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00:00 - Intro
0:05 - Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D are
03:15 - The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is
04:15 - A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is
05:10 - For natural numbers x,y, and z, if xy+yz=19 and yz+xz=51, then the minimum possible value of xyz is
07:10 - Let a,b,c be non-zero real numbers such that b^2l ess than 4ac, and f(x)=ax^2+bx+c. If the set S
consists of al integers m such that f(m) less than 0, then the set S must necessarily be
10:24 - Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes.....
13:35 - The average of three integers is 13 . When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is
16:11 - Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is
17:19 - Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is
25:17 - The largest real value of a for which the equation |x+a|+|x−1|=2 has an infinite number of solutions for x is
29:43 - A trapezium ABCD has side AD parallel to BC, less than BAD=90∘,BC=3~cm and AD=8~cm. If the perimeter of this trapezium is 36~cm , then its area, in sq. cm, is
31:05 - For any real number x, let [x] be the largest integer less than or equal to x.....
34:55 - n a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is
37:23 - Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%....
42:29 - Let a and b be natural numbers. If a^2+ab+a=14 and b^2+ab+b=28, then (2a+b) equals
44:22 - Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is
45:54 - In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks.....
53:06 - For any natural number n, suppose the sum of the first n terms of an arithmetic progression is (n+2n2). If the nth term of the progression is divisible by 9 , then the smallest possible value of n is
55:02 - All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the area of the rectangle is
56:21 - The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original000
57:28 - Let A be the largest positive integer that divides all the numbers of the form
1:00:32 - Let 0≤a≤x≤100 and f(x)=|x−a|+|x−100|+|x−a−50|. Then the maximum value of f(x)
becomes 100 when a is equal to
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