Notesale: Turn your study into money

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CAT workshop- Algebra- Part 1
Question: Total integer pair(s) (x, y) satisfying the equation x + y = xy is/are
1) 0

2) 1

3) 2

4) 3

Question: How many positive integer pairs (a, b) satisfy the equation ab = a + b + 20?
A
...
2

C
...
4

Question: In a broken calculator, the keys '+' and '×' have their functions switched
...
0

B
...
2

D
...

A
...
2

B
...
5

C
...
2

D
...
2

Question: When the sum of two natural numbers is multiplied by each number separately,
the products obtained are 2418 and 3666
...
16

2
...
26

4
...

(a) 0

(b) 3

(c) 2

(d) 1

Question: If the polynomial ax4 + bx3 + cx2 + dx + e has the property that the product of its
roots is 1/3rd of the sum taking two roots at a time, then find the relationship between e
and c
...

A
...
394

C
...
432

Question: Find the nature of roots of the following equations:
(i) x2 + 9x + 27 = 0
(ii) 6x2 - 13x - 5 = 0
A
...
(i) Real (ii) Imaginary
(i) Imaginary (ii) Imaginary

C
...


Question: The roots of x3 − ax2 + bx − c = 0 are p, q and r, while the roots of x3 + dx2 + ex −
80 = 0 are p + 4, q + 4 and r + 4
...
32

B
...
216

D
...
25,000, are to be divided into two
groups, such that one-fourth of the number of diamonds in the first group would be 20
more than one-sixth of the number of diamonds in the second group
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If each teacher had been older by 1 year, each doctor by 6
years and each lawyer by 7 years, their average age would have increased by 5 years
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Michael Swrfieai went to purchase a certain number of
balls
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A leather
ball was 70 cents costlier than a tennis ball
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60 cents

2
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80 cents

4
...
6

B
...
8

D
...
A said to B, ''If you give me one of your
stamps, we shall have equal number of stamps''
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Find the total number of stamps
with A and B
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A student scores 1 mark for a correct answer, –1/3 for a

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