Correct option is (A) 10
Let p(x) = \(x^3+2x^2+3x+4\)
When p(x) is divided by \((x-1)\) then remainder will be p(1).
\(\therefore\) Remainder = p(1) \(=1^3+2\times1^2+3\times1+4\)
= 1+2+3+4 = 10
Correct option is (D) 41
Let p(x) = \(2x^3+3x^2+4x+5\)
When p(x) is divided by \((x-2)\) then remainder will be p(2).
\(\therefore\) Remainder = p(2) \(=2\times2^3+3\times2^2+4\times2+5\)
= 16+12+8+5 = 41
Correct option is (D) None
Let p(x) = \(3x^2+2x-6\)
The remainder when p(x) is divided by \((2x-1)\) is \(p(\frac12).\)
Now, \(p(\frac12)=3(\frac12)^2+2\times\frac12-6\)
\(=\frac34+1-6=\frac34-5\)
\(=\frac{3-20}4=\frac{-17}4\)
Hence, when \((3x^2+2x-6)\) is divided by \((2x-1),\) it leaves remainder \(\frac{-17}4.\)
The following situation creates an A.P. as:
204, 211, 218...... 295
Now, number of terms in the A.P.=
an= a+(n-1)d
295= 204+(n-1)7
91= 7(n-1)
n= 14
Sum of these terms,
Sn= n/2( a+an)
Sn= 14/2( 204+295 )
Sn= 7×499 = 3493
Therefore,...
We know that if a number is divided by 5, then remainder is remainder obtained by dividing unit place by 5.
∴ Here, 7 ÷ 5 gives 2 as a remainder.
Hence,
remainder...
