414 + Interview Questions in APPLICATIONS-OF-DERIVATIVES IN GENERAL AWARENESS Page 7 InterviewSolution

301.	Find the equation of normal at point (4, 3) for the hyperbola ` 3x^(2) - 4y^(2) = 14`.
Answer» Correct Answer - x + y = 7

Discussion

302.	If `f(x)=cosx,0lexle(pi)/2` then the real number c of the mean value theorem isA. `sin^(-1)((2)/(pi))`B. `cos^(-1)((2)/(pi))`C. `(pi)/(6)`D. `(pi)/(4)`
Answer» Correct Answer - A

Discussion

303.	The function `f(x)=x^(2)+2x-5` is increasing in the intervalA. `(2,oo)`B. `(-oo,-2)`C. `(-1,oo)`D. `(-oo,-1)`
Answer» Correct Answer - C

Discussion

304.	Find the equation of normal to the curves `x=t^2, y=2t+1` at point
Answer» Correct Answer - `tx + y = t^(3) + 2t + 1`

Discussion

305.	A value of c for which the conclusion of Mean value theorem holds for the function `f(x) = log_(e)x` on the interval [1, 3] isA. `log_(3)e`B. `log_(e)3`C. `(1)/(2) log_(e)3`D. `2 log_(3)e`
Answer» Correct Answer - D

Discussion

306.	Find the point on the curve `9y^2=x^3,`where the normal to the curve makes equal intercepts onthe axes.
Answer» Correct Answer - 4

Discussion

307.	Find the values of x for which the following functions are maximum or minimum: (i) ` x^(3)- 3x^(2) - 9x ` (ii) ` 4x^(3)-15x^(2)+12x+1` (iii) ` 1-x-x^(2)` (iv) `x^(4)-8x^(3)+22x^(2)-24x +7` (v) `(x^(2)-x+1)/(x^(2)+x+1)`
Answer» Correct Answer - (i) Max at x =-1, min at x = 3` "(ii) Max at x = 1/2, min at x = 2` (iii)Max at `x =- 1/2" "(iv)"Max at "x = 2,` min at x = 1, 3 (v) Min at x= 1 and max at x = - 1

Discussion

308.	`log_(e) 10.02`, given that `log_(e) 10 = 2.3026`
Answer» Correct Answer - 2.3046

Discussion

309.	Find the approximate values of : `log_(10)(1002)," given that "log_(10)e=0.4343`.A. `3.0086`B. `3.0087`C. `3.00086`D. `3.00087`
Answer» Correct Answer - D

Discussion

310.	Using differentials,find the approximate value of `(log)_e 4.04`, it being given that `(log)_(10)4=0. 6021`and `(log)_(10)e=0. 4343`.
Answer» Correct Answer - `0.606443`

Discussion

311.	If `f(x)=3x^(2)+4x-1`, then find the approximate value of `f(3.1)`.
Answer» Correct Answer - `40.2`

Discussion

312.	Find the equation of normal of the curve `2y= 7x - 5x^(2)` at those points at which the curve intersects the line x = y.
Answer» Correct Answer - `2x+7y =0, 3x-2y = 1`

Discussion

313.	The approximate value of `x^(3)-2x^(2)+3x+2,` when x=3.02 isA. `20.36`B. `20.036`C. `20.18`D. `20.018`
Answer» Correct Answer - A

Discussion

314.	Prove that function `f(x) = log_e x` is strictly increasing in the interval `(0,oo)`
Answer» For all `x_(1), x_(2) in [0, oo]`, we have `x_(1) ge x_(2) rArr log_(e) x_(1) ge log_(e) x_(2) rArr f(x_(1)) ge f(x_(2))`

Discussion

315.	`log_(10) (4.04)`, it being given that `log_(10) 4 = 0.6021 and log_(10) e = 0.4343`A. `1.3874`B. `1.3964`C. `1.4864`D. `1.3864`
Answer» Correct Answer - B

Discussion

316.	Find the approximate value of `log_e(101)` given `log_e 10=2*3026`A. `4.6152`B. `4.6052`C. `4.6125`D. `4.6025`
Answer» Correct Answer - A

Discussion

317.	If `f(x) = 2x^(2)+5x+2`, then find the approximate value of `f(2.01)`.
Answer» Correct Answer - `20.13`

Discussion

318.	Find the approximate value of `log_e(901)` given `log_e 3=10986`A. `2.1988`B. `2.1983`C. `2.1987`D. `2.1982`
Answer» Correct Answer - B

Discussion

319.	Find the approximate values of : `(4.01)^(5)`A. 1036.08B. 1036.06C. `1036.80`D. `1036.60`
Answer» Correct Answer - C

Discussion

320.	The approximate value of ` f(X) = x^(3) +5x^(2)-7x+9` at x= 1.1 isA. `8.6`B. `8.5`C. `8.4`D. `8.3`
Answer» Correct Answer - A

Discussion

321.	Find the approximate value of `(4.01)^3` .A. 66.44B. 64.84C. 64.88D. 64.48
Answer» Correct Answer - D

Discussion

322.	If `f(x) = 2x^(2)+5x+2`, then find the approximate value of `f(2.01)`.A. `27.02`B. `27.20`C. `27.04`D. `27.40`
Answer» Correct Answer - D

Discussion

323.	Find the approximate value of `e^(1.005)` (given `e = 2.7183`)A. `2.7319`B. `2.7318`C. `2.8542`D. `2.8541`
Answer» Correct Answer - A

Discussion

324.	Find the approximate value of `e^(1.005)` (given `e = 2.7183`)A. `2.7237`B. `2.2737`C. `2.3772`D. `2.7273`
Answer» Correct Answer - A

Discussion

325.	If the radius of asphere is measured as 9 cm with an error or 0.03 m, find the approximateerror in calculating its surface area.
Answer» Let r be the radius and S be the total surface area of the sphere. Given ` r = 9 m and Delta r = 0.03 cm` Now ` S = 4pi r^(2)` ` rArr (dS)/(dr) = 8 pi r` `:. Delta S = (dS)/(dr) * Delta r = 8 pi r * Dleta r` ` = 8 pi xx 900 xx 0.03 cm^(2)` ` = 216 pi cm^(2)`

Discussion

326.	For a gas equation PV=100, volume V is `25 cm^(3)`, pressure P is measured in`" dynes/cm"^(2)`. If volume is increasing at the rate of `0.25 cm^(3)" /sec"`., then the rate of change of pressure isA. `-0.02" dynes/cm"^(2)`B. `0.02" dynes/cm"^(2)`C. `-0.04" dynes/cm"^(2)`D. `0.04" dynes/cm"^(2)`
Answer» Correct Answer - C

Discussion

327.	Find the approximate values of : `cot^(-1)(1.001)`A. `(pi)/(4)+0.005`B. `(pi)/(4)+0.0005`C. `(pi)/(4)-0.005`D. `(pi)/(4)-0.0005`
Answer» Correct Answer - B

Discussion

328.	Find the approximate values of : `root(3)(26.96)`A. `2.9985`B. `2.9984`C. `2.9988`D. `2.9898`
Answer» Correct Answer - A

Discussion

329.	The approximate value of `sin^(-1)(0.51)," if "(1)/(sqrt(3))=0.5774` isA. `(pi)/(3)+0.1154`B. `(pi)/(3)+0.1155`C. `(pi)/(6)+0.01155`D. `(pi)/(6)+0.01154`
Answer» Correct Answer - C

Discussion

330.	Find the approximate values of : `tan^(-1)(1.001)`.A. `(pi)/(4)-0.0005`B. `(pi)/(4)+0.0005`C. `(pi)/(4)-0.005`D. `(pi)/(4)+0.005`
Answer» Correct Answer - B

Discussion

331.	Using differentials,find the approximate value of `(0. 009)^(1//3)`
Answer» Correct Answer - `0.208`

Discussion

332.	The approximate value of `root(3)(0.009)` isA. `0.2083`B. `0.2038`C. `0.2084`D. `0.2048`
Answer» Correct Answer - A

Discussion

333.	Find the approximate values of : `cos(89^(@)30)," given "1^(@)=0.0175^( c )`.A. `0.00875`B. `0.0875`C. `0.0175`D. `0.0876`
Answer» Correct Answer - A

Discussion

334.	Find the approximate values of : `tan(44^(@))," given "1^(@)=0.0175^( c )`.A. `0.09825`B. `0.9825`C. `0.0965`D. `0.965`
Answer» Correct Answer - D

Discussion

335.	The approximate value of `root(5)(32.1)` isA. `2.125`B. `2.0015`C. `2.0125`D. `2.00125`
Answer» Correct Answer - D

Discussion

336.	Approximate value of `tan^(-1)(0.999)` isA. `(pi)/(4)-0.0005`B. `(pi)/(4)-0.005`C. `(pi)/(4)-0.05`D. `(pi)/(4)-0.5`
Answer» Correct Answer - A

Discussion

337.	The approximate value of `root(3)(28)` isA. `3.038`B. `3.035`C. `3.036`D. `3.037`
Answer» Correct Answer - D

Discussion

338.	Find the approximate value of `root(3)(63)`A. `3.09792`B. `3.09791`C. `3.9792`D. `3.9791`
Answer» Correct Answer - C

Discussion

339.	Find the approximate value of `root(3)(27.027)` .A. `3.001`B. `3.01`C. `3.003`D. `3.037`
Answer» Correct Answer - A

Discussion

340.	Find the approximate value of cos `(29^@ 30prime)` given `1^@ = 0.0175^c and cos 30^@ = 0.8660`A. `0.8604`B. `0.8603`C. `0.8704`D. `0.4928`
Answer» Correct Answer - C

Discussion

341.	Find the approximate value of `root(10)(0.999)` .A. `0.0998`B. `0.9998`C. `0.0999`D. `0.9999`
Answer» Correct Answer - D

Discussion

342.	The apprximate value of `sin(31^(@))`, given that `1^(@)=0.0175, cos 30^(@)=0.8660` isA. `0.5051`B. `0.5052`C. `0.5151`D. `0.5152`
Answer» Correct Answer - D

Discussion

343.	Using differentials,find the approximate value of `sqrt(37)`
Answer» Correct Answer - `6.08`

Discussion

344.	Using differentials, find the approximate value of `(3. 968)^(3/2)`A. `7.409`B. `7.904`C. `7.804`D. `7.408`
Answer» Correct Answer - B

Discussion

345.	Using differentials,find the approximate value of `1/((2. 002)^2)`
Answer» Correct Answer - 0.2495 Let `f(x) = (1)/(x^(2))`. Then `f(x + delta x) - f(x) = (-2)/(x^(3)) .deltax` Take `x = 2 and delta x = 0.002`

Discussion

346.	Using differentials, find theapproximate value of `sqrt(49. 5)`
Answer» Correct Answer - 7.0357

Discussion

347.	Using differentials, find the approximate value of : `root(3)(127)`
Answer» Correct Answer - 5.027

Discussion

348.	Find the intervals in which `f(x)=x^4-4x^3+4x^2+15`is increasing or decreasing.
Answer» Correct Answer - (a) `f(x)` is increasing on `[0, 1] uu [2, oo]` (b) `f(x)` is decreasing on `[-oo, 0] uu [-1, 2]`

Discussion

349.	Using differentials, find the approximate values of the following: `1/(2.002)^(2)`
Answer» Correct Answer - `0.2495`

Discussion

350.	Using differentials, find the approximate values of the following: `sqrt(0.24)`
Answer» Correct Answer - 0.49

Discussion

Explore topic-wise InterviewSolutions in .

Find the equation of normal at point (4, 3) for the hyperbola ` 3x^(2) - 4y^(2) = 14`.

If `f(x)=cosx,0lexle(pi)/2` then the real number c of the mean value theorem isA. `sin^(-1)((2)/(pi))`B. `cos^(-1)((2)/(pi))`C. `(pi)/(6)`D. `(pi)/(4)`

The function `f(x)=x^(2)+2x-5` is increasing in the intervalA. `(2,oo)`B. `(-oo,-2)`C. `(-1,oo)`D. `(-oo,-1)`

Find the equation of normal to the curves `x=t^2, y=2t+1` at point

A value of c for which the conclusion of Mean value theorem holds for the function `f(x) = log_(e)x` on the interval [1, 3] isA. `log_(3)e`B. `log_(e)3`C. `(1)/(2) log_(e)3`D. `2 log_(3)e`

Find the point on the curve `9y^2=x^3,`where the normal to the curve makes equal intercepts onthe axes.

Find the values of x for which the following functions are maximum or minimum: (i) ` x^(3)- 3x^(2) - 9x ` (ii) ` 4x^(3)-15x^(2)+12x+1` (iii) ` 1-x-x^(2)` (iv) `x^(4)-8x^(3)+22x^(2)-24x +7` (v) `(x^(2)-x+1)/(x^(2)+x+1)`

`log_(e) 10.02`, given that `log_(e) 10 = 2.3026`

Find the approximate values of : `log_(10)(1002)," given that "log_(10)e=0.4343`.A. `3.0086`B. `3.0087`C. `3.00086`D. `3.00087`

Using differentials,find the approximate value of `(log)_e 4.04`, it being given that `(log)_(10)4=0. 6021`and `(log)_(10)e=0. 4343`.

If `f(x)=3x^(2)+4x-1`, then find the approximate value of `f(3.1)`.

Find the equation of normal of the curve `2y= 7x - 5x^(2)` at those points at which the curve intersects the line x = y.

The approximate value of `x^(3)-2x^(2)+3x+2,` when x=3.02 isA. `20.36`B. `20.036`C. `20.18`D. `20.018`

Prove that function `f(x) = log_e x` is strictly increasing in the interval `(0,oo)`

`log_(10) (4.04)`, it being given that `log_(10) 4 = 0.6021 and log_(10) e = 0.4343`A. `1.3874`B. `1.3964`C. `1.4864`D. `1.3864`

Find the approximate value of `log_e(101)` given `log_e 10=2*3026`A. `4.6152`B. `4.6052`C. `4.6125`D. `4.6025`

If `f(x) = 2x^(2)+5x+2`, then find the approximate value of `f(2.01)`.

Find the approximate value of `log_e(9*01)` given `log_e 3=1*0986`A. `2.1988`B. `2.1983`C. `2.1987`D. `2.1982`

Find the approximate values of : `(4.01)^(5)`A. 1036.08B. 1036.06C. `1036.80`D. `1036.60`

The approximate value of ` f(X) = x^(3) +5x^(2)-7x+9` at x= 1.1 isA. `8.6`B. `8.5`C. `8.4`D. `8.3`

Find the approximate value of `(4.01)^3` .A. 66.44B. 64.84C. 64.88D. 64.48

If `f(x) = 2x^(2)+5x+2`, then find the approximate value of `f(2.01)`.A. `27.02`B. `27.20`C. `27.04`D. `27.40`

Find the approximate value of `e^(1.005)` (given `e = 2.7183`)A. `2.7319`B. `2.7318`C. `2.8542`D. `2.8541`

Find the approximate value of `e^(1.005)` (given `e = 2.7183`)A. `2.7237`B. `2.2737`C. `2.3772`D. `2.7273`

If the radius of asphere is measured as 9 cm with an error or 0.03 m, find the approximateerror in calculating its surface area.

For a gas equation PV=100, volume V is `25 cm^(3)`, pressure P is measured in`" dynes/cm"^(2)`. If volume is increasing at the rate of `0.25 cm^(3)" /sec"`., then the rate of change of pressure isA. `-0.02" dynes/cm"^(2)`B. `0.02" dynes/cm"^(2)`C. `-0.04" dynes/cm"^(2)`D. `0.04" dynes/cm"^(2)`

Find the approximate values of : `cot^(-1)(1.001)`A. `(pi)/(4)+0.005`B. `(pi)/(4)+0.0005`C. `(pi)/(4)-0.005`D. `(pi)/(4)-0.0005`

Find the approximate values of : `root(3)(26.96)`A. `2.9985`B. `2.9984`C. `2.9988`D. `2.9898`

The approximate value of `sin^(-1)(0.51)," if "(1)/(sqrt(3))=0.5774` isA. `(pi)/(3)+0.1154`B. `(pi)/(3)+0.1155`C. `(pi)/(6)+0.01155`D. `(pi)/(6)+0.01154`

Find the approximate values of : `tan^(-1)(1.001)`.A. `(pi)/(4)-0.0005`B. `(pi)/(4)+0.0005`C. `(pi)/(4)-0.005`D. `(pi)/(4)+0.005`

Using differentials,find the approximate value of `(0. 009)^(1//3)`

The approximate value of `root(3)(0.009)` isA. `0.2083`B. `0.2038`C. `0.2084`D. `0.2048`

Find the approximate values of : `cos(89^(@)30)," given "1^(@)=0.0175^( c )`.A. `0.00875`B. `0.0875`C. `0.0175`D. `0.0876`

Find the approximate values of : `tan(44^(@))," given "1^(@)=0.0175^( c )`.A. `0.09825`B. `0.9825`C. `0.0965`D. `0.965`

The approximate value of `root(5)(32.1)` isA. `2.125`B. `2.0015`C. `2.0125`D. `2.00125`

Approximate value of `tan^(-1)(0.999)` isA. `(pi)/(4)-0.0005`B. `(pi)/(4)-0.005`C. `(pi)/(4)-0.05`D. `(pi)/(4)-0.5`

The approximate value of `root(3)(28)` isA. `3.038`B. `3.035`C. `3.036`D. `3.037`

Find the approximate value of `root(3)(63)`A. `3.09792`B. `3.09791`C. `3.9792`D. `3.9791`

Find the approximate value of `root(3)(27.027)` .A. `3.001`B. `3.01`C. `3.003`D. `3.037`

Find the approximate value of cos `(29^@ 30prime)` given `1^@ = 0.0175^c and cos 30^@ = 0.8660`A. `0.8604`B. `0.8603`C. `0.8704`D. `0.4928`

Find the approximate value of `root(10)(0.999)` .A. `0.0998`B. `0.9998`C. `0.0999`D. `0.9999`

The apprximate value of `sin(31^(@))`, given that `1^(@)=0.0175, cos 30^(@)=0.8660` isA. `0.5051`B. `0.5052`C. `0.5151`D. `0.5152`

Using differentials,find the approximate value of `sqrt(37)`

Using differentials, find the approximate value of `(3. 968)^(3/2)`A. `7.409`B. `7.904`C. `7.804`D. `7.408`

Using differentials,find the approximate value of `1/((2. 002)^2)`

Using differentials, find theapproximate value of `sqrt(49. 5)`

Using differentials, find the approximate value of : `root(3)(127)`

Find the intervals in which `f(x)=x^4-4x^3+4x^2+15`is increasing or decreasing.

Using differentials, find the approximate values of the following: `1/(2.002)^(2)`

Using differentials, find the approximate values of the following: `sqrt(0.24)`

Find the approximate value of `log_e(901)` given `log_e 3=10986`A. `2.1988`B. `2.1983`C. `2.1987`D. `2.1982`