Study questions platform-wide or filter by specific tests with correct answers revealed.
The Objective Resolution was passed in Pakistan in:
The Objective Resolution, the cornerstone of Pakistan's constitutional history, was passed on March 12, 1949.
When you see a clock from the back (mirror image), left and right are reversed. This is equivalent to a horizontal mirror reflection.
A clock seen from behind at 8:15:
In mirror image, the hour hand at 8 appears at \(12 - 8 = 4\. The minute hand at 15 min (pointing to 3) appears at the 9 position (45 min).
So the actual time = 4:45.
Rule: Mirror time + Actual time = 12:00 (for hour) and 60 (for minutes). Hour: \(12 - 8 = 4\. Minutes: \(60 - 15 = 45\. Actual time = 4:45.
- First dimension: Isoelectric focusing (IEF) on immobilised pH gradient (IPG) gels — proteins migrate to their pI where net charge = 0.
- Second dimension: SDS-PAGE — proteins are separated by molecular mass.
Let $A$ be a $2\times2$ symmetric matrix with integer entries. If the sum of the diagonal elements of $A^2$ equals 1, find the number of such possible matrices.
Let $A=\begin{pmatrix}a&b\\b&c\end{pmatrix}$. Then $A^2=\begin{pmatrix}a^2+b^2&ab+bc\\ab+bc&b^2+c^2\end{pmatrix}$.
Sum of diagonal of $A^2 = a^2+2b^2+c^2 = 1$.
Since $a,b,c$ are integers and $a^2+2b^2+c^2=1\geq0$: $b=0$ (since $2b^2\leq1$ with integer $b$ forces $b=0$), then $a^2+c^2=1$.
Solutions: $(a,c)\in\{(1,0),(−1,0),(0,1),(0,−1)\}$ and $b=0$: 4 matrices. But we should check $b=\pm1$: $2(1)=2>1$, not possible. Hmm — that gives only 4. But checking $b=0$, $a^2+c^2=1$: integer solutions are $(\pm1,0)$ and $(0,\pm1)$ — exactly 4 pairs, each with $b=0$. So $\mathbf{4}$ matrices... but wait: $b$ can also vary if we allow it. Total = $\mathbf{4}$ matrices.
Factory data: Budgeted production 10,000 units; Budgeted overheads $50,000; Actual overheads $60,000; Under-absorption $5,000. What was the actual production?
Option A (9,000 units) is correct.
OAR = $50,000 ÷ 10,000 = $5 per unit
Under-absorption = Actual overheads − Absorbed overheads
$5,000 = $60,000 − (Actual units × $5)
Actual units = $55,000 ÷ $5 = 9,000 units
Sign in to join the conversation and share your thoughts.
Log In to Comment