32581 + Interview Questions in Mathematics Page 228 InterviewSolution

11351.	An express train makes a run of 240 km at a certain speed. Another train , whose speed is 12 km/hr less than the first train takes an hour longer to make the same trip . Find the speed of the express train in km/hr.
Answer» An express train makes a run of 240 km at a certain speed. Another train , whose speed is 12 km/hr less than the first train takes an hour longer to make the same trip . Find the speed of the express train in km/hr.

Discussion

11352.	Find the median Find the mode of the following data. xi1014182125fi1015799
Answer» Find the median Find the mode of the following data. $\begin{matrix} x_{i} & 10 & 14 & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 \end{matrix}$

11352.

Find the median Find the mode of the following data. xi1014182125fi1015799

Answer»

Find the median

Find the mode of the following data.
$\begin{matrix} x_{i} & 10 & 14 & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 \end{matrix}$

Discussion

11353.	In the following figure, O is the centre of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take π = 3.142)
Answer» In the following figure, O is the centre of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take π = 3.142)

Discussion

11354.	14. The angle of elevation of the top of the tower observed from each three points on the A,B,C on the ground forming same angle alpha .if R is circum Radius of the ΔABC , then height of the tower.
Answer» 14. The angle of elevation of the top of the tower observed from each three points on the A,B,C on the ground forming same angle alpha .if R is circum Radius of the ΔABC , then height of the tower.

Discussion

11355.

Kanika, Disha and Kabir were partners sharing profits in the ratio of 2 : 1 : 1. On 31st March, 2016, their Balance Sheet was as under: Liabilities Amount (₹) Assets Amount (₹) Trade creditors 53,000 Bank 60,000 Employees' Provident Fund 47,000 Debtors 60,000 Kanika's Capital 2,00,000 Stock 1,00,000 Disha's Capital 1,00,000 Fixed assets 2,40,000 Kabir's Capital 80,000 Profit and Loss A/c 20,000 4,80,000 4,80,000 Kanika retired on 1st April, 2016. For this purpose, the following adjustments were agreed upon:(a) Goodwill of the firm was valued at 2 years' purchase of average profits of three completed years preceding the date of retirement. The profits for the year: 2013-14 were ₹ 1,00,000 and for 2014-15 were ₹ 1,30,000.(b) Fixed Assets were to be increased to ₹ 3,00,000.(c) Stock was to be valued at 120%.(d) The amount payable to Kanika was transferred to her Loan Account.Prepare Revaluation Account, Capital Accounts of the partners and the Balance Sheet of the reconstituted firm.

Answer» Kanika, Disha and Kabir were partners sharing profits in the ratio of 2 : 1 : 1. On 31st March, 2016, their Balance Sheet was as under:


Liabilities	Amount (₹)	Assets	Amount (₹)
Trade creditors	53,000	Bank	60,000
Employees' Provident Fund	47,000	Debtors	60,000
Kanika's Capital	2,00,000	Stock	1,00,000
Disha's Capital	1,00,000	Fixed assets	2,40,000
Kabir's Capital	80,000	Profit and Loss A/c	20,000



	4,80,000		4,80,000

Kanika retired on 1st April, 2016. For this purpose, the following adjustments were agreed upon:

(a) Goodwill of the firm was valued at 2 years' purchase of average profits of three completed years preceding the date of retirement. The profits for the year:

2013-14 were ₹ 1,00,000 and for 2014-15 were ₹ 1,30,000.

(b) Fixed Assets were to be increased to ₹ 3,00,000.

(c) Stock was to be valued at 120%.

(d) The amount payable to Kanika was transferred to her Loan Account.

Prepare Revaluation Account, Capital Accounts of the partners and the Balance Sheet of the reconstituted firm.

Discussion

11356.	A farmer runs a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time will the tank be filled?
Answer» A farmer runs a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time will the tank be filled?

Discussion

11357.	Solve equation, given below, using factorisation method: (1+1x+1)(1−1x−1)=78
Answer» Solve equation, given below, using factorisation method: $(1 + \frac{1}{x + 1}) (1 - \frac{1}{x - 1}) = \frac{7}{8}$

11357.

Solve equation, given below, using factorisation method: (1+1x+1)(1−1x−1)=78

Answer»

Solve equation, given below, using factorisation method:

$(1 + \frac{1}{x + 1}) (1 - \frac{1}{x - 1}) = \frac{7}{8}$

Discussion

11358.	A random survey of the number of children of various age groups playing in park was found as follows:Age (in years)Number of children1−252−333−565−7127−10910−151015−174Draw a histogram to represent the data above.
Answer» A random survey of the number of children of various age groups playing in park was found as follows: $\begin{matrix} Age (in years) & Number of children 1 - 2 & 5 2 - 3 & 3 3 - 5 & 6 5 - 7 & 12 7 - 10 & 9 10 - 15 & 10 15 - 17 & 4 \end{matrix}$ Draw a histogram to represent the data above.

Discussion

11359.	Logarithm question Find x log10 3+ log10(4x +1)=log10(x+1) +1
Answer» Logarithm question Find x log₁₀3+ log₁₀(4x +1)=log₁₀(x+1) +1

11359.

Logarithm question Find x log10 3+ log10(4x +1)=log10(x+1) +1

Answer»

Logarithm question

Find x log₁₀3+ log₁₀(4x +1)=log₁₀(x+1) +1

Discussion

11360.	The ratio between the altitudes of two similar triangles is 3 : 5; write the ratio between their : (i) medians. (ii) perimeters. (iii) areas.
Answer» The ratio between the altitudes of two similar triangles is 3 : 5; write the ratio between their : (i) medians. (ii) perimeters. (iii) areas.

Discussion

11361.	If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate :(i) α − β(ii) 1α-1β(iii) 1α+1β-2αβ(iv) α2β − αβ2(v) α4 + β4(vi) 1aα+b+1aβ+b(vii) βaα+b+αaβ+b(viii) aα2β+β2α+bαβ+βα
Answer» If α and β are the zeroes of the quadratic polynomial f(x) = ax² + bx + c, then evaluate : (i) α − β (ii) $\frac{1}{α} - \frac{1}{β}$ (iii) $\frac{1}{α} + \frac{1}{β} - 2 αβ$ (iv) α²β − αβ² (v) α⁴ + β⁴ (vi) $\frac{1}{a α + b} + \frac{1}{a β + b}$ (vii) $\frac{β}{a α + b} + \frac{α}{a β + b}$ (viii) $a (\frac{α^{2}}{β} + \frac{β^{2}}{α}) + b (\frac{α}{β} + \frac{β}{α})$

Discussion

11362.	The area of a sector of a circle of radius 2 cm is π cm2. Find the angle contained by the sector.
Answer» The area of a sector of a circle of radius 2 cm is $π c m^{2}$ . Find the angle contained by the sector.

Discussion

11363.	if a polynomial , y=ax^2+bx+c , has a0 , than what will be the value of c . Is c >0 or c
Answer» if a polynomial , y=ax^2+bx+c , has a<0 , b >0 , than what will be the value of c . Is c >0 or c<0 , expain

Discussion

11364.	If k+1=sec^2A(1+sinA)(1-sinA),then find the value of k.
Answer» If k+1=sec^2A(1+sinA)(1-sinA),then find the value of k.

Discussion

11365.	The sum of father’s age and twice the age of his son is 70. If we double the age of the father and add it to the age of his son the sum is 95. Find their present ages.
Answer» The sum of father’s age and twice the age of his son is 70. If we double the age of the father and add it to the age of his son the sum is 95. Find their present ages.

Discussion

11366.	A toy is in the form of a cylinder with hemispherical ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, then find the cost of painting the toy at the rate of 70 paise per sq cm. [CBSE 2014]
Answer» A toy is in the form of a cylinder with hemispherical ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, then find the cost of painting the toy at the rate of 70 paise per sq cm. [CBSE 2014]

Discussion

11367.	sec (60° + A) - cosec (30° - A) = ___.
Answer» sec (60° + A) - cosec (30° - A) = ___.

Discussion

11368.	Find the point of intersection of y = 6x - 9 with the X axis.
Answer» Find the point of intersection of y = 6x - 9 with the X axis.

Discussion

11369.	Question 3In figure, if ∠1=∠2 and ΔNSQ≅ΔMTR, then prove that ΔPTS∼ΔPRQ.
Answer» Question 3 In figure, if $∠ 1 = ∠ 2$ and $Δ N S Q ≅ Δ M T R$ , then prove that $Δ P T S \sim Δ P R Q$ .

Discussion

11370.	In a ΔABC, ∠B=90o,AB=12 cm and BC = 5 cm. Find (i) cos A (ii) cosec A (iii) cos C (iv) cosec C.
Answer» In a $Δ A B C, ∠ B = 90^{o}, A B = 12 c m$ and BC = 5 cm. Find (i) cos A (ii) cosec A (iii) cos C (iv) cosec C.

11370.

In a ΔABC, ∠B=90o,AB=12 cm and BC = 5 cm. Find (i) cos A (ii) cosec A (iii) cos C (iv) cosec C.

Answer»

In a $Δ A B C, ∠ B = 90^{o}, A B = 12 c m$ and BC = 5 cm.

Find (i) cos A (ii) cosec A (iii) cos C (iv) cosec C.

Discussion

11371.	If the perimeter of a sector of circle of radius 5.7cm is 27.2cm then find area of corresponding sector
Answer» If the perimeter of a sector of circle of radius 5.7cm is 27.2cm then find area of corresponding sector

Discussion

11372.	Using factor theorem, factorize the polynomial x3−6x2+11x−6.
Answer» Using factor theorem, factorize the polynomial $x^{3} - 6 x^{2} + 11 x - 6$ .

Discussion

11373.	A hemispherical tank full of water is emptied by a pipe at the rate of 0.0005 litres/second. How much time will it take to empty two thirds of the tank, if it is 6 m in diameter?
Answer» A hemispherical tank full of water is emptied by a pipe at the rate of 0.0005 litres/second. How much time will it take to empty two thirds of the tank, if it is 6 m in diameter?

Discussion

11374.	cosec²48°-tan²52°=?
Answer» cosec²48°-tan²52°=?

Discussion

11375.	The length of a rectangular field is three times its breadth. If the area of the field be 147m2, find the length of the field.
Answer» The length of a rectangular field is three times its breadth. If the area of the field be $147 m^{2}$ , find the length of the field.

Discussion

11376.	In the following figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use π =227] [CBSE 2014]
Answer» In the following figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use π = $\frac{22}{7}$ ] [CBSE 2014]

Discussion

11377.	The probability of India winning an India-Pakistan match could be
Answer» The probability of India winning an India-Pakistan match could be

Discussion

11378.	The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are(a) (2, 4) (b) (3, 5) (c) (4, 2) (d) (5, 3) [CBSE 2012]
Answer» The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are (a) (2, 4) (b) (3, 5) (c) (4, 2) (d) (5, 3) [CBSE 2012]

Discussion

11379.	The distance between the directrices of the ellipse x236+y220=1 is ___________.
Answer» The distance between the directrices of the ellipse $\frac{x^{2}}{36} + \frac{y^{2}}{20} = 1$ is ___________.

Discussion

11380.	If one root of the equation 2x2 + ax + 6 = 0 is 3, then find the value of a
Answer» If one root of the equation 2 $x^{2}$ + ax + 6 = 0 is 3, then find the value of a

Discussion

11381.	Find the value of ∠CAB+∠CBA from the following figure.
Answer» Find the value of $∠ C A B + ∠ C B A$ from the following figure.

Discussion

11382.	Construct a ΔPQR with QR = 8, PQ= 6 PR = 4. Construct the incircle of the triangle and find the radius of the incircle.
Answer» Construct a $Δ$ PQR with QR = 8, PQ= 6 PR = 4. Construct the incircle of the triangle and find the radius of the incircle.

Discussion

11383.	If the HCF of 657 and 963 is expressible in the form 657x + 963 × – 15, find x.
Answer» If the HCF of 657 and 963 is expressible in the form 657x + 963 × – 15, find x.

Discussion

11384.	71. ABCD is a \|\|gm in which AB\|\|CD and BC\|\|AD. If the points P and Q divides BC and AD in the ratio of 2:5 then prove that- Area of APQD=5/2Area of PBCQ.
Answer» 71. ABCD is a \|\|gm in which AB\|\|CD and BC\|\|AD. If the points P and Q divides BC and AD in the ratio of 2:5 then prove that- Area of APQD=5/2Area of PBCQ.

Discussion

11385.	ABCD is a quadrilateral such that DA⊥AB and CB⊥AB, x = y and EF \|\| AD such that EF bisects ∠DEC. Then CD2 =
Answer» ABCD is a quadrilateral such that $D A ⊥ A B$ and $C B ⊥ A B$ , x = y and EF \|\| AD such that EF bisects $∠ D E C$ . Then $C D^{2}$ =

Discussion

11386.	From a light house the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the light house is h metres, the distance between the ships is(a) 3+ 1 h metres(b) 3- 1 h metres(c) 3 h metres(d) 1 + 1+13 h metres
Answer» From a light house the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the light house is h metres, the distance between the ships is (a) $(\sqrt{3} + 1) h m e t r e s$ (b) $(\sqrt{3} - 1) h m e t r e s$ (c) $\sqrt{3} h m e t r e s$ (d) $1 + (1 + \frac{1}{\sqrt{3}}) h m e t r e s$

Discussion

11387.	X and Y are points of linear on the sides AB and AC respectively of a triangle ABC such that AXAB=14, AY = 2 cm and YC = 6 cm. Find whether XY\|\|BC or not
Answer» X and Y are points of linear on the sides AB and AC respectively of a triangle ABC such that $\frac{A X}{A B} = \frac{1}{4}$ , AY = 2 cm and YC = 6 cm. Find whether $X Y \| \| B C$ or not

Discussion

11388.	A boat goes 12 km upstream and 40 km downstream in 8 hours. I can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.
Answer» A boat goes 12 km upstream and 40 km downstream in 8 hours. I can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

Discussion

11389.	A horse is tied to a pole with 28 m long string. Find the area where the horse can graze. (Take π = 22/7).
Answer» A horse is tied to a pole with 28 m long string. Find the area where the horse can graze. (Take π = 22/7).

Discussion

11390.	ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB=3.6 cm, AC=2.4 cm and AD=2.1 cm, then AE is equal to
Answer» ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If $A B = 3.6 c m, A C = 2.4 c m$ and $A D = 2.1 c m,$ then AE is equal to

Discussion

11391.	Prove the following trigonometric identities.secA-tanAsecA+tanA=cos2A1+sinA2
Answer» Prove the following trigonometric identities. $\frac{\sec A - \tan A}{\sec A + \tan A} = \frac{\cos^{2} A}{{(1 + \sin A)}^{2}}$

Discussion

11392.	"Divide 32 into two parts whose product is 240". Express it in the form of a quadratic equation.
Answer» "Divide 32 into two parts whose product is 240". Express it in the form of a quadratic equation.

Discussion

11393.	Write the value of 1-cos2θcosec2θ.
Answer» Write the value of $(1 - \cos^{2} θ) {cosec}^{2} θ$ .

Discussion

11394.	Find the remainder when p(x) = 3x2+x+−1 is divided by g(x) = 1 + x.
Answer» Find the remainder when p(x) = $3 x^{2} + x + - 1$ is divided by g(x) = 1 + x.

Discussion

11395.	The side of a cube is 4 cm long. Find its volume.
Answer» The side of a cube is 4 cm long. Find its volume.

Discussion

11396.	The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
Answer» The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

Discussion

11397.	Which of the following expressions is used to determine the mode?
Answer» Which of the following expressions is used to determine the mode?

Discussion

11398.	The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are(a) (20, 0)(b) (−23, 0)(c) 45, 0(d) None of these
Answer» The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are (a) (20, 0) (b) (−23, 0) (c) $(\frac{4}{5}, 0)$ (d) None of these

Discussion

11399.	In Fig. 7.240, if DE \|\| BC, then ar∆ADEarDECB= __________.
Answer» In Fig. 7.240, if DE \|\| BC, then $\frac{a r (∆ A D E)}{a r (D E C B)}$ = __________.

Discussion

11400.	. If two vertex of an equilateral triangle are (4, 3) and(2, 4), then centroid of the triangle can be
Answer» . If two vertex of an equilateral triangle are (4, 3) and (2, 4), then centroid of the triangle can be

Discussion

Explore topic-wise InterviewSolutions in .

An express train makes a run of 240 km at a certain speed. Another train , whose speed is 12 km/hr less than the first train takes an hour longer to make the same trip . Find the speed of the express train in km/hr.

Find the median Find the mode of the following data. xi1014182125fi1015799

In the following figure, O is the centre of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take π = 3.142)

14. The angle of elevation of the top of the tower observed from each three points on the A,B,C on the ground forming same angle alpha .if R is circum Radius of the ΔABC , then height of the tower.

A farmer runs a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time will the tank be filled?

Solve equation, given below, using factorisation method: (1+1x+1)(1−1x−1)=78

A random survey of the number of children of various age groups playing in park was found as follows:Age (in years)Number of children1−252−333−565−7127−10910−151015−174Draw a histogram to represent the data above.

Logarithm question Find x log​​​​10 3+ log​​​​10(4x +1)=log​​​10(x+1) +1

The ratio between the altitudes of two similar triangles is 3 : 5; write the ratio between their : (i) medians. (ii) perimeters. (iii) areas.

If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate :(i) α − β(ii) 1α-1β(iii) 1α+1β-2αβ(iv) α2β − αβ2(v) α4 + β4(vi) 1aα+b+1aβ+b(vii) βaα+b+αaβ+b(viii) aα2β+β2α+bαβ+βα

The area of a sector of a circle of radius 2 cm is π cm2. Find the angle contained by the sector.

if a polynomial , y=ax^2+bx+c , has a0 , than what will be the value of c . Is c >0 or c

If k+1=sec^2A(1+sinA)(1-sinA),then find the value of k.

The sum of father’s age and twice the age of his son is 70. If we double the age of the father and add it to the age of his son the sum is 95. Find their present ages.

A toy is in the form of a cylinder with hemispherical ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, then find the cost of painting the toy at the rate of 70 paise per sq cm. [CBSE 2014]

sec (60° + A) - cosec (30° - A) = ___.

Find the point of intersection of y = 6x - 9 with the X axis.

Question 3In figure, if ∠1=∠2 and ΔNSQ≅ΔMTR, then prove that ΔPTS∼ΔPRQ.

In a ΔABC, ∠B=90o,AB=12 cm and BC = 5 cm. Find (i) cos A (ii) cosec A (iii) cos C (iv) cosec C.

If the perimeter of a sector of circle of radius 5.7cm is 27.2cm then find area of corresponding sector

Using factor theorem, factorize the polynomial x3−6x2+11x−6.

A hemispherical tank full of water is emptied by a pipe at the rate of 0.0005 litres/second. How much time will it take to empty two thirds of the tank, if it is 6 m in diameter?

cosec²48°-tan²52°=?

The length of a rectangular field is three times its breadth. If the area of the field be 147m2, find the length of the field.

In the following figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use π =227] [CBSE 2014]

The probability of India winning an India-Pakistan match could be

The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are(a) (2, 4) (b) (3, 5) (c) (4, 2) (d) (5, 3) [CBSE 2012]

The distance between the directrices of the ellipse x236+y220=1 is ___________.

If one root of the equation 2x2 + ax + 6 = 0 is 3, then find the value of a

Find the value of ∠CAB+∠CBA from the following figure.

Construct a ΔPQR with QR = 8, PQ= 6 PR = 4. Construct the incircle of the triangle and find the radius of the incircle.

If the HCF of 657 and 963 is expressible in the form 657x + 963 × – 15, find x.

71. ABCD is a ||gm in which AB||CD and BC||AD. If the points P and Q divides BC and AD in the ratio of 2:5 then prove that- Area of APQD=5/2Area of PBCQ.

ABCD is a quadrilateral such that DA⊥AB and CB⊥AB, x = y and EF || AD such that EF bisects ∠DEC. Then CD2 =

From a light house the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the light house is h metres, the distance between the ships is(a) 3+ 1 h metres(b) 3- 1 h metres(c) 3 h metres(d) 1 + 1+13 h metres

X and Y are points of linear on the sides AB and AC respectively of a triangle ABC such that AXAB=14, AY = 2 cm and YC = 6 cm. Find whether XY||BC or not

A boat goes 12 km upstream and 40 km downstream in 8 hours. I can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

A horse is tied to a pole with 28 m long string. Find the area where the horse can graze. (Take π = 22/7).

ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB=3.6 cm, AC=2.4 cm and AD=2.1 cm, then AE is equal to

Prove the following trigonometric identities.secA-tanAsecA+tanA=cos2A1+sinA2

"Divide 32 into two parts whose product is 240". Express it in the form of a quadratic equation.

Write the value of 1-cos2θcosec2θ.

Find the remainder when p(x) = 3x2+x+−1 is divided by g(x) = 1 + x.

The side of a cube is 4 cm long. Find its volume.

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

Which of the following expressions is used to determine the mode?

The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are(a) (20, 0)(b) (−23, 0)(c) 45, 0(d) None of these

In Fig. 7.240, if DE || BC, then ar∆ADEarDECB= __________.

. If two vertex of an equilateral triangle are (4, 3) and(2, 4), then centroid of the triangle can be

Logarithm question Find x log10 3+ log10(4x +1)=log10(x+1) +1