Find the sum of each of the following Aps: (i) 2, 7, 12, 17, … to 19 terms (ii) 9, 7, 5, 3,…. To 14 terms. (iii) -37, -33, -29,… to 12 terms (iv) `(1)

Correct Answer - D `(d)` `x_(1)+x_(2)+x_(3)+……+x_(100)=(100)/(2)(x_(1)+x_(100))=-1` `impliesx_(1)+x_(100)=-(1)/(50)` `x_(2)+x_(4)+…+x_(100)=(50)/(2)(x_(1)+d+x_(100))=1` `impliesx_(1)+x_(100)+d=(1)/(25)` `impliesd=(3)/(50)` ltbr `x_(1)+x_(1)+99d=(-1)/(50)` `impliesx_(1)=(-149)/(50)` `x_(100)=x_(1)+99d` `=(-149)/(50)+99xx(3)/(50)` `=(74)/(25)`

Correct Answer - B `(b)` Let `A=[{:(a,b,c),(p,q,r),(x,y,z):}]` Given `{:(a+b+c=1),(p+q+r=1),(x+y+z=1):}` `impliesA^(2)=[{:(a,b,c),(p,q,r),(x,y,z):}][{:(a,b,c),(p,q,r),(x,y,z):}]` `=[{:(a^(2)+bp+cx,,ab+bq+cy,,ac+br+cz),(pa+qp+rx,,qb+q^(2)+ry,,pc+qr+rz),(xa+yp+zx,,xb+yq+zy,,xc+yr+z^(2)):}]` Sum of elements of `R_(1)=a^(2)+bp+cx+ab+bq+cy+ac+br+cz` `=a(a+b+c)+b(p+q+r)+c(x+y+z)` `=a+b+c=0` Similarly sum of elements of `R_(2)=p(a+b+c)+q(p+q+r)+r(x+y+z)` `=p+q+r=1` `R_(3)=x(a+b+c)+y(p+q+r)+z(x+y+z)` `=x+y+z=1` `:.` sum of element...

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Correct Answer - (i)`-(1)/(3)x^(-4//3)` (ii)`6t^(5)` (iii)`3u^(3)` (iv)`2r+(1)/(3)r^(-2//3)` (v)`6t^(2)-6t+5` (vi)`6x` (vii)`1+lnx` (viii)`xcosx+sinx` (ix)`cos^(2)x-sin^(2)x` (x)0 (xi)`-2sin2x` (xii)`4pir^(2)` (xiii)`8pir`

Correct Answer - `x^(3)-5x^(2)-2x+24`

Correct Answer - `12, 6, 3 or 3, 6, 12`

Correct Answer - `3/2(1-1/3^(n))`

Correct Answer - `(i) T_(n) = (5n-1), T_(20) = 99 (ii) T_(n) = (3n +1), T_(25) = 76`

Correct Answer - `(i) 5/18 (ii) 1/12 (iii) 5/12`

First Term of the AP (a) = 5 Common difference (d) = 8 - 5 = 3 Last term = a40 = a + (40 - 1) d = 5 + 39 × 3...