Match the following:
List-I (Metal in drinking water) | List-II (Maximum prescribed concentration in ppm) |
---|---|
A) Mn | I) \( 0.05 \) |
B) Zn | II) \( 3.0 \) |
C) Cd | III) \( 0.005 \) |
D) Cu | IV) \( 5.0 \) |
Step 1: Recall the safe ppm limits for each metal in drinking water.
Manganese (Mn): Maximum permissible limit is 0.05 ppm
Zinc (Zn): Maximum permissible limit is 5.0 ppm
Cadmium (Cd): Maximum permissible limit is 0.005 ppm
Copper (Cu): Maximum permissible limit is 3.0 ppm
Step 2: Matching List-I with List-II
A) Mn → \( I \) (0.05)
B) Zn → \( IV \) (5.0)
C) Cd → \( III \) (0.005)
D) Cu → \( II \) (3.0)
If \( \vec{u}, \vec{v}, \vec{w} \) are non-coplanar vectors and \( p, q \) are real numbers, then the equality:
\[ [3\vec{u} \quad p\vec{v} \quad p\vec{w}] - [p\vec{v} \quad \vec{w} \quad q\vec{u}] - [2\vec{w} \quad q\vec{v} \quad q\vec{u}] = 0 \]
holds for:
Statement-I: In the interval \( [0, 2\pi] \), the number of common solutions of the equations
\[ 2\sin^2\theta - \cos 2\theta = 0 \]
and
\[ 2\cos^2\theta - 3\sin\theta = 0 \]
is two.
Statement-II: The number of solutions of
\[ 2\cos^2\theta - 3\sin\theta = 0 \]
in \( [0, \pi] \) is two.
If \( A \) and \( B \) are acute angles satisfying
\[ 3\cos^2 A + 2\cos^2 B = 4 \]
and
\[ \frac{3 \sin A}{\sin B} = \frac{2 \cos B}{\cos A}, \]
Then \( A + 2B = \ ? \)