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Suppose determinant = 0 holds for some positive integer n

Suppose holds for some positive integer n. Then \(\begin{array}{l}\sum_{k=0}^n \frac{^nC_k}{k+1}\end{array} \) equals. Solution: The answer is 6.20

Five person A, B, C, D and E are seated in a circular arrangement.

Five person A, B, C, D and E are seated in a circular arrangement. If each of them is given... View Article

Let |X| denote the number of elements in set X.

Let |X| denote the number of elements in set X. Let S = {1,2,3,4,5,6} be a sample space, where each... View Article

The value of [latex]sec^{-1}(1/4 \sum_{k=0}^{10} sec(7\pi/12 + k\pi/2))sec(7\pi/12 + (k+1)\pi/2))[/latex]

The value of \(\begin{array}{l}sec^{-1}(1/4 \sum_{k=0}^{10} sec(7\pi/12 + k\pi/2))sec(7\pi/12 + (k+1)\pi/2))\end{array} \) in the interval [-π/4, 3π/4] equals Solution: The answer... View Article

Let x ϵ R and let P

Let x ϵ R and let And R = PQP-1. Then which of the following options is/are correct? a) For... View Article

Let P₁ = I = [latex]begin{bmatrix} 1 &0 &0 \ 0 & 1 & 0\ 0& 0 & 1 end{bmatrix}[/latex]

Where PKT denotes the transpose of the matrix PK. Then which of the following options is/are correct? a) X –... View Article

For non-negative integers n, let f(n)

For non-negative integers n, let Assuming cos-1x takes value in [0, π], which of the following options is/are correct? a)... View Article

Let F: R -> R be a function. We say that f has

Let F: R -> R be a function. We say that f has Then which of the following options is/are... View Article

Three lines L1: [latex]vec{r}=lambda hat{i}, lambda epsilon R[/latex], L2: [latex]vec{r}= hat{k}+mu hat{j}, mu epsilon R[/latex] and L3: [latex]vec{r}= hat{i}+hat{j}+nu hat{k}, nu epsilon R[/latex] are given

Three lines L1: \(\begin{array}{l}\vec{r}=\lambda \hat{i}, \lambda \epsilon R\end{array} \), L2: \(\begin{array}{l}\vec{r}= \hat{k}+\mu \hat{j}, \mu \epsilon R\end{array} \) and L3: \(\begin{array}{l}\vec{r}=... View Article

For a ∈ R, |a|> 1, let [latex]\lim_{n \to \infty }\left ( \frac{1+\sqrt[3]{2}+…\sqrt[3]{n}}{n^{\frac{7}{3}}(\frac{1}{(an+1)^{2}}+\frac{1}{(an+2)^{2}}+…\frac{1}{(an+n)^{2}})} \right ) = 54[/latex]

For a ∈ R, |a| > 1, let \(\begin{array}{l}\lim_{n \to \infty }\left ( \frac{1+\sqrt[3]{2}+…\sqrt[3]{n}}{n^{\frac{7}{3}}(\frac{1}{(an+1)^{2}}+\frac{1}{(an+2)^{2}}+…\frac{1}{(an+n)^{2}})} \right ) = 54\end{array} \) . Then... View Article

Let f: R -> R be given by f(x) = (x – 1) (x – 2) (x – 5).

Let f: R -> R be given by f(x) = (x – 1) (x – 2) (x – 5). Define... View Article

Let the curve y=y(x) be the solution of the differential equation, dy / dx = 2 (x + 1).

Let the curve y=y(x) be the solution of the differential equation, dy / dx = 2 (x + 1). If... View Article

Let [latex]P=\begin{bmatrix} -30 &20 &56 \\ 90&140 &112 \\ 120&60 &14 \end{bmatrix}[/latex] and [latex]A=\begin{bmatrix} 2 &7 &\omega ^2 \\ -1&-\omega &1 \\ 0&-\omega &-\omega+1 \end{bmatrix}[/latex] where 𝛚 = (- 1 + i √3) / 2, and I₃ be the identity matrix of order 3.

Let \(\begin{array}{l}P=\begin{bmatrix} -30 &20 &56 \\ 90&140 &112 \\ 120&60 &14 \end{bmatrix}\end{array} \) and \(\begin{array}{l}A=\begin{bmatrix} 2 &7 &\omega ^2 \\... View Article

Let z and w be two complex numbers such that [latex]w=zbar{z}-2z+2[/latex], |(z + i) / (z – 3i)| = 1 and Re (w) has a minimum value.

Let z and w be two complex numbers such that \(\begin{array}{l}w=z\bar{z}-2z+2\end{array} \), |(z + i) / (z – 3i)| =... View Article

The total number of 3 × 3 matrices A having entries from the set {0, 1, 2, 3} such that the sum of all the diagonal entries of AA^T is 9, is equal to

Solution: (766) \(\begin{array}{l}AA^T=\begin{bmatrix} x &y &z \\ a&b &c \\ d &e &f \end{bmatrix}\begin{bmatrix} x&a &d \\ y&b &e \\... View Article

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