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8 months ago

Mensuration Formula Maths

In the given figure, PQRS is a square and M and N are midpoints of their respective sides. Find the area of the quadrilateral PMRN.

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Payal Gupta

Contributor-Level 10

Since M is the midpoint of side PQ, the length of MQ is 2.

Hence, the area of? MQR = $\frac{1}{2}$ × 2 × 4 = 4.

Also area of? NSR = 4. Thus, the unshaded area of the figure = 4 + 4 = 8.

Hence, the area of quadrilateral PMRN

= Area of the square PQRS – The unshaded area of the figure

= 16 – 8 = 8

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8 months ago

Maths Class 12th

The first term of a series in A.P. is 17, the last term is $- 12 \frac{3}{8}$ and the sum of the series is $25 \frac{7}{16}$ Find the common difference.

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Payal Gupta

Contributor-Level 10

Let n = the number of terms.

Then, $25 \frac{7}{16} = \frac{n}{2} [17 + (- 12 \frac{3}{8})] = \frac{n}{2} \times 4 \frac{5}{8}$

$\Rightarrow \frac{407}{16} = 37 \frac{n}{16}$ $\Rightarrow n = \frac{407}{37} = 11$

Let d be the common difference.

Then $- 12 \frac{3}{8}$ (= the eleventh term) = 17 + 10d

$\Rightarrow 10 d = - 12 \frac{3}{8} - 17 = - \frac{235}{8}$

$\Rightarrow d = \frac{- 235}{8 \times 10} = - \frac{47}{16}$

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8 months ago

Maths Class 12th

Two container A & B contain oil. 60% of contents of container A was transferred to container B. Then 50% contents of container B was transferred to A. The quantity of oil in container A to that of container B is now 11 : 7. What was ratio of initial volumes of oil in containers of A and B?

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Payal Gupta

Contributor-Level 10

Let oil in containers be A & B.

After 1st operation

Container A = 0.4 A

Container B = 0.6 A + B

After 2nd operation

Container A = 0.4 A + 0.3 A + 0.5 B

Container B = 0.3 A + 0.5 B

= $\frac{(0.7 A + B)}{11} = \frac{(0.3 A + B)}{7}$

1.6A = 2B $\Rightarrow$ $\frac{A}{5} = \frac{B}{4}$

Volume of A : B = 5 : 4.

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8 months ago

IIIT Bhagalpur - Indian Institute of Information Technology VIT-AP University

Which is better: VIT AP for CSE or IIIT Bhagalpur for mechatronics?

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8 months ago

Maths Class 12th

In the figure given below, ABCD is a rectangle. The area of the isosceles right triangle ABE = 7 cm²; EC = 3(BE). The area of ABCD (in cm²) is

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Payal Gupta

Contributor-Level 10

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8 months ago

Maths Class 12th

There are three glasses of equal capacity. The ratio of milk & water in the three is 2 : 5, 3 : 4, 4 : 5. The mixture of these three is put into a bucket. Find ratio of water to milk in the bucket.

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Payal Gupta

Contributor-Level 10

I	II	III
2 : 5	3 : 4	4 : 5

Hence new ratio

$\frac{(\frac{2}{7} + \frac{3}{7} + \frac{4}{9})}{(\frac{5}{7} + \frac{4}{7} + \frac{5}{9})}$

= 73 : 116

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8 months ago

Maths Class 12th

A car running from point P₁ to point P₂ meets with an accident 50 km from point P₁, after which it travels with three- fifths of its original velocity and arrives 3 hours late at point P₂; if the accident had occurred 50 km further on, it would have been only 2 hours late. Find the distance from point P₁ to point P₂.

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Payal Gupta

Contributor-Level 10

Let the distance be x km and speed be y km/hr and t be the time in hours. Then the equation will be x = yt …. (1),

Therefore, $\frac{50}{y} + \frac{[x - 50]}{3 y / 5} = t + 3 . . . . . (2)$

Also, $\frac{100}{y} + \frac{[x - 100]}{3 y / 5} = t + 2 . . . . . (3)$

On solving the above equations, we get speed is $\frac{100}{3}$ km/hr time is 6 hrs, and distance is 200 km.

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8 months ago

Mensuration Formula Maths

Two runners ride from A to B a distance of 55 km, and the first arrives 30 minutes before the second. They then ride from B to A, the first giving the second a start of 4 km and yet arrive 6 minutes before him. Find the speed of A.

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Payal Gupta

Contributor-Level 10

Let the speed of A be x km/hr and speed of B be y km/hr, then:

$\frac{55}{x} = \frac{55}{y} - \frac{1}{2} . . . . . (1)$

Also, $\frac{55}{x} = \frac{51}{y} - \frac{1}{10} . . . . . (2)$

On solving both equation (1) & (2) we get x = 11 km/hr and y = 10 km/hr.

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8 months ago

Maths Class 12th

There is a right circular cone of base radius 5 cm. This cone is cut into two portions by a plane parallel to its base such that the portion above the plane is a cone of base radius 3 cm and the portion below the plane has a height of 6 cm. Find the volume of the bottom solid.

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Payal Gupta

Contributor-Level 10

Volume of smaller cone

$= \frac{1}{3} π {(3)}^{2} \times 9 = 27 π$

$= \frac{1}{3} π {(5)}^{2} \times 15 = 125 π$

$\Rightarrow$ Volume of the solid = 125π – 27π = 98 π

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8 months ago

Maths Class 12th

A Banana seller sells x dozen Bananas. If he had sold 100 dozen Bananas more at 20 paise a dozen less or if he had sold 120 dozen less at 30 paise a dozen more, he would have received the same amount for his Bananas. How many dozens does he sell?

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Payal Gupta

Contributor-Level 10

Px= (P-0.2) (x+100)= (P+0.3) (x-120)

Solving x=1000

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8 months ago

Maths Class 12th

A shopkeeper buys 216 packets of biscuits at the rate of Rs. $\frac{x}{8}$ per pkt. He sells 8 dozen at the rate of Rs. 2.36 x per dozen and the rest at 16 $(\frac{x}{4} + 1)$ paise each. What is the value of profit?

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Payal Gupta

Contributor-Level 10

Total S.P. will be

$8 \times [2.36 x] + \frac{16}{100} [\frac{x}{4} + 1] 120 = 18.88 x + 4.8 x + 19.2$

$= [\frac{x}{8}] 216 = 27 x$

Profit = 23.68x + 19.2 − 27x = 19.2 - 3.32x

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8 months ago

Maths Class 12th

The digits of a three-digit number A are written in reverse order to form another three digit number B. If B > A and B – A is perfectly divisible by 7, then which of the following is necessarily true?

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Payal Gupta

Contributor-Level 10

Let A = abc and B = cba

Therefore, B – A = 100c + 10b + a – (100a + 10b + c) = 99 (c – a). B – A is a multiple of 7.

Therefore, c – a = 7 (a, c) (1, 8) or (2, 9).

Hence, number is between 108 to 198 or 209 to 299.

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8 months ago

Maths Class 12th

8 litres of wine are drawn from a cask and replaced by 8 litres of water. 8 litres of the mixture are next drawn and again replaced by 8 litres of water. If the ratio of wine to water in the cask is now 81 : 19, how much wine was in the cask at first? (There was no water in the cask at first.)

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Payal Gupta

Contributor-Level 10

Let there be x litres of wine in the beginning

${(\frac{x - 8}{x})}^{2} = \frac{81}{100}$

$\Rightarrow$ x = 80 litres

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8 months ago

Maths Class 12th

A hound ran to catch a rabbit 70 m apart. The rabbit has 35 jumps in one minute & the hound has 50 jumps in 2 minutes. If 2 jumps of the rabbit equal 40 cm & one jump of the hound equal 60 cm, in what time will the hound catch the rabbit?

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Payal Gupta

Contributor-Level 10

Suppose the hound catches the rabbit in t minutes

Number of jumps by the rabbit = 35t & distance covered = 20 * 35t = 700 t cm.

Similarly Distance covered by hound = 25t * 60 = 1500t cm.

Now, 1500 t – 700t = 7000 cm or t = $\frac{35}{4}$ min.

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8 months ago

Maths Class 12th

S1, S2 and S3 are three contestants for a race of 2,000 metres. If S1 can give S2 a start of 100 metres and S3 a start of 138 metrse, then of how many metres would S2 give a start to S3 in a similar race?

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Payal Gupta

Contributor-Level 10

When S1 runs 1900 metres, S3 would run 1862 metres. Hence, the start given is 38/1900 * 2000 = 40 metres

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8 months ago

St. Teresas Institute Of Education Teaching & Education

Is hijab allowed at St. Teresas Institute of Education for students pursuing B.Ed?

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8 months ago

M.Sc Botany

Can one pursue M.Sc in Botany after completing graduation?

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8 months ago

Tezpur University Colleges in Tezpur

I have done B.Sc. How do I apply for B.Ed at Tezpur University?

1 Follower 6 Views

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8 months ago

Career CBSE 12th

How to become a Chemical Engineer after 12th?

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Vidhi Jain

Contributor-Level 10

Have a look at some basic steps on how to become a chemical engineer after 12th grade:

You must opt for a full fledged course in Chemical Engineering, be it a B.E/BTech degree or Diploma course for which you should have at least 50 to 60% marks in Class 12 board exams and give relevant entrance exams.
You should focus on your coursework and take up future relevant elective subjects and complete practical laboratory courses with dedication.
Pursue internships and take part in projects to get hands-on knowledge of the workings of the field and put that on your resume.
A strong resume is the key to an excellent career graph, which must h

...more

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8 months ago

Engineering Chemical Engineering

Which books are a must read for Chemical Engineering students?

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Vidhi Jain

Contributor-Level 10

Some Chemical Engineering books you can refer to complete your course syllabus are

Chemical Reaction Engineering by Octave Levenspiel
Chemical Process Safety: Fundamentals with Applications by Joseph F. Louvar and Daniel A. Crowl
Biochemical Engineering Fundamentals by J. E. Bailey and D. F. Ollis
Unit Operations of Chemical Engineering by Warren L. McCabe and Julian C. Smith
Chemical Engineering Thermodynamics – Theory and Applications by R. Ravi

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