Instructions

For the following questions answer them individually

Question 91

The number of solutions $$(x, y, z)$$ to the equation $$x - y - z = 25$$, where x, y, and z are positive integers such that $$x\leq40,y\leq12$$, and $$z\leq12$$ is

Question 92

For how many integers n, will the inequality $$(n - 5) (n - 10) - 3(n - 2)\leq0$$ be satisfied?

Backspace

789

456

123

0.-

Clear All

Submit
789

456

123

0.-

Clear All

Question 93

If $$f_{1}(x)=x^{2}+11x+n$$ and $$f_{2}(x)=x$$, then the largest positive integer n for which the equation $$f_{1}(x)=f_{2}(x)$$ has two distinct real roots is

Backspace

789

456

123

0.-

Clear All

Submit
789

456

123

0.-

Clear All

Question 94

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

Backspace

789

456

123

0.-

Clear All

Submit
789

456

123

0.-

Clear All

Question 95

Let AB, CD, EF, GH, and JK be five diameters of a circle with center at 0. 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?

Backspace

789

456

123

0.-

Clear All

Submit
789

456

123

0.-

Clear All

Question 96

The shortest distance of the point $$(\frac{1}{2},1)$$ from the curve y = I x -1I + I x + 1I is

Question 97

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

Question 98

In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

Question 99

$$f(x) = \frac{5x+2}{3x-5}$$ and $$g(x) = x^2 - 2x - 1$$, then the value of $$g(f(f(3)))$$ is

Question 100

Let $$a_1$$, $$a_2$$,............., $$a_{3n}$$ be an arithmetic progression with $$a_1$$ = 3 and $$a_{2}$$ = 7. If $$a_1$$+ $$a_{2}$$ +...+ $$a_{3n}$$= 1830, then what is the smallest positive integer m such that m($$a_1$$+ $$a_{2}$$ +...+ $$a_n$$) > 1830?

Incase of any issue contact support@cracku.in

CAT Geometry QuestionsCAT Time, Distance and Work QuestionsCAT Logarithms, Surds and Indices QuestionsCAT Venn Diagrams QuestionsCAT Number Systems Questions

CAT Set Theory QuestionsCAT Special Charts QuestionsCAT Quant Based LR QuestionsCAT Truth Lie Concept QuestionsCAT Selection With Condition Questions