List of Posts written during Feb 2020

This is a list of of posts written during the month Feb 2020
(Rev. 01-Dec-2022)

List of Posts

This is the complete list of categories of posts written during Feb 2020. They have been ordered by the publish date, with the most recent first.

1. Published: 06-Feb-2020
In a triangle ABC, the points F and E respectively on AB and AC sides are such that FE || BC and FE divide the triangle into two parts with equal area. If AD ⊥ BC and AD intersect FE at point G, then GD: AG =?

2. Published: 07-Feb-2020
The average of twelve numbers is 42. The last five numbers have an average of 40 and the first four numbers have an average of 44. The sixth number is 6 less than the fifth number and 5 less than the seventh number. What will be the average of the 5th and 7th numbers?

3. Published: 07-Feb-2020
Trigonometric: $\displaystyle \frac{2 + \tan^2 \theta + \cot^2 \theta}{\sec \theta \cosec \theta} = ?$

4. Published: 07-Feb-2020
Four years ago, the ratio of the ages of A and B was 4: 5. Eight years from now, the ratio of the ages of A and B will be 11: 13. What is the sum of the present age of both of them?

5. Published: 07-Feb-2020
A truck covers a distance of 384 km at a certain speed. If the speed is reduced by 16 km / h, it will take two hours more to cover the same distance. What is the 75% of the original speed (in km / h)?

6. Published: 07-Feb-2020
Someone sold an item at a loss of 15%. If he sold it for Rs 30.60 more then he would get 9% profit. In order to get 10% profit, he has to sell the item in what amount?

7. Published: 07-Feb-2020
If a number of 9 digits is 985x3678y, the number is divisible by 72, then the value of (4x - 3y) will be:

8. Published: 07-Feb-2020
An amount becomes 8,028 in 3 years at a fixed percentage interest rate and 12,042 in 6 years, when the interest is compounded annually. What is the actual amount?

9. Published: 07-Feb-2020
The ratio of efficiencies of A, B and C is 2 : 5 : 3. On working together, all three of them can complete work in 27 days. In how many days will both B and C together complete the 4/9th part of that work?

10. Published: 07-Feb-2020
If 120 is reduced by x%, the same result will be obtained if 40 is increased by x%. Then x% of 210 will be what percentage less than (x + 20) % of 180?

11. Published: 07-Feb-2020
After giving two successive discounts each of x% on the marked price of an item, total discount is Rs. 259.20. If the face value of the object is Rs. 720, what will be the value of x?

12. Published: 07-Feb-2020
The radius of a circle with O center is 10 cm, PQ and PR are the chords of 12 cm. PO cuts the chord QR at point S. What is the length of OS?

13. Published: 07-Feb-2020
A circle is drawn inside a triangle ABC. The circle touches the sides AB, BC and AC at the points R, P and Q respectively. If AQ = 4.5 cm, PC = 5.5 cm and BR = 6 cm, then the perimeter of triangle ABC is?

14. Published: 08-Feb-2020
In ∆ ABC, the bisectors of ∠B and ∠C meet at point O inside the triangle. If ∠BOC = 122 degree , what will be the measure of ∠A?

15. Published: 08-Feb-2020
If $\displaystyle \sin \theta = \frac{p^2 - 1}{p^2 + 1}$, then $\displaystyle \cos \theta = ?$

16. Published: 08-Feb-2020
If $\displaystyle x^{4} + x^{-4} = 194, x \gt 0$, then what would be the value of $\displaystyle (x - 2)^2 ?$

17. Published: 10-Feb-2020
If $\displaystyle \frac{5\sqrt 5 x^3 - 81\sqrt 3 y^3}{\sqrt 5 x - 3\sqrt 3 y} =$ $\displaystyle Ax^2 + By^2 +Cxy,$ then $\displaystyle 6A + B - \sqrt {15}C = ?$

18. Published: 11-Feb-2020
If $\displaystyle x + y + z = 19$, $\displaystyle x^2 + y^2 + z^2 = 133$ and $\displaystyle xz = y^2$, then the difference between $\displaystyle x$ and $\displaystyle z$ is?

19. Published: 11-Feb-2020
If $\displaystyle 4 - 2\sin^2 \theta - 5\cos \theta = 0$, with $\displaystyle 0\degree \lt \theta \lt 90 \degree$, then the value of $\displaystyle \sin \theta + \tan \theta$ is?

20. Published: 11-Feb-2020
A solid cube with a volume of 13824 cu. cm is cut into eight cubes of the same volume. The ratio of the surface area of the original cube and the total sum of the surface area of three smaller cubes will be?

21. Published: 13-Feb-2020
$\displaystyle \bigg(\frac{\sin \theta - 2\sin^3 \theta}{2\cos^3 \theta - \cos \theta}\bigg)^2 + 1 = ?$

22. Published: 13-Feb-2020
Raju's income is 20% more than his expenditure. If his income increases by 60% and his expenditure increase by 70%, then what percentage of the savings will increase/decrease?

23. Published: 13-Feb-2020
The ratio of competencies A, B and C is 4: 5: 3. On working together, all three of them complete work in 25 days. In how many days will both A and C together complete 35% of the work?

24. Published: 13-Feb-2020
Renu bought an item for 1,240 and sold it at a loss of 25%. With that amount, she bought another item and sold it for 40% profit. What percentage of profit did Renu get?

25. Published: 13-Feb-2020
The nominal value of an article is 315. It is sold in 288. If this leads to a loss of 4%, then what percentage of the item was marked more than the cost?

26. Published: 16-Feb-2020
The following program first creates an empty 2-dimensional array, then stores star('*') character into all the elements that would fall on or near the circumference of the circle.

27. Published: 17-Feb-2020
The following program draws two arms of a given angle. The horizontal arm is fairly simple. But the inclined arm is drawn by using a 2-D array by filling stars in those elements that satisfy the equation y = x tanθ.

28. Published: 17-Feb-2020
A takes 30 minutes longer than B to cover a distance of 15 km at a certain speed. However, if A doubles his speed, he covers the same distance in an hour less time than B. What is the speed of B (in km / h)?

29. Published: 17-Feb-2020
This program creates a digital clock that displays the current system time as in the familiar dot matrix numeric clocks. The time keeps updating every 15 seconds. The display character can be set to any ASCII character.

30. Published: 18-Feb-2020
This is a ten line C, C++ program that connects to the internet and downloads the html source of a web page. The given program supports both http and https requests and works even if there is a url redirect from one protocol to the other, ie., from http-to-https or from https-to-http.

31. Published: 18-Feb-2020
The average weight of some students in a class is 68.5 kg. If four new students of 72.2 kg, 70.8 kg, 70.3 kg, 66.7 kg are enrolled in the class, the average weight of students increases by 300 g. Initially, how many students were there in the class?

32. Published: 18-Feb-2020
If x is subtracted from each of 23, 39, 32 and 56, then the numbers obtained in this sequence are in proportion. What will be the mean proportional between (x + 4) and (3x+ 1)?

33. Published: 19-Feb-2020
This program connects to the internet and downloads the html source of a web page. After that it extracts links (urls) from the downloaded string, and displays them on the console. The program can be easily altered to extract urls from a string or a text file also.

34. Published: 20-Feb-2020
A native C++ program that connects to an rss feed site and reads the XML title and description tags in a loop. We have used a bbc rss-xml feed in this progam to create a news ticker.

35. Published: 20-Feb-2020
A circle inside a triangle ABC, whose center O is created. On increasing AO, it meets the circle [or triangle] on K and AD ⊥BC. If ∠B = 80° and ∠C = 64°, then the measure of ∠DAK is?

36. Published: 25-Feb-2020
This is a minor project for summer training /internship of engineering and school students. This project contains source code and also complete project report. The features of this project are that it allows a student to check leap year, view colored calendar, and add appointments, and view them alongside.

37. Published: 28-Feb-2020
In ΔABC, AD ⊥ BC and BE ⊥ AC. AD and BE cut each other at F. If BF = AC, what will be the measure of ∠ABD?

38. Published: 28-Feb-2020
Circles of radius 10 cm and 8 cm cut each other at points P and Q. PQ = 12 cm and the distance between the centers of the circle is x cm, then the value of x (correct to 1 decimal place)?

39. Published: 29-Feb-2020
ΔABC is similar to ΔDEF. The area of ∆ABC is 100 sq. cm and the area of ∆DEF is 49 sq. cm. If ΔABC's altitude is 5 cm, then ΔDEF will have corresponding altitude?

40. Published: 29-Feb-2020
If θ is acute and cos^2 θ = 3 (cot^2 θ - cos^2 θ), then the value of (trigonometric expression) is?

41. Published: 29-Feb-2020
Following is a pure native C program to take picture from your attached web camera. The best thing is that this is a really short, 2 line program. We have tested with logitech USB camera.