CTET Solved Paper - CTET September 2016 Paper2
31. The sum of all possible values of a, for which the 4-digit number 547a is divisible by 3, is
- Option : B
- Explanation : The value of a should be decided in such a way that the sum of the digits is divided by 3 completely.
547a = 5+4+7+a = Number divisible by 3
=16+a (it should be divided by 3 completely)
=> a= 2, 5, 8
=2 + 5 + 8 (sum of values of a)
= 15
32. A common factor of x4 - 256, x3 - 4x2 + 3x - 12 and x2 - 7x + 12 is
- Option : C
- Explanation : x4 - 256 =0
=> (x2)2 - (42)2 = 0
=> (x2 - 42)(x2 - 42) = 0
=> (x - 4)(x + 4)(x2 + 42) = 0.....(i)
Now, x3 - 4x2 + 3x -12 = 0
=> x2 (x - 4) +3 (x - 4)=0
=> (x2 + 3)(x - 4) = 0 .....(ii)
And, x2 - 7x + 12=0
=> x2 - 4x - 3x +12=0
=> x(x - 4) -3(x - 4)=0
=> (x - 3)(x - 4) =0 ......(iii)
In all the above eqs.(i), (ii) and (iii) (x-4) is the common factor
- Option : A
- Explanation :
4x+1) 8x3 - 6x2 +10x + 3 (2x2 - 2x +3
8x3 + 2x2
- -
____________________________________________________
- 8x2 + 10x +3
-8x2 - 2x
+ +
_____________________________________________________
12x + 3
12x + 3
- -
______________________________________________________
0
Now, quotient is 2x2 - 2x + 3 = 2x2 + k (given)
=> k = -2x + 3
=> k + 3 - 2x
- Option : D
- Explanation : (9x2 + 15 - x)(-1 - x + x2)
= -9x2 - 9x3 + 9x4 -15 -15x + 15x2 + x + x2 - x3
= 9x4 - 10x3 + 7x2 - 14x -15
A = -10, B= 7, C = -14
Now, A + B + C = -10 +7 + 14
= 11
