MCQ
The sum $1^2-2.3^2+3.5^2-4.7^2+5.9^2-\ldots +15.29^2$ is $.......$.
- A$6950$
- B$6956$
- C$6953$
- ✓$6952$
✓
Answer
Correct option: D.
$6952$
d
Separating odd placed and even placed terms we get
Separating odd placed and even placed terms we get
$S =\left(1 \cdot 1^2+3 \cdot 5^2+\ldots .15 \cdot(29)^2\right)-\left(2 \cdot 3^2+4.7^2\right.+\ldots .+14 \cdot(27)^2$
$S =\sum \limits_{ n =1}^8(2 n -1)(4 n -3)^2-\sum_{ n =1}^7(2 n )(4 n -1)^2$
Applying summation formula we get
$=29856-22904=6952$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $y = \sec ({\tan ^{ - 1}}x),$ then ${{dy} \over {dx}}$ is
→If the distance between the foci of an ellipse is $6$ and the distance between its directrices is $12$, then the length of its latus rectum is
→If ${\log _{10}}3 = 0.477$, the number of digits in ${3^{40}}$ is
→A box contains $100$ tickets numbered $1, 2 ...... 100$. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than $10$. The minimum number on them is $5$ with probability
→Let $a,b,c$ be non-zero real numbers such that
→$\int_0^1 {(1 + {{\cos }^8}x)(a{x^2} + bx + c)\,dx} = \int_0^2 {(1 + {{\cos }^8}x)(a{x^2} + bx + c)\,dx} $
Then the quadratic equation $a{x^2} + bx + c = 0$ has
If the diagonals of $a$ parallelogram are represented by the vectors $3i + j - 2k$ and $i + 3j - 4k,$ then its area in square unit is
→The coordinates of the radical centre of the three circles ${x^2} + {y^2} - 4x - 2y + 6 = 0,{x^2} + {y^2} - 4x - 2y + 6 = 0,$${x^2} + {y^2} - 12x + 2y + 30 = 0$ are
→$\tan \left[ {{{\sec }^{ - 1}}\sqrt {1 + {x^2}} } \right] = $
→Let $X_n=\{1,2,3, \ldots, n\}$ and let a subset $A$ of $X_n$ be chosen so that every pair of elements of $A$ differ by at least 3. (For example, if $n=5, A$ can be $\phi,\{2\}$ or $\{1,5\}$ among others). When $n=10$, let the probability that $1 \in A$ be $p$ and let the probability that $2 \in A$ be Then,
→The figure shows a portion of the graph $y=2 x-4 x^3$.The line $y=c$ is such that the areas of the regions marked $I$ and $II$ are equal. If $a, b$ are the $x$-coordinates of $A, B$ respectively, then $a+b$ equals
→