Summation of Determinant

Q. 121, 169, 289, 361, 529, ?

Q.

$\mathrm{If}{D}_r=\left(\begin{array}{ccc}{2}^{r-1}& 2.3^{r-1}& 4.5^{r-1}\\ \alpha & \beta & \gamma \\ 2^n-1& 3^n-1& 5^n-1\end{array}\right|,\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}{\sum }_{r=1}^n{D}_r\mathrm{is}$

1. $0$

2. $\alpha \beta \gamma$

3. $\alpha -2^n+\beta -3^n+\gamma -4^n$

4. $\alpha +\beta +\gamma$

Q. What is the derivation of the formula of( sine inverse (x)+sine inverse (y))

Q. If $D_k=\left|\begin{array}{ccc}1& n& n\\ 2k& n^2+n+1& n^2+n\\ 2k-1& n^2& n^2+n+1\end{array}\right|$ and ${\sum }_{k=1}^n{D}_k=56$, then n equals

1. 4
2. 6
3. 8
4. None of these

Q. Find the wrong term 15, 35, 61, 92, 131, 175, 22

Q. if f(x)=cos2x+sec2x, then f(x) is ?

Q. 120. If |z1+z2|=|z1|+|z2|, then proved that argument (z1)=argument (z2)

Q.

⁸C_r = ⁸C_p. So

1. r = p or r - p = 8

2. r = p or r = 2p

3. r = p or r = 8p

4. r = p or r + p = 8

Q. Which one of the following hold good?

1. $b^2{c}^2+c^2{a}^2+a^2{b}^2\ge abc(a+b+c)$
2. $\frac{bc}{a}+\frac{ca}{b}+\frac{ab}{c}\ge a+b+c$
3. $\frac{bc}{a^3}+\frac{ca}{b^3}+\frac{ab}{c^3}\ge \frac{1}{a}+\frac{1}{b}+\frac{1}{c}$
4. $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge \frac{1}{\sqrt{\left(bc\right)}}+\frac{1}{\sqrt{\left(ca\right)}}+\frac{1}{\sqrt{\left(ab\right)}}$

Q.

1. 1

2. 7

3. Zero

4. 8

Q.

1. 366, 70

2. 216, 70

3. 70, 286

4. 70, 366

Q.

1. 0

2. 

3. 

4. 1

Q. $\mathrm{If}{U}_n=\left(\begin{array}{ccc}n& 1& 5\\ n^2& 2N+1& 2N+1\\ n^3& 3N^2& 3N\end{array}\right|,\mathrm{then}\underset{n=1}{\overset{N}{\sum U_n=}}$
.

1. N + 2
2. \N
3. N
4. N + 1

Q. If a, b, c are in A.P., b, c, d are in G.P. and $\frac{1}{c},\frac{1}{d},\frac{1}{e}$ are in A.P., prove that a, c, e are in G.P.

Q.

Let $A=\left(\begin{array}{ccc}1& 0& 0\\ 2& 1& 0\\ 3& 2& 1\end{array}\right)$ , If ${\mu }_1$ and ${\mu }_2$ are column matrices such that $A{\mu }_1=\left(\begin{array}{c}1\\ 0\\ 0\end{array}\right)$ and $A{\mu }_2=\left(\begin{array}{c}0\\ 1\\ 0\end{array}\right)$, then ${\mu }_1+{\mu }_2$ is equal to:

1. $\left(\begin{array}{c}-1\\ 1\\ 0\end{array}\right)$

2. $\left(\begin{array}{c}-1\\ 1\\ -1\end{array}\right)$

3. $\left(\begin{array}{c}-1\\ -1\\ 0\end{array}\right)$

4. $\left(\begin{array}{c}1\\ -1\\ -1\end{array}\right)$