Archives

25 May 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 25th May 2021. Important news and views to boost... View Article

Niccolò Dei Conti [AD 1395 – AD 1469]

Nicolò Dei Conti commonly called Niccolò Conti was an Italian traveller and a merchant who visited India in 1420 AD at the Vijayanagara empire... View Article

Rights and Liabilities of the Government

Articles 294 to 300 in Part XII of the Constitution of India deals with the property contracts, rights, liabilities, obligations, and suits of... View Article

State Human Rights Commission

The State Human Rights Commission is charged with the protection of Human Rights or investigating any violations that occur within their... View Article

Parliamentary Forums

Parliamentary Forums are established in order to provide a platform for interaction and discussion of critical issues with the ministers... View Article

Second Battle of Panipat

The Second Battle of Panipat took place on 5 November 1556, between the emperor of north India, Hemu, and the forces of the Mughal emperor Akbar.... View Article

∫{(e^x) [(x – 1) / x²]} dx =

1) (ex / x2) + c 2) (- ex / x2) + c 3) (ex / x) + c 4) (- ex / x) + c Solution: (3) (ex / x) + c ∫{(ex) [(x - 1) / x2]} dx = ∫{[xex - ex] /... View Article

[latex]\int e^{e^{e^{x}}} \cdot e^{e^{x}} \cdot e^{x} d x=\cdots+C[/latex]

1) ee^x 2) (1 / 2) e2 ee^x 3) ee^e^x 4) (1 / 2) ee^x Solution: (3) ee^e^x... View Article

∫{(dx) / (x² √(4 – x²))} =

1) (1 / 4) [(√4 - x2) / x] + c 2) (1 / 2) [(√4 - x2) / x] + c 3) (- 1 / 4) [(√4 - x2) / x] + c 4) (- 1 / 2) [(√4 - x2) / x] + c Solution: (3)... View Article

∫[(4e^x + 6e^-x) / (9e^x – 4e^-x)] dx =

1) 2) 3) 4) 5) Solution: (3)... View Article

∫{e^x [sin x + cos x] / (1 – sin² x)} dx =

1) ex cosec x + c 2) ex + cot x + c 3) ex sec x + c 4) ex tan x + c Solution: (3) ex sec x + c ∫{ex [sin x + cos x] / (1 - sin2 x)} dx =... View Article

∫{√[(e^x + a) / (e^x – a)]} dx =

1) 2) 3) 4) Solution: (1)... View Article

∫{(1 + cot² x) / (1 + cot x)} dx =

∫{sin 2x / [sin⁴ x + cos⁴ x]} dx =

1) 2 tan-1 (tan2 x) + c 2) tan-1 (x tan2 x) + c 3) tan-1 (tan2 x) + c 4) None of these Solution: (4) None of these... View Article

∫[2^x / (√(1 – 4^x))] dx =

1) (log 2) sin-1 2x + c 2) (1 / 2) sin-1 2x + c 3) (1 / log 2) sin-1 2x + c 4) 2 log 2 sin-1 2x + c Solution: (3) (1 / log 2) sin-1 2x + c... View Article

If {√(cot x) / [sin x cos x]} dx = P √cot x + Q, then the value of P is

1) -2 2) 2 3) 3 4) -3 Solution: (1) -2... View Article

If f (x) = ∫dx / [(1 + x²)^3/2] and f (0) = 0, then the value of f (1) is

1) 1 / √2 2) - 1 / √2 3) √2 4) - √2 Solution: (1) 1 / √2... View Article

If n ∈ N and I_n = ∫(log x)ⁿ dx, then I_n + nI_n-1 =

1) [log x]n+1 / (n + 1) 2) x (log x)n + c 3) (log x)n-1 4) [(log x)n / n] Solution: (2) x (log x)n + c... View Article

∫{e^x [(x² + 1) / (x + 1)²]} dx =

1) [- ex / (x + 1)] + c 2) [ex / (x + 1)] + c 3) [xex / (x + 1)] + c 4) {ex [(x - 1) / (x + 1)]} + c Solution: (4) {ex [(x - 1) / (x + 1)]} + c... View Article

∫{(2 dx) / [(e^x + e^-x)²]} =

1) [- e-x / (ex + e-x)] + c 2) [1 / (ex + e-x)] + c 3) [1 / (ex + 1)2] + c 4) [1 / (ex + e-x)2] + c Solution: (1) [- e-x / (ex + e-x)] + c... View Article

M	T	W	T	F	S	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
31