Explore topic-wise InterviewSolutions in Current Affairs.

(i) Ligand act as a point charge. 

(ii) Metal ion has electrostatic attraction force with the ligand. (Or any other)

Chemical reaction, a process in which one or more substances, the reactants, are converted to one or more different substances, the products. Substances are either chemical elements or compounds. A chemical reaction rearranges the constituent atoms of the reactants to create different substances as products.

Electrolysis of water to form oxygen and hydrogen is an endothermic reaction because electrical energy is absorbed during this reaction.

Correct answer is M¹L²T^-2A^-2

लुकास का अभिकर्मक केंद्रित हाइड्रोक्लोरिक एसिड में निर्जल जस्ता क्लोराइड का एक समाधान है इस इस समाधान का उपयोग कम आणविक भार के अल्कोहल को वर्गीकृत करने के लिए किया जाता है

Taking the equation of the plane in cartesian form we get,

 (x\(\vec {i}\) + y\(\vec {j}\) + j\(\vec {k}\)) ⋅  (3\(\vec {i}\) + 4\(\vec {j}\) + 12\(\vec {k}\))  = 26

i.e. 3x + 4y + 12z – 26 = 0 

The length of the perpendicular from (0, 0, 0) to the above plane is

\(\pm\frac{-26}{\sqrt {9 + 16 + 144}}\) 

= +26/13

= 2 units

Given that dy/dx + 2y = e^-x

This is a linear differential equation. 

Here P = 2; Q = e 

∫P dx = ∫2 dx = 2x 

Thus, I.F = e∫Pdx = e^2x 

Hence the solution of (1) is ye^{∫ Pdx} = Qe^{∫ Pdx} dx + c

That is, ye^2x = ∫e^-x e^2x dx + c (or) ye^2x = e^x + c (or) y = e^-x + ce^-2x is the required solution.

We observe that the straight line (x - 1)/4 = (2 - y)/6 = (z - 4)/12 is parallel to the vector 4\(\hat {i}\) - 6\(\hat {j}\) + 12\(\hat {k}\) and the straight line (x- 3)/-2 = (y - 3)/3 = (5 - z)/6  is parallel to the vector.  -2\(\hat {i}\) + 3\(\hat {j}\) - 6\(\hat {k}\).

Since  4\(\hat {i}\) - 6\(\hat {j}\) + 12\(\hat {k}\), =  -2(-2\(\hat {i}\) + 3\(\hat {j}\) - 6\(\hat {k}\)) the two vectors are parallel, and hence the two straight lines are parallel.

Given that I =   \(\int_0^{π/2}\)(sin² x + cos⁴ x) dx

  = \(\int_0^{π/2}\)(sin² xdx + \(\int_0^{π/2}\) cos⁴ xdx

= 1/2 - π/2 + 3/4 x 1/2 x π/2 

= 7π/16

The correct option is (A) 1 / 4

Explanation:

S = {HH ,HT , TH , TT} 

For at least two T’s = {TT} 

required probability = 1 / 4

\(\int\cfrac{x^2}{1-x^2}dx\)

= \(\int\cfrac{1-1+x^2}{1-x^2}dx\)

= \(\int\cfrac{1-(1+x^2)}{1-x^2}dx\)

= \(\int\cfrac{1}{1-x^2}dx\) - \(\int dx\)

= \(\cfrac12\)ln \(\left|\cfrac{h\,x}{1-x}\right|\)- x + c

\(\int \frac {x\,dx}{x^3+x^2+x+1} = \int \frac {x\, dx}{(x^2+1) (x+1)}\)

Let \(\frac {x}{(x^2+1) (x+1)} = \frac {A}{x+1} + \frac {Bx+C}{x^2+1}\)

∴ x = A (x²+1) + (Bx + C) (x + 1)

Put x = -1, we get

2A = -1 = A = -1/2

Put x = 0, We get 

A + C = 0 = C = A = 1/2

Put x = 1, We get

2A + 2B + 2C = 1

= 2B = 1-2A-2C

= 1 + 1 -1

= 1

= B = 1/2

∴ \(\frac {x}{(x^2+1)(x+1)} = \frac {-1}{2} \frac {1}{x+1} + \frac 12 \frac {1}{x^2+1} + \frac 12 \frac {1}{x^2+1}\)

= \(\int \frac {x}{(x^2+1)(x+1)}dx = \frac {-1}{2} \int \frac {1}{x+1}dx + \frac 14 \int \frac {2x}{x^2+1}dx+\frac 12 \int \frac {1}{x^2+1}dx\)

= \(\frac {-1}{2} log [x+1] + \frac 14lg [x^2+1] + \frac 12 ta\vec n \,x+C\)

= \(\frac {1}{4} log (\frac {x^2+1}{(x+1)^2}) + \frac 12 ta\vec n \,x+C\)

\(\int\frac{(x^2-1)dx}{x^2+x+1}\)

Let x² - 1 = A(x² + x + 1) + B(2x + 1) + C

⇒ x² - 1 = Ax² + (A + 2B)x + A + B + C

\(\therefore\) A = 1, A + 2B = 0 and A + B + C = -1

⇒ B = -1/2

and C = -1 - A - B

 = -1 - 1 + 1/2

 = -2 + 1/2

= -3/2

\(\therefore\) x² - 1 = (x² + x + 1) - 1/2 (2x + 1) - 3/2

⇒ \(\frac{x^2-1}{x^2+x+1}=1-\frac12\times\frac{2x+1}{x^2+x+1}dx\) - \(\frac32\int\frac{1}{x^2-x+1}dx\) 

 = x - 1/2 log|x² + x + 1| - 3/2 \(\int\cfrac{1}{(x+1/2)^2+(\sqrt3/2)^2}dx+C\)

 = x - 1/2 log|x² + x + 1| - 3/2 x \(\frac1{\sqrt3/2}\) tan^-1(\(\frac{x+1/2}{\sqrt2/3}\)) + C

 = x - 1/2 log |x² + x + 1| - √3 tan^-1(\(\frac{2x+1}{\sqrt3}+C\))

The correct answer is option 4, i.e. None of these.

• Two months will have same calendar if the no of days between them is divisible by 7
• June + July + August + September + October = 30 + 31 + 31 + 30 + 31 = 153 (not divisible by 7)
• April + June + July = 31 + 30 + 31 = 92 (not divisible by 7)
• October + November + December = 31 + 30 + 31 = 92 (not divisible by 7)

a. Industrial wastes poured into water bodies

c. Robertson’s cooked meat medium

Yeast extract is an excellent source of B Vitamin.

The protein moiety of an enzyme is known as Apo enzyme.

The major constituents in agar are Polysaccharides.

Nitrites are oxidized to nitrates by a microorganism Nitrobacter.

Multiple antibiotic resistance is mediated by Plasmid.

d. All the three

a. Succinic dehydrogenase by malonic acid

\(\tau\) = 400 N^-m 

M = 40 kg

α = 20 rad/s² 

I = ?

k = ?

We know that

\(\tau\) = Iα

∵ I = Mk² 

\(\tau\) = Mk²α

k = \(\sqrt{\frac{\tau}{M\alpha}}\) where k = radius of gyration.

k = \(\sqrt{\frac{400}{40 \times 20}}\)

k = \(\sqrt{\frac{1}{2}}\)

Radius of gyration k = 0.70 m

Moment of inertia I = Mk² 

I = 40 × \(\frac{1}{2}\)

I = 20 kg m²

The main product of glycolysis under aerobic conditions is Pyruvate.

Given

L = 60 cm

L = 0.60 m

M = 10 g

M = .010 kg

n = 90 rpm

n = \(\frac{90}{60}\) = 1.5 rps

We know that, moment of inertia thin uniform rod transverse axis through its centre.

I = \(\frac{ML^2}{12}\)

I = \(\frac{.010 \times (0.60)^2}{12}\)

I = 0.0003

I = 3 × 10^-4 kg m² 

Rotational kinetic energy K.E = \(\frac{1}{2}\,I\omega^2\) 

∵ \(\omega = 2\pi n\)

\(=\frac{1}{2} \times (0.0003) \times (2\pi n)^2\)

\(=\frac{1}{2} \times (0.003) \times (2\pi \times 1.5)^2\)

\(=\frac{1}{2} \times 0.003 \times 9\pi^2\)

K.E = 0.133 Joule

Correct answer is (b)

We know that

\(\tau\) = r × F

∵ \(\tau\) \(= \frac{dL}{dt},\) \(F = \frac{dP}{dt}\)

\(\left(\frac{dL}{dt}\right) = r \times \left(\frac{dP}{dt}\right)\)

\(\left(\frac{dL}{dt}\right) - r \times \left(\frac{dP}{dt}\right) = 0\)

(a) Carbon dioxide is fixed in the two following ways:

(i) By the process of photosynthesis in plants.

(ii) Many marine animals use carbonates dissolved in sea-water to make their cells.

(b) Diseases caused due to an increased content of pollutants in the air produced due to the burning of fossil fuels are- ophthalmic problems, skin injuries, gastro-intestinal, cardio-vascular and respiratory diseases and some types of cancer.

Here, mass of the body, M = 150g

volume of the body, V = 250 cm³ 

density of the body, \(d = \frac{M}{V} = \frac{150\,g}{250\,cm^3}\)

\(= 0.6 \frac{g}{cm^3}\)

Since the density of the body \(\left(0.6 \frac{g}{cm^3}\right)\) is less than the density of water \(\left(1 \frac{g}{cm^3}\right),\) the body will float on water.

Answer (d) DNA and RNA

Answer (c) Rhinovirus

An electron is a charged particle (negatively charged) which revolves around the nucleus and spins on its own axis. A magnetic field is generated due to the orbital motion and spin of the electron. The spinning of an electron in an orbit is very much similar to flow of electric current in a closed circuit. Therefore, an unpaired electron is regarded as a micro magnet which has a definite magnetic moment. A substance which contains an unpaired electron when placed in a magnetic field interacts with the applied field. Consequently, an attractive force is exerted and the paramagnetic property is shown. The number of unpaired electrons determines the magnitude of magnetic moment. Higher the number of unpaired electrons more is the magnetic moment and greater will be the paramagnetic behaviour of the substance.

In the case of paired electrons, the electrons in each pair will have opposite spin. The magnetic field created by the electrons of same pair is equal and opposite in nature. Hence, the magnetic field which is created by one electron is cancelled by the other. So the net effect of the magnetic moment is zero. These kinds of substances show diamagnetic property and are repelled by the applied magnetic field.

1. (b) 2. (c) 3. (d) 4. (a)

An optically active complex of the type [M(AA)₂X₂]ⁿ⁺ indicates cisoctahedral structure, e.g. cis-[Pt(en)₂Cl₂]²⁺ or cis-[Cr(en)₂Cl₂]⁺

Answer (c) deoxyribose

When alcohols react with a hydrogen halide, a substitution takes place producing an alkyl halide and water: The order of reactivity of alcohols is 3° > 2° > 1° methyl.

A concentrated solution is a solution where the solvent has a lot of solute in the solution. A solution that is filled to capacity is called a saturated solution.

Metalloids are a very small group of elements found in the periodic table of elements along the zig-zag line that distinguishes metals from non-metals and is drawn from between boron and aluminum to the border between polonium and astatine.

Cu²⁺ (aq) + 2e^- → Cu(s)