A problem in mathematics is given to three students whose chances of solving it are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) respectively. The probability that the problem is solved is

If \(A=\{1,2,3,4, \cdots, n\}\) and \(B=\{x, y\}\), then the number of surjections from \(A\) to \(B\) is

If \(|\vec{a}|=10,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=12\), then value of \(|\vec{a} \times \vec{b}|\) is :

If \(f(x)=3 x^2+10 x-5\), then by using differentials the appropriate value of \(f(2.03)\) is

The particular solution of the differential equation \(\left[\log \left(\frac{d y}{d x}\right)=3 x+4 y\right.\) satisfying \(y=0\) when \(x=0\) is :

It is given that mean and variance of a binomial variate X are 2 and 1 respectively. Find the probability that X takes value greater than or equal to 1.

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C work together but pipe C is closed after 10 hours, then the time taken by pipe A and B to fill the remaining tank is:

The value of \(\int_1^2 \frac{\sqrt{x}}{\sqrt{3-x}+\sqrt{x}} d x\) is:

Observe the figures and answer the question.

Identify the parts of the embryonal axis of a dicot embryo:
A. Epicotyle
B. Plumule
C. Radicle
D. Scutellum
Choose the correct answer from the options given below:

Among the following, which alkyl halide has the highest boiling point?

Match List I with List II

LIST I	LIST II
A. Photodiode	I. junction area is kept much larger and biasing not required
B. Light emitting diode	II. used to detect intensity of radiation
C. Solar cell	III. Used as a voltage regulator
D. Zener diode	IV. emits spontaneous radiation under forward bias

Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
When \(1 mol CrCl _3 \cdot 6 H _2 O\) is treated with excess of \(AgNO _3, 3 mol\) of AgCl are obtained. The formula of the complex is:

At resonance of a series LCR circuit.
A. Phase difference between \(X_L\) and \(X_C\) is 90\(^\circ\)
B. Source frequency \(= \frac{1}{2\pi\sqrt{LC}}\)
C. Peak current acquires maximum value
D. Inductive reactance is equal in magnitude to Capacitive reactance.
E. The total impedance of the circuit is maximum Choose the correct answer from the options given below:
Choose the correct answer from the options given below: