) 2/9 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow \infty}\left(\frac{x^{3}}{3 x^{2}-4}-\frac{x^{2}}{3 x+2}\right)... View Article

If f : R → R is a positive increasing function with lim_x→∞ f (3x) / f (x) = 1. Then lim_x→∞ f (2x) / f (x) =

1) 1 2) 2/3 3) 3/2 4) 3 Solution: (1) 1 \(\begin{array}{l}\begin{array}{l} 0<f(x)<f(2 x)<f(3 x) \text { as } f(x)... View Article

The value of lim_x→0 (1 / x³) ∫₀^x [t log (1 + t)] / [t⁴ + 4] dt is

1) 0 2) 1/12 3) 1/24 4) 1/64 Solution: (2) 1/12 \(\begin{array}{l}\lim _{x \rightarrow 0} \frac{1}{x^{3}} \int_{0}^{x} \frac{t \ln (1+t)}{t^{4}+4}... View Article

lim_x→0 [(16^x + 9^x) / 2]^1/x =

1) 25/2 2) 12 3) 1 4) 1/4 Solution: (2) 12

If f'(x) = f(x), f(0) = 1, then lim_x→0 [f (x) – 1] / x =

1) 0 2) 1 3) -1 4) 2 Solution: (2) 1 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 0} \frac{f(x)-1}{x} \quad\left(\frac{0}{0} \text {... View Article

lim_x→∞ [1 + (4 / (x – 1))]^x+3 =

1) e4 2) e2 3) e3 4) e Solution: (1) e4 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow \infty}\left(1+\frac{4}{x-1}\right)^{x+3}\left(1^{\infty} \text { form }\right)... View Article

lim_k→∞ [1³ + 2³ + ……. + k³] / [k⁴] =

1) 0 2) 2 3) 1/3 4) ∞ 5) 1/4 Solution: (5) ¼ \(\begin{array}{l}\begin{array}{l} \lim _{k \rightarrow \infty}\left(\frac{1^{3}+2^{3}+\cdots+k^{3}}{k^{4}}\right) \\ \Rightarrow... View Article

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