Jharkhand TGT (JSSC) Mock Test - 5 - Jharkhand (JSSC) PRT/TGT MCQ

Here, f(x) = x² and g(x) = √x

fog(x) = f(g(x))

= [g(x)]²

= [√x]²

= x

⇒ fog(x) = [√x]²

So, fog(2) = (√ 2)² = 2 and fog(-4) = (√-4)²

But, f(x) belongs to Real number, so fog (-4) = 4 is not true

Line parallel to is given as

Distance from origin is

Required lines are

Substituting the given options in the above equations for getting the correct answer.

Clearly satisfies , so there is no need to check other options.

Given:

As we know,

Considering the given equation,

The value of is .

Given:

and

and

and

If two planes intersect each other, the intersection will always be a line.

Now, the direction ratios of the line are .

Given,

We have,

By eq. eq. (2)

By eq. (1) - eq. (2)

From & both sec and tan are positive only in the first quadrant.

Here,

Here,

We know that,

The order of a differential equation is the order of the highest derivative appearing in it.

The degree of a differential equation is the degree of the highest derivative occurring in it, after the equation has been expressed in a form free from radicals as far as the derivatives are concerned.

Given the differential equation is,

Taking cube on both sides, we get,

Taking square on both sides, we get,

Highest derivate is

So, the order of the given differential equation

The power of the highest derivate

So, the degree of the given differential equation

Given,

As we know,

∴ The value of given identities is 8.

Let

So, Statement 1 is true.

Consider,

Consider

Taking log both sides,

Differentiating both sides,

Putting the value from (2) to (1)

Comparing x² - y² = 0 with the general equation ax² + 2hxy + by² + 2gx + 2fy + c = 0, we can say that a = 1, b = -1 and all other coefficients are 0.

Δ = abc + 2fgh - af² - bg² - cf² = 0.

∴ The equation represents a pair of straight lines.

Static field intensity at the surface of a conductor is directly normal to the surface this statement is correct regarding an ideal conductor in a static electric field.

Under the static condition, the electric field inside the solid perfect conductor is zero in electrostatic equilibrium even if it is isolated, charged, and present in the external electrostatic field.

Now, it is known that a perfect solid conductor is an equipotential body. The potential inside the conductor is the same as the potential at the surface. Since the surface of the solid conductor is an equipotential surface hence the electric field will be perpendicular or in other words normal to the perfectly solid conductor surface.

Since, is always +ve for convex mirror

By the mirror formula

So,

Now,

(negative sign shows negative y-axis)

Ferromagnetic substances are those which gets strongly magnetised when placed in an external magnetic field. They have strong tendency to move from a region of weak magnetic field to strong magnetic field, i.e., they get strongly attracted to a magnet.

The individual atoms (or ions or molecules) in a ferromagnetic material possess a dipole moment as in a paramagnetic material. However, they interact with one another in such a way that they spontaneously align themselves in a common direction over a macroscopic volume called domain.

Air is an example of paramagnetic material since under an external magnetic field it forms an electric dipole.

Paramagnetic substances are those which develop feeble magnetization in the direction of the magnetizing field. Such substances are feebly attracted by magnets and tend to move from weaker to stronger parts of a magnetic field. Magnetic susceptibility is small and positive i.e. x>0.

The relative permittivity of the water is highest among the other materials given.

Permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Thus, permittivity is the measure of a material's ability to resist an electric field.

Relative permittivity is the ratio of its absolute permittivity ' to free space (empty of matter) permittivity ' i.e.,

For critical angel,

In class B amplifier, the output current flows for half input cycle.

Class-B amplifiers use two or more transistors biased in such a way so that each transistor only conducts during one half cycle of the input waveform. In these amplifiers one transistor only amplifies one half or 180° of the input waveform cycle while the other transistor amplifies the other half or remaining 180° of the input waveform cycle. It is also known as a push-pull amplifier configuration.

A metallic rod when placed in a strong magnetic field, aligns itself at right angles to the magnetic field. The nature of the material is diamagnetic.

Diamagnetic substances are those which develop feeble magnetization in the opposite direction of the magnetizing field.

Such a large difference in electronegativity shows that Cesium is electropositive while Fluorine is electronegative in nature. So, Cesium can donate an electron to fluorine. So they form ionic bond or electrovalent bond.

Deuterium and hydrogen both have same atomic number but different mass number so they have different physical properties but similar chemical properties since they have same electronic configuration.

Cellulose would be the most abundant in the diet of strict vegetarians. Cellulose, a fibrous carbohydrate found in all plants, is the structural component of plant cell walls. Because the earth is covered with vegetation, cellulose is the most abundant of all carbohydrates, accounting for over 50% of all the carbon found in the vegetable kingdom.

Starch consists of unbranched amylose and branched amylopectin. Starch is a soft, white, tasteless powder that is insoluble in cold water, alcohol, or other solvents. Starch is a polysaccharide comprising glucose monomers joined in α 1, 4 linkages. The simplest form of starch is the linear polymer amylose; amylopectin is the branched form.

Atomic radii decrease across a period in the periodic table due to an increase in the effective nuclear charge.

The element with electronic configuration 1s^2, 2s², 2p⁶, 3s² is an s-block element placed at the extreme left of the periodic table. Whereas, the others are p-block elements placed at the extreme right.

Therefore, the atomic radii of the element with electronic configuration 1s² 2s² 2p⁶ 3s² are largest.

Rayon was developed as an alternative for silk. It is prepared by the chemical processing of wood pulp or cellulose. It resembles the texture and look of natural silk and can be woven like silk fibres. Hence, it is also called artificial silk.

Structural polysaccharides include cellulose, hemicellulose and chitin.

Cellulose: It is the most abundant organic compound. It is a highly ductile fibrous homopolysaccharide that forms the structural element of the cell wall of all plants, some fungi and protists. Cotton fiber contains about 90% cellulose while wood contains 25-50% cellulose. Other substances in the cell include lignin, hemicellulose, pectin, wax, etc.

Hemicellulose: This refers to a component of the plant cell wall that has a simpler structure than cellulose. It occupies 20 - 30% of the dry weight of the wood.

Chitin: It is the second most common polysaccharide. It is a complex heteropolysaccharide. Found as structural components of fungal wall and external skeleton of arthropods. It is a polymer of N-acetyl glucosamine. It provides both strength and elasticity. These harden due to the impregnation of are linked by monomers.

Dmitri Mendeleev arranged the Periodic Table of Elements in the order of increasing atomic masses.

Mendeleev’s Periodic Table (1869) is based upon Mendeleev’s periodic law, which states, “Properties of the elements are the periodic function of their atomic masses.”