HPSC PGT Mathematics Mock Test - 8 - HPSC TGT/PGT MCQ

The correct answer is Ethanol + Methanol​.

• Ethanol + Methanol​ is denatured alcohol.
• Denatured alcohol is ethanol that has additives to make it poisonous, bad-tasting, foul-smelling, or nauseating to discourage its recreational consumption.
• The term denatured alcohol refers to alcohol products adulterated with toxic and/or bad tasting additives (e.g., methanol, benzene, pyridine, castor oil, gasoline, isopropyl alcohol, and acetone), making it unsuitable for human consumption.
• The most common additive used is methanol (5–10%), giving rise to the term methylated spirits. Denatured alcohol is used as a lower-cost solvent or fuel for home-scale or industrial use.

Key Points

• Denatured alcohol is ethanol or grain alcohol that contains additional chemicals called denaturants that make it unfit for human consumption.
• Denatured alcohol is fine for some types of lab work and as an ingredient in certain products, but it's not safe to drink.
• Ethanol is an organic chemical compound. It is simple alcohol with the chemical formula C₂H₆O.
• Its formula can be also written as CH₃−CH₂−OH or C₂H₅OH and is often abbreviated as EtOH.

Additional Information

• Alcohol (ethanol or ethyl alcohol) is the ingredient found in beer, wine, and spirits that causes drunkenness.
• Alcohol is formed when yeast ferments (breaks down without oxygen) the sugars in different food. 

Concept

Size of element:

• The atomic size of an element is determined by the atomic radius of an element.
• Atomic radius is the distance between the center of an atom to its outermost (valence) shell having electrons.
• The atomic size of any element is mentioned in form of Atomic radius.
• Unit of Atomic radius is Amstrong (A^o).

Valency of an element:

• Valency is the combining capacity of an atom of an element.
• It is otherwise the valence electrons an atom uses to form a chemical bond.

The molar mass of the element:

• It is defined as the mass of one atom of an element.
• The unit is g/mol.
• For all substances, the molar mass of in g/mol is numerically equal to the formula mass in atomic mass units.

Explanation:

• The maximum number of univalent atoms that may combine with an atom of the element is the Valency.
• The valency of an element is always an integer.
• With regard to covalent compounds, the term valency describes the number of bonds usually formed by each element.
• In ionic compounds, often, the number of positive or negative charges that appear on the atom in its ion helps to state its valency.
• The chemical behavior is largely influenced by the valency of the element.

Hence, Valency of an element is the property that determines an element's chemical behavior.

The correct answer is Rakhigarhi.

Key Points

• Rakhigarhi site of Indus valley civilisation situated at Rakhigarhi village in Hisar district.
• The site is located in the Sarasvati river plain, some 27 km from the seasonal Ghaggar river.
• The Global Heritage Fund declared Rakhigarhi one of the 10 most endangered heritage sites in Asia.
•  A team of Indian and South Korean researchers carried out excavations in Rakhigarhi.
• The team unearthed a fire altar, parts of a city wall, drainage structures as well as a hoard of semi-precious beads.

Additional InformationImportant Sites of Harappan Civilization:

The correct answer is Gavambhavana.

• In ancient times, Gohana was known as Gavambhavana and was considered a sacred place.
  • ​Gohana is a city in Sonipat district in the Indian state of Haryana.

Additional Information

• Haryana is an Indian state located in the northern part of the country.
  • It was separated from the former state of East Punjab on 1 November 1966 on linguistic grounds.
  • It ranks 21st in terms of area with less than 1.4% of India's land area.
  • The state capital is Chandigarh, which it shares with the neighboring state of Punjab.

The logic followed here is:

1) Intact and Unflawed are synonyms meaning not damaged and perfect.

2) Entire and Partial are antonyms.

3) Bright and Luminous are synonyms.

4) Pure and Perfect are synonyms.

Both the words are synonyms in all the options except option 2, where the given words are antonyms.

Hence, the correct answer is "Entire : Partial".

The word that can be prefixed to make the following new words is ‘Mis’.

Mis + Interpret = Misinterpret

Mis + Behave = Misbehave

Mis + Understand = Misunderstand

Mis + Take = Mistake

Kinesthetic/tactile persons learn best through a hands-on approach, actively exploring the physical world around them. Thus, using the hands-on approach may not help Sita much.

Order = 3 , degree not defined ,because the function y’ present in exponential form.

A relation R on a non empty set A is said to be transitive if fx Ry and yRz ⇒ x Rz, for all x ∈ R.

⇒ x² = x²

∴ f is one-one

Let y∈R and let y=x³. then x=y^⅓ ∈ R

Thus for each y in the codomain R there exists y^1/3 in R such that 

f(y¹³)=(y¹³)³=y

∴ f is onto.

Hence f is one -one onto.

Centre is (1, 3) and radius = 2
If r = radius of second circle then r² = 2² + (3 - 1)² + (2 - 1)²
⇒ r = 3.
Hence (C) is the correct answer.

From the graph it is clear that h is continuous. Also h is differentiable except possible at x = 0 & 1


so h is not differentiable at 1
similarly h' (0 +)= 0 but h ' (0 - ) = 1

The orthogonal projection on x- axis is given by : 

n,n + 1, n +2  are consecutive integers their sum is muttiple of 3, so 

Beside the ground floor, there are seven floors.
The total number of ways in which each of the five persons can leave cabin at any of the 7 floors =7⁵
And the favorable number of ways, that is, the number of ways, in which 5 persons leave at different floors is ⁷P₅

• The set containing all objects or elements and of which all other sets are subsets is a Universal set.
• Here, option A has all the elements of set P, Q and R. So {1, 2, 3, 4, 5, 6, 7, 9} may be considered as universal set for all the three sets P, Q and R.

R is reflexive and transitive but not symmetric 

Integers contain all the natural numbers. So it can be a universal set for natural numbers. In other options, there are only some of the elements of natural numbers.

let, X =5,6,7,8,9,13,12,15.
(5+6+7+8+9+13+12+15)÷9 = 9.
and hence a = 9.
the mean deviation about the mean is summation of |X-a|÷ the total number
i.e , |X-a| = 4,3,2,1,3,0,4,3,6 and the total no. is 9.
hence summation of |X-a| = 26,
the mean deviation is 26 ÷ 9 = 2.89 ans

number of type 3k → 10
3k + 1 → 10
3k + 2 → 10
Either all the no. are of the same type or one No. from each type

if it is common tangent, then m³ = 8 m = 2. 

A.B = [(-1(-1) + 2(-2) + 3(-3)   -1(-3) + 2(1) + 3(2)]

A.B = [1 - 4 - 9     3 + 2 + 6]

A.B = [-12   11]

Any square matrix when multiplied with its inverse gives the identity matrix. Note that non square matrices are not invertible.

To solve this problem, we'll use the tangent addition formula:

• tan(A + B) = (tanA + tanB) / (1 - tanA * tanB)

We can rewrite 45° as 22° + 23°. So,

• tan(45°) = tan(22° + 23°)

Using the tangent addition formula:

• 1 = (tan22° + tan23°) / (1 - tan22° * tan23°)

Cross-multiplying, we get:

• 1 - tan22° * tan23° = tan22° + tan23°

Rearranging the terms, we get:

• tan22° + tan23° + tan22°.tan23° = 1

Therefore, the value of tan22° + tan23° + tan22°.tan23° is 1.

Coefficient of x⁵ in (1 + x)¹⁰ 
Coefficient of x²⁵ in (1 + x)³⁰

f ‘ (x) = 2x – 2 = 2 (x - 1) < 0 if x < 1 i.e. x x∈ (−∞,1) x∈ (−∞,1). Hence f is strict decreasing in left decreasing in (−∞,1)

Tangent, T : 2x−y+1=0
Slope of tangent, T to the circle is 2
The line joining the centre and the point of contact of tangent is perpendicular with the tangent.
Thus, slope of line OA = −1/2 
Equation of OA, (y−5) = −1/2(x−2)
x + 2y = 12
∴ Intersection with x−2y=4 will give coordinates of centre which are (8,2)
∴r = OA = √(8−2)² + (2−5)²
 =3√5