If x is a positive real number then the minimum value of (x + 7) (x + 19)/(x + 3) is:
Correct Answer
36
If f(x) = x2 – 7x and g(x) = x + 3, then the minimum value of f(g(x)) – 3x is
(CAT 2021)
Correct Answer
1. -16If 3x + 2 |y| + y = 7 and x + |x| + 3y = 1, then x + 2y is:
(CAT 2021)
Correct Answer
4. 0
Find the range of (x2 + 4x + 8)/(x2 + 4x + 5)
Correct Answer
(1,4)
Find the sum of all negative integral values of x where |x – | x – 2 | + 3 | – 4 < 3
Correct Answer
-5
Consider the function f(x) = (x + 4) (x + 6) (x + 8) ………….. (x + 98). The number of integers x for which f(x) is less than 0 are:
Correct Answer
24
How many integer values of x will satisfy this (x² – 16|x| + 60) / (x² – 14x + 49) < 0
Correct Answer
2 integer value of x
For how many positive integral values of k is (k-11)(k-15)(k − 19)… (k – 99) < 0?
Correct Answer
43
Correct Answer
9
Correct Answer
1. 8f(x) = (x² + 2x -15) /(x² – 7x – 18) is negative if and only if (CAT 2021)
Correct Answer
2. -5 < x < -2 or 3 < x < 9
Correct Answer
4. |k| ≠ 2Consider 2 APs 2,6,10……. and 5,12,19………….If S is a set containing the first 100 members of each progression then how many distinct elements are there in S?
Correct Answer
186
Three positive integers x, y and z are in arithmetic progression. If y − x greater than 2 and xyz = 5 (x + y + z), then z − x equals: (CAT 2021)
Correct Answer
1. 14Correct Answer
-20/7
Correct Answer
10
a + b + c + d = 4 All a,b,c,d are integers Find minimum possible value of 1/a + 1/b + 1/c + 1/d
Correct Answer
3
Correct Answer
1152
Correct Answer
2. 2 / (A + B - 3)
Correct Answer
3. 4 < a < 5
If log2 [3 + log2 {4 + log4 (x – 1)}] – 2 = 0, then 4x equals: (CAT 2021)
Correct Answer
5
If 5 – log10 √(1 + x) + 4 log10 √(1 – x) = log10 (1/√(1 – x²), then 100x equals
Correct Answer
99
Log (x+3) (x² – x ) < 1
Correct Answer
(-3, -2) ∪ (-1, 0) ∪ (1, 3)
Correct Answer
9 integral valuesCorrect Answer
90°
Correct Answer
1. 17Suppose one of the roots of the equation ax² – bx + c = 0 is 2 + root13, where a, b and c are rational numbers and a is not equal to zero. If b = c³, then |a| equals to: (CAT 2021)
Correct Answer
2. 2
Let m and n be positive integers, If x² + mx + 2n = 0 and x² + 2nx + m = 0 have real roots, then the smallest possible value of m+ n is: (CAT 2020)
Correct Answer
4. 6Correct Answer
2
Correct Answer
79
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