CAT Question Bank (Quant) - Gaurav Sharma - Set 1
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Q93) The midpoints of the adjacent sides of a triangle are joined. The midpoints of the adjacent sides of the resultant triangles are also joined. The ratio of the area of the central small triangle to the original triangle is:
a) 1 : 4
b) 1 : 8
c) 1 : 12
d) 1 : 16
e) 1 : 24
Q94) In a convex octagon,two diagonals are drawn at random.The probability that the diagonals intersect inside the octagon is ?
Q95) What is the number of distinct terms in the expansion of (a + b + c)^20?
Q96) BE and AD are the medians of an equilateral triangle ΔABC and intersecting at O. Find the area of quadrilateral DOEC. A(ΔABC) = 156 sq. cm.
a) 26 sq. cm
b) 39 sq. cm
c) 52 sq. cm
d) 65 sq. cm
e) 78 sq. cm
Q97) Adjacent sides of a parallelogram are 21 cm and 27 cm. One of its diagonals is 24 cm in length. Find its other diagonal.
a) 25 cm
b) 42 cm
c) 32 cm
d) 22 cm
e) 45 cm
Q98) At first, a room is empty. Each minute, either one person enters or two people leave. After exactly 3^1999 minutes, could the room contain
a) 3^1000 +1
b) 3^1000 + 2
Q99) In one exam, students were asked to find out the sum of all numbers less than 400 that are divisible by 8 but leave a remainder 1 when divided by 7. However, by mistake, Atul calculated the sum of all the numbers less than 400 that are divisible by 7 but leave a remainder 1 when divided by 8. By how much was Atul's answer different from the answer to the problem originally asked?
Q100) There is a 3 digit no. ABC. The no. Is a perfect square and the no. of factors of ABC is also a perfect square.
- If A + B + C is also a perfect square then what is the no of factors of the six digit number ABCABC.
- what is the no of factors of the 6 digit no ABCABC if the cube of the product of the digits of the no ABC is not divisible by 5?