Question and Answers Forum

AllQuestion and Answers: Page 1931

Question Number 15322 Answers: 0 Comments: 6

Question Number 15318 Answers: 2 Comments: 6

Question Number 15311 Answers: 0 Comments: 0

In a toll-booth at a bridge , some cars can pass by paying a tax of Rs. 10 and some special vehicles are exempted from paying tax. The booth has to track number of vehicles and total tax collected. Define a class ′tollbooth′. It should contain two data items of type int to hold the number of cars and total tax connected. A constructor initalizes these two variable to zero. A memberfunction freecar() only increments the car total. Finally another memberfunction show() displays the two totals. Write a C++ program such that the user has to press the key ′T′ for printing number of taxable cars and total tax, ′F′ for printing number of free cars and ′Esc′ to exit.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{toll}-\mathrm{booth}\:\mathrm{at}\:\mathrm{a}\:\mathrm{bridge}\:,\:\mathrm{some}\:\mathrm{cars}\:\mathrm{can}\:\mathrm{pass}\:\mathrm{by}\:\mathrm{paying}\:\mathrm{a}\:\mathrm{tax}\:\mathrm{of}\:\mathrm{Rs}.\:\mathrm{10}\:\mathrm{and} \\ $$$$\mathrm{some}\:\mathrm{special}\:\mathrm{vehicles}\:\mathrm{are}\:\mathrm{exempted}\:\mathrm{from}\:\mathrm{paying}\:\mathrm{tax}.\:\mathrm{The}\:\mathrm{booth}\:\mathrm{has}\:\mathrm{to}\:\mathrm{track}\: \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{vehicles}\:\mathrm{and}\:\mathrm{total}\:\mathrm{tax}\:\mathrm{collected}.\:\mathrm{Define}\:\mathrm{a}\:\mathrm{class}\:'\mathrm{tollbooth}'.\:\mathrm{It}\:\mathrm{should}\:\mathrm{contain} \\ $$$$\mathrm{two}\:\mathrm{data}\:\mathrm{items}\:\mathrm{of}\:\mathrm{type}\:\mathrm{int}\:\mathrm{to}\:\mathrm{hold}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{cars}\:\mathrm{and}\:\mathrm{total}\:\mathrm{tax}\:\mathrm{connected}. \\ $$$$\mathrm{A}\:\mathrm{constructor}\:\mathrm{initalizes}\:\mathrm{these}\:\mathrm{two}\:\mathrm{variable}\:\mathrm{to}\:\mathrm{zero}.\:\mathrm{A}\:\mathrm{memberfunction}\:\mathrm{freecar}\left(\right)\:\mathrm{only} \\ $$$$\mathrm{increments}\:\mathrm{the}\:\mathrm{car}\:\mathrm{total}.\:\mathrm{Finally}\:\mathrm{another}\:\mathrm{memberfunction}\:\mathrm{show}\left(\right)\:\mathrm{displays}\:\mathrm{the} \\ $$$$\mathrm{two}\:\mathrm{totals}. \\ $$$$\:\:\:\mathrm{Write}\:\mathrm{a}\:\mathrm{C}++\:\mathrm{program}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{user}\:\mathrm{has}\:\mathrm{to}\:\mathrm{press}\:\mathrm{the}\:\mathrm{key}\:'\mathrm{T}'\:\mathrm{for} \\ $$$$\mathrm{printing}\:\mathrm{number}\:\mathrm{of}\:\mathrm{taxable}\:\mathrm{cars}\:\mathrm{and}\:\mathrm{total}\:\mathrm{tax},\:'\mathrm{F}'\:\mathrm{for}\:\mathrm{printing}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{free} \\ $$$$\mathrm{cars}\:\mathrm{and}\:'\mathrm{Esc}'\:\mathrm{to}\:\mathrm{exit}. \\ $$

Question Number 15302 Answers: 0 Comments: 0

Prove that number of commutative binary operations on a set having n elements is n^((n(n − 1))/2) .

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{number}\:\mathrm{of}\:\mathrm{commutative} \\ $$$$\mathrm{binary}\:\mathrm{operations}\:\mathrm{on}\:\mathrm{a}\:\mathrm{set}\:\mathrm{having}\:{n} \\ $$$$\mathrm{elements}\:\mathrm{is}\:{n}^{\frac{{n}\left({n}\:−\:\mathrm{1}\right)}{\mathrm{2}}} \:. \\ $$

Question Number 15301 Answers: 1 Comments: 0

With the help of graph, find the solution set of inequation tan x > −(√3) .

$$\mathrm{With}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{graph},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequation}\:\mathrm{tan}\:{x}\:>\:−\sqrt{\mathrm{3}}\:. \\ $$

Question Number 15300 Answers: 1 Comments: 3

Find the values of α and β, 0 < α, β < (π/2) satisfying the following equation cos α cos β cos (α + β) = −(1/8) .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\alpha\:\mathrm{and}\:\beta,\:\mathrm{0}\:<\:\alpha,\:\beta\:<\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation} \\ $$$$\mathrm{cos}\:\alpha\:\mathrm{cos}\:\beta\:\mathrm{cos}\:\left(\alpha\:+\:\beta\right)\:=\:−\frac{\mathrm{1}}{\mathrm{8}}\:. \\ $$

Question Number 15298 Answers: 1 Comments: 4

Solve for x and y x^2 + 2x sin(xy) + 1 = 0

$$\mathrm{Solve}\:\mathrm{for}\:{x}\:\mathrm{and}\:{y} \\ $$$${x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:\mathrm{sin}\left({xy}\right)\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 15294 Answers: 0 Comments: 1

A straigth conductor of length L is charged with q charge. What will be the electric field in the equatorial line at a distance d ? Ans: ((2q)/(4Πε_0 d(√(L^2 +4d^2 ))))

$$\mathrm{A}\:\mathrm{straigth}\:\mathrm{conductor}\:\mathrm{of}\:\mathrm{length} \\ $$$$\mathrm{L}\:\mathrm{is}\:\mathrm{charged}\:\mathrm{with}\:\mathrm{q}\:\mathrm{charge}.\:\mathrm{What} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{electric}\:\mathrm{field}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{equatorial}\:\mathrm{line}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{d}\:? \\ $$$$\mathrm{Ans}:\:\frac{\mathrm{2q}}{\mathrm{4}\Pi\epsilon_{\mathrm{0}} \mathrm{d}\sqrt{\mathrm{L}^{\mathrm{2}} +\mathrm{4d}^{\mathrm{2}} }} \\ $$

Question Number 15288 Answers: 0 Comments: 1

Question Number 15284 Answers: 1 Comments: 3

Question Number 15266 Answers: 0 Comments: 0

calculate the pH of 1(N) HCl.

$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{pH}\:\mathrm{of}\:\mathrm{1}\left(\mathrm{N}\right)\:\mathrm{HCl}. \\ $$

Question Number 15264 Answers: 1 Comments: 0

The solution set of inequation cos x + (1/2) ≥ 0 is [−π, π] (1) [0, ((2π)/3)] (2) [−((2π)/3), ((2π)/3)] (3) [0, (π/2)] (4) [−(π/2), ((3π)/2)]

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequation} \\ $$$$\mathrm{cos}\:{x}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\geqslant\:\mathrm{0}\:\mathrm{is}\:\left[−\pi,\:\pi\right] \\ $$$$\left(\mathrm{1}\right)\:\left[\mathrm{0},\:\frac{\mathrm{2}\pi}{\mathrm{3}}\right] \\ $$$$\left(\mathrm{2}\right)\:\left[−\frac{\mathrm{2}\pi}{\mathrm{3}},\:\frac{\mathrm{2}\pi}{\mathrm{3}}\right] \\ $$$$\left(\mathrm{3}\right)\:\left[\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right] \\ $$$$\left(\mathrm{4}\right)\:\left[−\frac{\pi}{\mathrm{2}},\:\frac{\mathrm{3}\pi}{\mathrm{2}}\right] \\ $$

Question Number 15263 Answers: 1 Comments: 0

The equation asinx + cos2x = 2a − 7 possesses a solution if (1) a > 6 (2) 2 ≤ a ≤ 6 (3) a > 2 (4) a

$$\mathrm{The}\:\mathrm{equation}\:{a}\mathrm{sin}{x}\:+\:\mathrm{cos2}{x}\:=\:\mathrm{2}{a}\:−\:\mathrm{7} \\ $$$$\mathrm{possesses}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{if} \\ $$$$\left(\mathrm{1}\right)\:{a}\:>\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}\:\leqslant\:{a}\:\leqslant\:\mathrm{6} \\ $$$$\left(\mathrm{3}\right)\:{a}\:>\:\mathrm{2} \\ $$$$\left(\mathrm{4}\right)\:{a} \\ $$

Question Number 15262 Answers: 0 Comments: 7

Solve : x^2 − 6x + [x] + 7 = 0.

$$\mathrm{Solve}\::\:{x}^{\mathrm{2}} \:−\:\mathrm{6}{x}\:+\:\left[{x}\right]\:+\:\mathrm{7}\:=\:\mathrm{0}. \\ $$

Question Number 15267 Answers: 2 Comments: 6

In an acute angled ΔABC, the minimum value of tan A tan B tan C is?

$$\mathrm{In}\:\mathrm{an}\:\mathrm{acute}\:\mathrm{angled}\:\Delta{ABC},\:\mathrm{the} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:{A}\:\mathrm{tan}\:{B}\:\mathrm{tan}\:{C}\:\mathrm{is}? \\ $$

Question Number 15292 Answers: 3 Comments: 0

Light version of Q#13724 Expansion of 100! has 24, 0′s at the end. Find the first non-zero digit from right. 100!=.....d000...00 What is the value of d?

$$\mathrm{Light}\:\mathrm{version}\:\mathrm{of}\:\mathcal{Q}#\mathrm{13724} \\ $$$$\mathcal{E}\mathrm{xpansion}\:\mathrm{of}\:\mathrm{100}!\:\mathrm{has}\:\mathrm{24},\:\mathrm{0}'\mathrm{s}\:\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{non}-\mathrm{zero}\:\mathrm{digit}\:\mathrm{from}\:\mathrm{right}. \\ $$$$\mathrm{100}!=.....\mathrm{d000}...\mathrm{00} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{d}? \\ $$

Question Number 15234 Answers: 0 Comments: 2

A question related to Q.15184 Find the maximum of f(x)=(ln x)^(1/x)

$$\mathrm{A}\:\mathrm{question}\:\mathrm{related}\:\mathrm{to}\:\mathrm{Q}.\mathrm{15184} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{ln}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$

Question Number 15233 Answers: 1 Comments: 0

Find the general solution of the following homogeneous system of equation x_1 + x_2 − 2x_3 = 0 3x_1 − x_2 − 6x_3 = 0 −2x_1 + 3x_(2 ) + 4x_3 = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{homogeneous}\:\mathrm{system}\:\mathrm{of} \\ $$$$\mathrm{equation}\:\: \\ $$$$\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{x}_{\mathrm{2}} \:−\:\mathrm{2x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$\mathrm{3x}_{\mathrm{1}} \:−\:\mathrm{x}_{\mathrm{2}} \:−\:\mathrm{6x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$−\mathrm{2x}_{\mathrm{1}} \:+\:\mathrm{3x}_{\mathrm{2}\:} +\:\mathrm{4x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$

Question Number 15232 Answers: 1 Comments: 0

For what values of a does the following system have a non trivial solution ax_1 + 3x_2 − 2x_3 = 0 −x_1 + 4x_2 + ax_3 = 0 5x_1 − 6x_2 − 7x_3 = 0

$$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{a}\:\:\mathrm{does}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system}\:\mathrm{have}\:\mathrm{a}\:\mathrm{non}\:\mathrm{trivial}\: \\ $$$$\mathrm{solution}\: \\ $$$$\mathrm{ax}_{\mathrm{1}} \:+\:\mathrm{3x}_{\mathrm{2}} \:−\:\mathrm{2x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$−\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{4x}_{\mathrm{2}} \:+\:\mathrm{ax}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$\mathrm{5x}_{\mathrm{1}} \:−\:\mathrm{6x}_{\mathrm{2}} \:−\:\mathrm{7x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$

Question Number 15235 Answers: 1 Comments: 0

∫(log (√(x )) )^2 dx=?

$$\int\left(\mathrm{log}\:\sqrt{\mathrm{x}\:}\:\right)^{\mathrm{2}} \mathrm{dx}=? \\ $$

Question Number 15217 Answers: 1 Comments: 0

Question Number 15216 Answers: 0 Comments: 0

[((z−2)/(z+2))]=6

$$\left[\frac{\mathrm{z}−\mathrm{2}}{\mathrm{z}+\mathrm{2}}\right]=\mathrm{6} \\ $$

Question Number 15194 Answers: 0 Comments: 2

The equation determinant (((x−a),(x−b),(x−c)),((x−b),(x−c),(x−a)),((x−c),(x−a),(x−b)))=0, where a, b, c are different, is satisfied by

$$\mathrm{The}\:\mathrm{equation}\:\begin{vmatrix}{{x}−{a}}&{{x}−{b}}&{{x}−{c}}\\{{x}−{b}}&{{x}−{c}}&{{x}−{a}}\\{{x}−{c}}&{{x}−{a}}&{{x}−{b}}\end{vmatrix}=\mathrm{0}, \\ $$$$\mathrm{where}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{different},\:\mathrm{is}\:\mathrm{satisfied}\:\mathrm{by} \\ $$

Question Number 15193 Answers: 0 Comments: 0

The value of the determinant △= determinant ((( 2a_1 b_1 ),(a_1 b_2 +a_2 b_1 ),(a_1 b_3 +a_3 b_1 )),((a_1 b_2 +a_2 b_1 ),( 2a_2 b_2 ),(a_2 b_3 +a_3 b_2 )),((a_1 b_3 +a_3 b_1 ),(a_3 b_2 +a_2 b_3 ),( 2a_3 b_3 )))is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{determinant} \\ $$$$\bigtriangleup=\begin{vmatrix}{\:\:\:\mathrm{2}{a}_{\mathrm{1}} {b}_{\mathrm{1}} }&{{a}_{\mathrm{1}} {b}_{\mathrm{2}} +{a}_{\mathrm{2}} {b}_{\mathrm{1}} }&{{a}_{\mathrm{1}} {b}_{\mathrm{3}} +{a}_{\mathrm{3}} {b}_{\mathrm{1}} }\\{{a}_{\mathrm{1}} {b}_{\mathrm{2}} +{a}_{\mathrm{2}} {b}_{\mathrm{1}} }&{\:\:\:\:\mathrm{2}{a}_{\mathrm{2}} {b}_{\mathrm{2}} }&{{a}_{\mathrm{2}} {b}_{\mathrm{3}} +{a}_{\mathrm{3}} {b}_{\mathrm{2}} }\\{{a}_{\mathrm{1}} {b}_{\mathrm{3}} +{a}_{\mathrm{3}} {b}_{\mathrm{1}} }&{{a}_{\mathrm{3}} {b}_{\mathrm{2}} +{a}_{\mathrm{2}} {b}_{\mathrm{3}} }&{\:\:\:\:\mathrm{2}{a}_{\mathrm{3}} {b}_{\mathrm{3}} }\end{vmatrix}\mathrm{is} \\ $$

Question Number 15192 Answers: 0 Comments: 0

Let D_r = determinant ((2^(r−1) ,(2 ∙ 3^(r−1) ),(4 ∙ 5^(r−1) )),(( α),( β),( γ)),((2^n −1),(3^n −1),( 5^n −1))). Then the value of Σ_(r=1) ^n D_r is

$$\mathrm{Let}\:{D}_{{r}} =\begin{vmatrix}{\mathrm{2}^{{r}−\mathrm{1}} }&{\mathrm{2}\:\centerdot\:\mathrm{3}^{{r}−\mathrm{1}} }&{\mathrm{4}\:\centerdot\:\mathrm{5}^{{r}−\mathrm{1}} }\\{\:\:\:\alpha}&{\:\:\:\beta}&{\:\:\:\:\:\gamma}\\{\mathrm{2}^{{n}} −\mathrm{1}}&{\mathrm{3}^{{n}} −\mathrm{1}}&{\:\:\mathrm{5}^{{n}} −\mathrm{1}}\end{vmatrix}. \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{D}_{{r}} \:\:\mathrm{is} \\ $$

Question Number 15191 Answers: 0 Comments: 1

If m is a positive integer and △_r = determinant ((( 2r−1),(^m C_r ),( 1)),(( m^2 −1),( 2^m ),( m+1)),((sin^2 (m^2 )),(sin^2 (m)),(sin^2 (m+1)))) then the value of Σ_(r=0) ^m △_r is

$$\mathrm{If}\:{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{and} \\ $$$$\bigtriangleup_{{r}} =\begin{vmatrix}{\:\:\:\mathrm{2}{r}−\mathrm{1}}&{\:^{{m}} {C}_{{r}} }&{\:\:\:\:\:\:\:\:\mathrm{1}}\\{\:\:{m}^{\mathrm{2}} −\mathrm{1}}&{\:\:\:\:\mathrm{2}^{{m}} }&{\:\:\:{m}+\mathrm{1}}\\{\mathrm{sin}^{\mathrm{2}} \left({m}^{\mathrm{2}} \right)}&{\mathrm{sin}^{\mathrm{2}} \left({m}\right)}&{\mathrm{sin}^{\mathrm{2}} \left({m}+\mathrm{1}\right)}\end{vmatrix} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\underset{{r}=\mathrm{0}} {\overset{{m}} {\sum}}\bigtriangleup_{{r}} \:\:\:\mathrm{is} \\ $$

Pg 1926 Pg 1927 Pg 1928 Pg 1929 Pg 1930 Pg 1931 Pg 1932 Pg 1933 Pg 1934 Pg 1935

Contact: info@tinkutara.com