Minimum value of
(x^3+2x+ 1/x)/x + x^2+2x+1 ?
Mention approach too. Thanks
consider the set s = {1,2,3,4....16}. how many subsets of s are there in which no two elements have a difference less than 4.
If a and b are the roots of (a^2 - 5a+ 3)x^2 + (3a - 1)x + 2 = 0, for what value of a is a = 2b ?
A) 2/3 B) -2/3 C) 1/3 D) -1/3
Any other approach besides crude maths solving.
|f'p' is one of the roots of the quadratic equation 4x^2 + 2x- 1 =0 ,what is the second root?
A 4P^3-3P
B 4p-3p^3
c 3p-4p^3
D 3p^3 -4p
Do mention the approach too. Thanks.
Puys please suggest books to get through the basics of functions..
##cat 16
How many different arrangement can be made out of the letters in the ex-pression a^3b^2c^4 when written at full length?
$$cat16
In the country of Twenty, there are exactly twenty
cities, and there is exactly one direct road between
any two cities. No two direct roads have an
overlapping road segment. After the election dates
are announced, candidates from their respective
cities start visiting the other cities. Following are
the rules that the election commission has laid
down for the candidates:
. Each candidates must visit each of the other
cities exactly once.
. Each candidates must use only the direct
roads between two cities for going from one
city to another.
. The candidates must return to his own city at
the end of the campaign.
. No direct road between two cities would be
used by more than one candidate.
The maximum possible number of candidates is
5
6
7
8
9
##cat 16
A number 30 to power 10 has :-
1.) How many factors having at least five trailing successive zeros in the end?
2.) How many factors having seven trailing successive zeros in the end?
3.) How many factors which end in a zero and have a first non-zero even digit from the right?
Quantitative Aptitude and Data sufficiency Quiz for CAT
Dear readers,
This quiz consists of questions from various past actual cat papers. Leave your answers/ responses in the comments section below and soon we'll let you know the correct answers!
1. Two positive integers differ by 4 and sum of their reciprocals is 21/10. Then one of the numbers is?
a. 3 b. 1 c. 5 d. 21
2. Three bells chime at an interval of 18 min, 24 min and 32 min. At a certain time they begin to chime together. What length of time will elapse before they chime together again?
a. 2 hr and 24 min b. 4 hr and 48 min c. 1 hr and 36 min d. 5 hr
Direction for questions 3 to 10: Each of these questions is followed by two statements, I and II. Mark the answer as.
a. if the question can be answered with the help of statement I alone.
b. if the question can be answered with the help of statement II, alone.
c. if both statement I and statement II are needed to answer the question.
d. if the question cannot be answered even with the help of both the statements.
3. If x, y and z are real numbers, is z - x even or odd?
I. xyz is odd.
II. xy + yz + zx is even.
4. What is the profit percentage?
I. The cost price is 80% of the selling price.
II. The profit is Rs. 50.
5. What is the area of the triangle?
I. Two sides are 41 cm each.
II. The altitude to the third side is 9 cm long.
6. What is the price of bananas?
I. With Rs. 84, I can buy 14 bananas and 35 oranges.
II. If price of bananas is reduced by 50%, then we can buy 48 bananas in Rs. 12.
7. What is the first term of an arithmetic progression of positive integers?
I. Sum of the squares of the first and the second term is 116.
II. The fifth term is divisible by 7.
8. What is the length of rectangle ABCD?
I. Area of the rectangle is 48 square units.
II. Length of the diagonal is 10 units.
9. What is the number x?
I. The LCM of x and 18 is 36.
II. The HCF of x and 18 is 2.
10. Is x + y - z + t even?
I. x + y + t is even.
II. t and z are odd.
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Let N is an integer less then 100 which has maximum number of factors. Find the sum of all possible values of N. Approch?
A took out his new bike for a test ride. At 9 am, he arrived ata milestone that showed three digit number. At 10 am he arrived at a second milestone that showed a 2 digit number and both the digitss were also there in the number on the first milestone. At 11 am, he arrived at a third milestone that showed the reverse of the second number. The sum of all the digits in all 3 numbers was the same. A was travelling at uniform speed throughout in the same direction. The numbers on the milestones indicate the distance to the nearest town in kilometers.
What was the speed at which A travelled?
What was the ratio of the tens digit to the units digit in the number on the second milestone?
##silly _pointers## notes ## formula
IxI + IyI= N
total no of integral solutions = 4 *N
IxI +IyI +Iz|= N
total no of integral solutions = 4N^2 +2
IxI +IyI +Iz|= 0 only one solution
IxI +IyI +Iz|= -N(-ve) No solution
x^2 - y^2 =N( 4k+2 form) zero solutions
x^2 +y^2 less than equal toN = 2N^2 +2N +1 soltuions
_________/\_______
Does anybody know how to solve q23 ?
I was trying to post question through pagalguy app but it is not working. Any suggestions ?
How many pairs of real numbers (x, y) satisfy the equation
(x + y)^2 = (X + 3) (y- 3) ?
A) 0 B) 1 c) 2 D) Infinitely many
Do mention the approach too.
- There are three numbers a,b, c such that HCF (a, b) = l, HCF (b, c) = m and HCF (c, a) = n. HCF (l, m) = HCF (l, n) = HCF (n, m) = 1. Find LCM of a, b, c.
Find tne sum of all tne real roots of the equation
(3-x)^5 + (x-5)^5 = -32 ?
Do Mention the approach too. Thanks.
The lcm and GCD of A and B are x and y respectively. The LCM of 2A and B is 2x and that of 2A and 3B is also 2x. Which of the following statement is definitely false?
A. A/y is not a multiple of 3
B. y is a multiple of 3
C. A/9 is an integer
D. B/y is odd
If 2n has 28 factors, 3n has 30 factors, how many factors does n have ?
A man undertakes to do a certain work in 150 days. He employs 200 men. He finds that only a quarter of the work is done in 50 days. The number of additional men that should be appointed so that the whole work will be finished in time is...? How to solve by taking total work say 300...?plz help...