32581 + Interview Questions in Mathematics Page 277 InterviewSolution

13801.

Prepare Trading and Profit and Loss Account and Balance Sheet from the following Trial Balance and information as on 31st March, 2019: Name of Account Debit (₹) Credit (₹) Drawings and Capital 15,000 3,25,000 Plant and Machinery 2,00,000 – Motor Vehicle 1,50,000 – Return Inward and Outward 25,000 37,000 Stock on 1st April, 2018 82,000 – Purchases and Sales 4,40,000 6,75,000 Carriage Inward 6,000 – Trade Expenses 2,500 – Bad Debts 4,250 – Provision for Doubtful Debts – 6,000 Commission – 4,000 Rent, Rates & Taxes 12,000 – Salaries and Wages 24,000 – Debtors and Creditors 70,000 55,000 Fuel and Water 4,750 – Cash in Hand 16,500 – Cash at Bank 50,000 – Total 11,02,000 11,02,000 Adjustments:(i) Closing Stock was valued at ₹ 1,12,500.(ii) Commission include ₹ 1,200 being commission received in advance.(iii) Salaries and wages is outstanding for the month of Feb. & March, 2019.(iv) Depreciate Plant & Machinery by 15% and Motor Vehicle by 20%.(v) Write off ₹ 500 as further Bad Debts and maintain provision for doubtful debts at 1% on debtors.

Answer» Prepare Trading and Profit and Loss Account and Balance Sheet from the following Trial Balance and information as on 31st March, 2019:

Name of Account	Debit (₹)	Credit (₹)
Drawings and Capital	15,000	3,25,000
Plant and Machinery	2,00,000	–
Motor Vehicle	1,50,000	–
Return Inward and Outward	25,000	37,000
Stock on 1st April, 2018	82,000	–
Purchases and Sales	4,40,000	6,75,000
Carriage Inward	6,000	–
Trade Expenses	2,500	–
Bad Debts	4,250	–
Provision for Doubtful Debts	–	6,000
Commission	–	4,000
Rent, Rates & Taxes	12,000	–
Salaries and Wages	24,000	–
Debtors and Creditors	70,000	55,000
Fuel and Water	4,750	–
Cash in Hand	16,500	–
Cash at Bank	50,000	–

Total	11,02,000	11,02,000

Adjustments:

(i) Closing Stock was valued at ₹ 1,12,500.

(ii) Commission include ₹ 1,200 being commission received in advance.

(iii) Salaries and wages is outstanding for the month of Feb. & March, 2019.

(iv) Depreciate Plant & Machinery by 15% and Motor Vehicle by 20%.

(v) Write off ₹ 500 as further Bad Debts and maintain provision for doubtful debts at 1% on debtors.

13803.	If 2x,x+10,3x+2 are in AP, then x= ___
Answer» If $2 x, x + 10, 3 x + 2$ are in AP, then $x =$ ___

13804.	Find the equation of a line whose: y-intercept = 2 and slope = 3.
Answer» Find the equation of a line whose: y-intercept = 2 and slope = 3.

13805.	What is the maximum value of 1cosec θ?
Answer» What is the maximum value of $\frac{1}{cosec θ}$ ?

13806.	Solve the following quadratic equations by factorization:4x2 + 5x = 0
Answer» Solve the following quadratic equations by factorization: 4x² + 5x = 0

13807.	The mean of 35 observations is 20, out of which mean of first 18 observations is 15 and mean of last 18 observation is 25. Find the 18th observation.
Answer» The mean of 35 observations is 20, out of which mean of first 18 observations is 15 and mean of last 18 observation is 25. Find the 18th observation.

13808.	If α and β are the zeroes of a polynomial f(x) = 6x2 + x − 2, find the value of αβ+βα
Answer» If α and β are the zeroes of a polynomial f(x) = 6x² + x − 2, find the value of $(\frac{α}{β} + \frac{β}{α})$

13809.	Two trains,each of length 100 m,are running on parallel tracks.One overtakes the other in 20 second and one crosses the other in 10 second.Calculate the velocities of two trains.Explain in detail why net dis†an ce is 200m and give the solution
Answer» Two trains,each of length 100 m,are running on parallel tracks.One overtakes the other in 20 second and one crosses the other in 10 second.Calculate the velocities of two trains.Explain in detail why net dis†an ce is 200m and give the solution

13810.	If the median of the following frequency distribution is 46, find the missing frequencies. Variable frequency 10-20. 12 20-30. 30 30-40. ? 40-50. 65 50-60. ? 60-70. 25 70-80. 18 Total. 229
Answer» If the median of the following frequency distribution is 46, find the missing frequencies. Variable frequency 10-20. 12 20-30. 30 30-40. ? 40-50. 65 50-60. ? 60-70. 25 70-80. 18 Total. 229

13811.	The two sides of a right-angled triangle are given as shown in the figure. Find the third side.
Answer» The two sides of a right-angled triangle are given as shown in the figure. Find the third side.

13814.	The second and fourth numbers in an arithmetic sequences are 8 and 2. Find the first and the third numbers.
Answer» The second and fourth numbers in an arithmetic sequences are 8 and 2. Find the first and the third numbers.

13815.	If θ is an acute angle such that cos θ=35, then sin θ tan θ-12 tan2 θ=(a) 16625(b) 136(c) 3160(d) 1603
Answer» If θ is an acute angle such that $\cos θ = \frac{3}{5}, then \frac{\sin θ \tan θ - 1}{2 \tan^{2} θ} =$ (a) $\frac{16}{625}$ (b) $\frac{1}{36}$ (c) $\frac{3}{160}$ (d) $\frac{160}{3}$

13816.	How can we find the area of a parallelogram?
Answer» How can we find the area of a parallelogram?

13817.	A cone of height 12cm and radius of base 10cm is divided by a plane parallel to the base into a cone and a frustum ofequal volume. Find the ratio of height of the new cone and frustum formed
Answer» A cone of height 12cm and radius of base 10cm is divided by a plane parallel to the base into a cone and a frustum ofequal volume. Find the ratio of height of the new cone and frustum formed

13818.	If cot^1 ((2n)/pi) > pi/3; then number of values n is
Answer» If cot^1 ((2n)/pi) > pi/3; then number of values n is

13819.	In order to paint a solid frustum , which area would be taken into consideration ?
Answer» In order to paint a solid frustum , which area would be taken into consideration ?

13820.	Very-Short and Short-Answer QuestionsHow many three-digit natural numbers are divisible by 9? [CBSE 2013]
Answer» Very-Short and Short-Answer Questions How many three-digit natural numbers are divisible by 9? [CBSE 2013]

13822.	Sin 2A = 2 sin A is true when A =(a) 0°(b) 30°(c) 45°(d) 60°
Answer» Sin 2A = 2 sin A is true when A = (a) 0° (b) 30° (c) 45° (d) 60°

13823.	The parallel sides of a trapezium are 12 cm and 9 cm and the diatance between them is 8 cm. Find the area of the trapezium.
Answer» The parallel sides of a trapezium are 12 cm and 9 cm and the diatance between them is 8 cm. Find the area of the trapezium.

13824.	If [2a+ba−2b5c−d4c+3d]=[4−31124], then b is
Answer» If $[\begin{matrix} 2 a + b & a - 2 b 5 c - d & 4 c + 3 d \end{matrix}] = [\begin{matrix} 4 & - 3 11 & 24 \end{matrix}]$ , then $b$ is

13825.	Family y = Ax + A3 of curves will correspond to a differential equation of order _______________ and degree _______________.
Answer» Family y = Ax + A³ of curves will correspond to a differential equation of order _______________ and degree _______________.

13826.	Two dice are thrown simultaneously. The probability of getting a doublet is
Answer» Two dice are thrown simultaneously. The probability of getting a doublet is

13827.	If one zero of the polynomial (a^2+9)x^2+13x+6a is reciprocal of the other. Find a.
Answer» If one zero of the polynomial (a^2+9)x^2+13x+6a is reciprocal of the other. Find a.

13828.	Solve for x, y and z in the below Linear equation by substitution method :10x+5y−8z=−55x−4y+z=3 x+2y−z=3
Answer» Solve for x, y and z in the below Linear equation by substitution method : $10 x + 5 y - 8 z = - 5 5 x - 4 y + z = 3 x + 2 y - z = 3$

13829.	Find the area of a quadrilateral ABCD, the coordinates of whose varities are A (-3, 2), B (5, 4), C (7, -6) and (-5, -4).
Answer» Find the area of a quadrilateral ABCD, the coordinates of whose varities are A (-3, 2), B (5, 4), C (7, -6) and (-5, -4).

Explore topic-wise InterviewSolutions in .

Which term of the series : 21, 18, 15, ............. is -81 ? Can any term of this series be zero ? If yes, find the number of terms.

If 2x,x+10,3x+2 are in AP, then x= ___

Find the equation of a line whose: y-intercept = 2 and slope = 3.

What is the maximum value of 1cosec θ?

Solve the following quadratic equations by factorization:4x2 + 5x = 0

The mean of 35 observations is 20, out of which mean of first 18 observations is 15 and mean of last 18 observation is 25. Find the 18th observation.

If α and β are the zeroes of a polynomial f(x) = 6x2 + x − 2, find the value of αβ+βα

Two trains,each of length 100 m,are running on parallel tracks.One overtakes the other in 20 second and one crosses the other in 10 second.Calculate the velocities of two trains.Explain in detail why net dis†an ce is 200m and give the solution

If the median of the following frequency distribution is 46, find the missing frequencies. Variable frequency 10-20. 12 20-30. 30 30-40. ? 40-50. 65 50-60. ? 60-70. 25 70-80. 18 Total. 229

The two sides of a right-angled triangle are given as shown in the figure. Find the third side.

The second and fourth numbers in an arithmetic sequences are 8 and 2. Find the first and the third numbers.

If θ is an acute angle such that cos θ=35, then sin θ tan θ-12 tan2 θ=(a) 16625(b) 136(c) 3160(d) 1603

How can we find the area of a parallelogram?

A cone of height 12cm and radius of base 10cm is divided by a plane parallel to the base into a cone and a frustum ofequal volume. Find the ratio of height of the new cone and frustum formed

If cot^1 ((2n)/pi) > pi/3; then number of values n is

In order to paint a solid frustum , which area would be taken into consideration ?

Very-Short and Short-Answer QuestionsHow many three-digit natural numbers are divisible by 9? [CBSE 2013]

If the median of the following data is 32.5, find the missing frequencies. Class interval: 0−10 10−20 20−30 30−40 40−50 50−60 60−70 Total Frequency: f1 5 9 12 f2 3 2 40

Sin 2A = 2 sin A is true when A =(a) 0°(b) 30°(c) 45°(d) 60°

The parallel sides of a trapezium are 12 cm and 9 cm and the diatance between them is 8 cm. Find the area of the trapezium.

If [2a+ba−2b5c−d4c+3d]=[4−31124], then b is

Family y = Ax + A3 of curves will correspond to a differential equation of order _______________ and degree _______________.

Two dice are thrown simultaneously. The probability of getting a doublet is

If one zero of the polynomial (a^2+9)x^2+13x+6a is reciprocal of the other. Find a.

Solve for x, y and z in the below Linear equation by substitution method :10x+5y−8z=−55x−4y+z=3 x+2y−z=3

Find the area of a quadrilateral ABCD, the coordinates of whose varities are A (-3, 2), B (5, 4), C (7, -6) and (-5, -4).

30. Two vertices B and C of a triangle are mirror image of each other with respect to line y=x.B is(3,4) and orthocentre of triangleABC is at origin.If A is(h,k)then find the value of 7(h+k).

Find the median of the following data. Class interval0−1010−2020−3030−4040−50Frequency81014108

If [a+b25ab]=[6258] , find the values of a and b.

Find the missing term in the given sequence2, 1, 1, 2, 7, ?

A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

What is the value of y in x + y = 6 and x - y = 4.

The value of sqrt((x - y) ^ 2) + sqrt((y - x) ^ 2) is

An integer is chosen at random between 1 and hundred find the probability that it is divisible by 8 and not divisible by 8

What is the sub-duplicate ratio of 49:121?

Question 29Find the sum of all the 11 terms of an AP whose middle most term is 30.

The value of k for which x2–4x+k=0 has coincident roots is ___ .

NEBULOUS

Let a1,a2,a3,…… be terms of an A.P. If a1+a2+…+apa1+a2+…+aq=p2q2,p≠q then what is the value of a6a21? [3 MARKS]

A carpenter makes stools for electricians with a square top of side 0.5m and at a height 1.5m above the ground. Also, each leg is inclined at an angle of 60∘ to the ground. The lengths of two steps in metres correct up to two places of decimals is

If sin(A+B)=1, cos(A–B)=1 and 0∘&lt;A+B≤90∘, find A and B.

ABCDEF is a regular hexagon with centre O (in the following figure). If the area of triangle OAB is 9 cm2, find the area of : (i) the hexagon and (ii) the circle in which the haxagon is incribed.

In the figure, tangents and are drawn to a circle with centre from an external point . If is a tangent to the circle at and = 15 cm, find the perimeter of ΔPCD

Vinod deposits Rs 700 every month in a recurring deposit account at the interest rate of 9% per annum for 12 months. What maturity amount he gets on his recurring deposit account.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find out the number of toys produced on that day.

Let M be a 3×3 matrix satisfying M⎡⎢⎣010⎤⎥⎦=⎡⎢⎣−123⎤⎥⎦,M⎡⎢⎣1−10⎤⎥⎦=⎡⎢⎣11−1⎤⎥⎦, and M⎡⎢⎣111⎤⎥⎦=⎡⎢⎣0012⎤⎥⎦ Then the sum of the diagonal entries of M is

Family y = Ax + A3 of curves will correspond to a differential equation of order _ and degree _.

If sin(A+B)=1, cos(A–B)=1 and 0∘<A+B≤90∘, find A and B.

13831.	30. Two vertices B and C of a triangle are mirror image of each other with respect to line y=x.B is(3,4) and orthocentre of triangleABC is at origin.If A is(h,k)then find the value of 7(h+k).
Answer» 30. Two vertices B and C of a triangle are mirror image of each other with respect to line y=x.B is(3,4) and orthocentre of triangleABC is at origin.If A is(h,k)then find the value of 7(h+k).

13833.	If [a+b25ab]=[6258] , find the values of a and b.
Answer» If $[\begin{matrix} a + b & 2 5 & a b \end{matrix}] = [\begin{matrix} 6 & 2 5 & 8 \end{matrix}]$ , find the values of a and b.

13834.	Find the missing term in the given sequence2, 1, 1, 2, 7, ?
Answer» Find the missing term in the given sequence 2, 1, 1, 2, 7, ?

13836.	What is the value of y in x + y = 6 and x - y = 4.
Answer» What is the value of y in x + y = 6 and x - y = 4.

13837.	The value of sqrt((x - y) ^ 2) + sqrt((y - x) ^ 2) is
Answer» The value of sqrt((x - y) ^ 2) + sqrt((y - x) ^ 2) is

13838.	An integer is chosen at random between 1 and hundred find the probability that it is divisible by 8 and not divisible by 8
Answer» An integer is chosen at random between 1 and hundred find the probability that it is divisible by 8 and not divisible by 8

13839.	What is the sub-duplicate ratio of 49:121?
Answer» What is the sub-duplicate ratio of 49:121?

13840.	Question 29Find the sum of all the 11 terms of an AP whose middle most term is 30.
Answer» Question 29 Find the sum of all the 11 terms of an AP whose middle most term is 30.

13841.	The value of k for which x2–4x+k=0 has coincident roots is ___ .
Answer» The value of $k$ for which $x^{2} - 4 x + k = 0$ has coincident roots is ___ .

13843.	Let a1,a2,a3,…… be terms of an A.P. If a1+a2+…+apa1+a2+…+aq=p2q2,p≠q then what is the value of a6a21? [3 MARKS]
Answer» Let $a_{1}, a_{2}, a_{3}, \dots \dots$ be terms of an A.P. If $\frac{a_{1} + a_{2} + \dots + a_{p}}{a_{1} + a_{2} + \dots + a_{q}} = \frac{p^{2}}{q^{2}}, p \neq q$ then what is the value of $\frac{a_{6}}{a_{21}}$ ? [3 MARKS]