CAT 2017 – Slot 1 – Quantitative Ability – For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied
Q. 1: For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?
On solving the equation, we get n^2 – 18n + 56 ≤ 0
Factorize and we get, (n-4)(n-14) ≤ 0
4 ≤ n ≤ 14
No of values of n =11
Answer: 11
Q. 2: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
f1(x) = f2(x)
x^2 + 11x +n = x
x^2 + 10x + n =0
To have distinct and real roots, D>0
D = b^2-4ac = 100 – 4n > 0
On solving the inequality, we get, n<25
So, max positive integer value of n = 24.
Answer: 24
Q. 3: If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)^2 + (a – c)^2 + (a – d)^2 is
a + b + c + d = 30
a, b, c, d are integers. (a – b)^2 + (a – c)^2 + (a – d)^2 would have its minimum value when each bracket has the least possible value. Let (a, b, c, d) = (8, 8, 7, 7) The given expression would be 2. It cannot have a smaller value.
Answer: 2
Q. 4: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
There are 11 points from which a triangle can be formed. But there are 5 lines which have 3 points linearly.
Number of triangles formed = 11C3 – 5 (because of the lines)
165 – 5 = 160 triangles
Answer: 160
Q. 5: The shortest distance of the point 
from the curve y = |x -1| + |x + 1| is
Correct Answer:- A
Explanation:-
The graph of y = |x – 1| + |x + 1| is shown above.
from the graph is 1.Checkout Other Questions of CAT 2017 Slot 1 Paper:
Verbal Ability : | Q.01- Q.06 | Q.07- Q.12 | Q.13- Q.18 | Q.19- Q.21 | Q.22- Q.24 | Q.25- Q.29 | Q.30 – Q.34 |
Logical Reasoning : | Q.01- Q.04 | Q.05- Q.08 | Q.09- Q.12 | Q.13- Q.16 | Q.17- Q.20 | Q.21- Q.24 | Q.25 – Q.28 | Q.29 – Q.32 |
Quantitative Aptitude: | Q.01- Q.05 | Q.06- Q.10 | Q.11- Q.15 | Q.16- Q.20 | Q.21- Q.25 | Q.26- Q.30 | Q.31 – Q.34 |
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