2 The quadratic equation ar² + bx +c = 0 has equal roots if: (AI 3-4ac =0 b-4ac 20 7. (B) ICI -4ac <0 The sum of roots of the equation (x+ 3)°- 3x + 2x = 0 is: 8. I시 -4 6' 2x 3. (x- 3)(x-5) 9. 3 [A] (x-3) (x-5) 5 [B] (x-3) (x-5) 3 5 10. [C] (x-3) (x-5) 5 [D] (x-3) (x-5)
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Answer Q1, 2, 3
![2
The quadratic equation ar' +bx +c =0 has equal roots if:
(AI -dac 0
= 4 is:
81
1.
7.
The value of x
for which log,
[A) 3
[B]
b-4ac 20
4
IC) b-4ac < 0
IDI b-4ac s 0
The sum of roots of the equation (x+ 3) - 3.x + 2x = 0 is:
[C)
3
[D]
An arithimetic progression has first term 5 and common
difference 3. The " term is given by
Sn+2
-4
8.
(A]
(B]
[C)
(B)
-4
2-3n
31+2
4
6
2x
5n-2
3.
20
(x- 3)(x-5)
9.
E(3r +2) =
3
5
[A]
[A}
[B]
(C] 708
[D] 38
The expansion of (5-4x)" is valid when:
670
(x-3) (x-5)
632
3
[B]
(х- 3) (х-5)
5
10.
[C)
(x-3) (x-5)
4
[A)
3.
5
[D]
(x- 3) (x-5)
(B]
-I<x<l
4.
Given that P, Q and R are constants,
can be
[C)
(D]
0<x< 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4957fe4-4c01-40d3-938e-f3efa5fe6d1c%2F0b452e21-5645-496f-ae04-ee5bdb8febf4%2F8t4clma_processed.jpeg&w=3840&q=75)
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