Pb(NO3)2 and Zn(NO3)2
Pb(NO3)2 and Bi(NO3)2
AgNO3 and Bi(NO3)3
Pb(NO3)2 and Hg(NO3)2
Pb(NO3)2 and Zn(NO3)2
- Pb(NO3)2 reacts with NaOH to form a white precipitate of Pb(OH)2 and with HCl to form a white precipitate of PbCl2. However, Zn(NO3)2 does not react with NaOH to form a white precipitate, so this mixture is incorrect.
- Option B:
Pb(NO3)2 and Bi(NO3)2
- Pb(NO3)2 reacts with NaOH to form Pb(OH)2 and with HCl to form PbCl2.
- Bi(NO3)2 reacts with NaOH to form Bi(OH)3 and with HCl to form BiCl3, both of which are white precipitates.
- Therefore, this mixture fits the observed behavior, and is correct.
- Option C:
AgNO3 and Bi(NO3)3
- AgNO3 reacts with NaOH to form AgOH (white precipitate) and with HCl to form AgCl (white precipitate).
- Bi(NO3)3 reacts similarly to form Bi(OH)3 (white precipitate) with NaOH and BiCl3 (white precipitate) with HCl.
- Therefore, this mixture also fits the behavior, and is correct.
Step 5: Conclusion
The correct options are:
A Pb(NO3)2 and Zn(NO3)2
B Pb(NO3)2 and Bi(NO3)2
C AgNO3 and Bi(NO3)3
Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with
\(K_4\)[Fe(CN)\(_6\)] is : \[ {Cu}^{2+}, \, {Fe}^{3+}, \, {Ba}^{2+}, \, {Ca}^{2+}, \, {NH}_4^+, \, {Mg}^{2+}, \, {Zn}^{2+} \]
Match List I with List II:
Choose the correct answer from the options given below:
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 