Points X and Y are on the sides PQ and PR of triangle PQR respectively. The segments QY and RX intersect at the point Z. Given that QY = RY, PQ = RZ and QPR = 60°. Find RZY.
Three men - Arthur, Bernard and Charles - with their wives - Ann, Barbara and Cynthia, not necessarily in order - make some purchases. When their shopping is finished each finds that the average cost in dollars of the articles he or she has purchased is equal to the number of his or her purchases. Arthur has bought 23 more articles than Barbara, and Bernard has bought 11 more than Ann. Each husband has spent $63 more than his wife. What is the total amount spent by Charles and Cynthia?
Let ABCD be a quadrilateral. The circumcircle of the triangle ABC intersects the sides CD and DA in the points P and Q respectively, while the circumcircle of CDA intersects the sides AB and BC in the points R and S. The straight lines BP and BQ intersect the straight line RS in the same points M and N respectively. If BQP = 90°, find PMR.
In a group of people, there are 19 who like apples, 13 who like bananas, 17 who like cherries, and 4 who like dates. (A person can like more than 1 kind of fruit.) Each person who likes bananas also likes exactly one of apples and cherries. Each person who likes cherries also likes exactly one of bananas and dates. Find the minimum possible number of people in the group.
If F(x, n) be the number of ways of distributing "x" toys to "n" children so that each child received at the most 2 toys then F(4, 3) =
1. when toys are similar
2. when toys are different
If the area of a rectangular plot is 4400 square meters, then how many integral dimensions of the plot are possible whose breadths are at least 20 m?
(a) 8 (b) 7 (c) 9 (d) 11
Let X be a four-digit number with exactly three consecutive digits being same and is a multiple of 9. How many such X's are possible?
(a) 12 (b) 16 (c) 19 (d) 21 (e) None of the above.
How many pairs of factors of 864 are co-prime?
(a) 24 (b) 32 (c) 38 (d) 40
In how many ways can 5400 be written as a product of two factors which are co prime number?
(a) 3 (b) 4 (c) 5 (d) 6
From a square tin sheet of side 4 units, two circular holes of equal radii are punched. Find the minimum possible area of the sheet that remains after the holes are punched?(Assume that the two circles do not intersect each other)
Ans. 16-48π+32√2π
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my 10th percentage is 84, 12th percentage is 69 and btech percentage is 68. Should I prepare for cat as my aptitude is not very strong.?
A train, 600 m long, starts from Pune to Jammu at 5:40 p.m. At the same time, another train, 350 m long, starts from Jammu to Pune on a parallel track. On the way, the train from Pune crosses a tunnel in 35 seconds while the train from Jammu crosses the same tunnel in 40 seconds. After crossing each other inside the tunnel, the trains reach Jammu and Pune 4 hours and 9 hours later respectively.
--> When the two trains meet inside the tunnel, one train has travelled x km more than the other. What is x?
1. 216 km 2. 108 km 3. 135 km 4. 96 km
--> If both trains had started from Pune at 5:40 p.m., then the slower train would reach Jammu how many hours after the faster train had reached Jammu?
1. 1 hour 2. 2 ½ hours 3. 5 hours 4. 8 hours
Remainder of (26^99) when divided by 12 ?
Find the remainder when number represented by 22334 is raised to power 7^99 and is divided by 200.
1. 13
2. 343
3. 4
4. 7
Find the remainder when (10³ + 9³)^752 is divided by 12³.
1. 13
2. 343
3. 4
4. 7
How many 5-digit numbers exist having exactly two 4s in them?