Evaluate ∫-11 log (√(1 – x) + √(1 + x))dx
Answer: 2 ln(2) – (1 – π/2) f(-x) = f(x) ⇒ f is even ∴ I = 2∫01 log ((1... View Article
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If [latex]\lim_{x\to0}\left \{ 2-\cos x\sqrt{\cos 2x} \right \}^{\frac{x+2}{x^{2}}}=e^{\alpha }[/latex], then α = ?
Answer: 3 \(\begin{array}{l}\lim_{x\to0}\left \{ 2-\cos x\sqrt{\cos 2x} \right \}^{\frac{x+2}{x^{2}}}=e^{\alpha }\end{array} \) (1∞ form) ⇒ e(2+1)2/(1+1) = eα ⇒ e3 =... View Article
Find the number of integral terms in the expansion of [latex](4^{\frac{1}{4}} + 5^{\frac{1}{6}})^{120}[/latex]
a. 1 b. 21 c. 20 d. 11 Solution: Answer: (b) T(r+1) = 120Cr 4(120 – r)/45r/6 = 120Cr 2(120... View Article
All the letters of the word EXAMINATION are arranged. Find the probability that ‘M’ is at the 4th position.
a. 2/11 b. 1/11 c. 4/11 d. 8/11 Solution: Answer: (b) EXAMINATION Letters: AAIINNE T O X M Total possible... View Article
There are 6 batsmen, 7 bowlers and 2 wickets keepers. Find the number of ways of forming a team of 11 players having at least 4 batsmen, at least 5 bowlers and at least 1 wicket keeper.
a. 567 b. 525 c. 462 d. 777 Solution: Answer: (d) Team Size =11 players Case 1: 4 batsmen and... View Article
The number of solutions of tan-1√(x(x+1)) + sin-1√(x2+x+1) = π/2 is
Answer: Given tan-1√(x(x+1)) + sin-1√(x2+x+1) = π/2 ⇒ tan-1 √(x(x+1)) = π/2 – sin-1√(x2+x+1) ⇒ tan-1 √(x(x+1)) = cos-1√(x2+x+1) ⇒... View Article
What is the value of a+b when function f(x) is given
Question : If f(x) = \(\begin{array}{l}\left\{\begin{matrix} \sin x-e^{x} ,&x<0 \\ a+[-x], &0\leq x< 1 \\ 2x-b, & x\geq 1 \end{matrix}\right.\end{array}... View Article
If [latex]\vec{a}[/latex], [latex]\vec{b}[/latex], [latex]\vec{c}[/latex] are three mutually perpendicular vectors equally inclined to [latex]\vec{a}+\vec{b}+\vec{c}[/latex] at angle θ, then find the value of 36 cos2 2θ.
Answer: 4 \(\begin{array}{l}\vec{a}.\vec{b} = \vec{b}.\vec{c}=\vec{c}.\vec{a}=0\end{array} \) \(\begin{array}{l}(\vec{a}+\vec{b} +\vec{c}). (\vec{a}+\vec{b} +\vec{c})= \left | \vec{a} +\vec{b}+\vec{c}\right |^{2}\end{array} \) \(\begin{array}{l}\left | \vec{a} \right... View Article
Find the coefficient of x256 in (1- x)101(x2 + x + 1)100
Answer: 100C85 (1- x)101(x2 + x + 1)100 = (1 – x)(1- x)100(x2 + x + 1)100 = (1 –... View Article
The mean of 6 numbers is 6.5 and its variance is 10.25. If 4 numbers are 2,4,5 and 7, then find the other two.
Answer: a = 10 and b = 11 or a = 11 and b = 10 Let a and b... View Article
AIR Spotlight – NCW and Women Empowerment
AIR Spotlight is an insightful programme featured daily on the All India Radio Newsonair. In this program, many eminent panellists... View Article
What is the other name for sales return?
The other name for sales return is return inwards. Also read: Cash Book Purchase Book Sales Book and Sales Return... View Article
Is the sales book a ledger?
A sales book is regarded as a journal and not a ledger. Also read: Cash Book Purchase Book Sales Book... View Article
What is the other name of the sales book?
The other name of the sales book is a sales journal. Also read: Cash Book Purchase Book Sales Book and... View Article
What is the sales book?
A sales book is a book that contains details of all the credit sales made by the firm. It is... View Article
What information is included in the purchase book?
The purchase book records the basic information of a purchase like date of transaction, name of the supplier, supplier invoice... View Article
What goes in the purchases ledger?
Purchases ledger contains the accounts of the suppliers of the firm or the business. It records all the purchases made... View Article
Is purchase returns a debit or credit in the trial balance?
Purchase returns reduce the expenses of the business and therefore will be placed in the credit side of the trial... View Article
What is the difference between a purchase book and a purchase return book?
The difference between a purchase book and a purchase return book is that a purchase book is used to record... View Article
What is the other name of the purchase returns book?
The other name of the purchase returns book is the return outwards book. Also read: Cash Book Purchase Book Sales... View Article
