HPSC PGT Mathematics Mock Test - 3 - HPSC TGT/PGT MCQ

The correct answer is ​Purandara Dasa.

Key Points

​Purandara Dasa

• ​​He is considered the Pitamaha of Carnatic music.
• His compositions are mainly in the Kannada language.
• He was born in 1484.
• Raga Mayamalavagowla first carnatic music was discovered by Purandara Dasa.

Additional Information

• Trippunithura Narayanaiyer Krishnan (TN Krishnan) was born on October 6, 1928, in Cochin.
• He learned music from his father and was provided with the patronage of the Royal Family of Cochin.
• He was tutored by Semmangudi Srinivasa Iyer, another prominent Carnatic Violinist.
• Awards:
  • Padma Shri (1973)
  • Sangeet Natak Academy Award (1974)
  • Padma Bhushan (1992)
  • Sangeet Kalanidhi (1980).

The correct answer is Rahul Bhatia.

Key Points

• InterGlobe Aviation has announced the appointment of its Co-founder Rahul Bhatia as the company's Managing Director with immediate effect.
• The company is the parent of the country's largest airline IndiGo.
• Bhatia is the Co-founder and Promoter of InterGlobe Aviation. 
• Meleveetil Damodaran is the Chairman of IndiGo.
• The company is headquartered in Gurgaon, Haryana.

Additional Information

• Professor Dinesh Prasad Saklani has been appointed as the new Director of the National Council of Educational Research and Training (NCERT).
• He has been appointed for a period of five years or till he attains the age of 65 years, whichever is the earliest.
• Universal Acceptance Steering Group has appointed Paytm founder Vijay Shekhar Sharma as its ambassador.
• The Reserve Bank of India (RBI) has appointed Vinod Rai as the independent Chairman of the Unity Small Finance Bank (USFB).
• Senior bureaucrat Vikram Dev Dutt has been appointed as the chairman and managing director (CMD) of Air India Ltd. 
• Narendra Kumar Goenka has been appointed as the new chairman of the Apparel Export Promotion Council, AEPC.
• Reserve Bank of India has approved the appointment of Ittira Davis as managing director & chief executive officer of (MD & CEO) of Ujjivan Small Finance Bank for one tenure.

The correct answer is Kaithal.

Key Points

• Rahul Turan -
  • It is from a small village in Kaithal, Haryana, that got the title of Iron Man.
  • He has become the first soldier of the country to have won this title of the world championship

Additional Information

• ​He has become the first Indian soldier to win the Ironman World Championship held in the US on October 6.
• It is the toughest competition in the world.
• Around 5600 participants from all over the world participated in it.
• He had only practiced for one year in this competition.
• To win this, they have been practicing for many years, but they are not able to succeed.
• Rahul is currently a lieutenant in the Navy and is posted at the Mumbai Navy Centre.

‘Knife’ is related to ‘Cut’, means we use knife for cutting.

Similarly,

We use pen for writing.

Hence, Write is the correct answer.

Teachers can facilitate children's understanding of complex concepts by providing opportunities for exploration and discussion.

(a) The collection of all months of a year is a well-defined collection of objects because one can definitely identify a month that belongs to this collection. Hence, this collection is a set.

(b) A collection of novels is not a well-defined collection because one cannot identify a book that belongs to this collection. Hence, this collection is not a set.

(c) A collection of top rich persons can not be defined. Hence, this collection is not a set.

(d) The collection of the ten most talented writers of India is not a well-defined collection because the criteria for determining a writer's talent may vary from person to person. Hence, this collection is not a set.

xy - 3x - 2y + λ = 0.
Then abc + 2fgh − af² − bg² − ch² = 0
⇒ 3/2 − λ/4 = 0
⇒ λ = 6
∴ Equation of asymptotes is xy-3x-2y+6=0
⇒ (x-2)(y-3)=0
⇒x - 2 = 0 and y - 3 = 0

Therefore , the area of triangle 

Differentiating xy=16, (xdy)/x+y=0
⇒ dy/dx=−y/x=−1/16= Slope of tangent
⇒  Its (tangent's) equation : y=−1=−1/16(x−16)
⇒ 16y−16=−x+16 ⇒ 16y=−x−32
⇒ 16y+x+32=0
It will cut x−axis at A(−32, 0)
& y−axis at B(0, −2)
⇒  Area of △OAB= 1/2×2×32 
⇒ 32

Step 1: Write the determinant in the “first-row expansion” form

6 × [ (3 × –4) – (–1 × 5 ) ]
–  1 × [ (6 × –4) – (–1 × 3 ) ]

• 3 × [ (6 × 5 ) – (3 × 3 ) ]

Step 2: Evaluate each bracket

• (3 × –4) – (–1 × 5 ) = –12 + 5 = –7
• (6 × –4) – (–1 × 3 ) = –24 + 3 = –21
• (6 × 5 ) – (3 × 3 ) = 30 – 9 = 21

Step 3: Multiply by the corresponding first-row entry

• 6 × (–7) = –42
• –1 × (–21) = +21
• 3 × 21 = +63

Step 4: Add them up

–42 + 21 + 63 = 42

Answer: 42

Let marks required be x 
= (45 + 62 + x)/3 > 60
45+62+ x > 60*3
107 + x > 180 
x > 180 - 107
x > 73

So, 73 is the minimum score required in the third attempt to qualify.

A class of integers is called hereditary if, whenever any integer x belongs to the class, the successor of x (that is, the integer x + 1) also belongs to the class. The principle of mathematical induction is then: If the integer 0 belongs to the class F and F is hereditary, every nonnegative integer belongs to F.

⇒ (1-x)(2-x)(3-x) = 0 ⇒x = 1,2,3

b² = ac 
ax² + 2bx+c = 0 

2 liens are parallel

To be reflexive, a line must be perpendicular to itself, but which is not true. So, R is not reflexive
For symmetric, if  l₁ R l₂ ⇒ l₁ ⊥ l₂.
⇒  l₂ ⊥ l₁ ⇒ l₁ R l₂ hence symmetric
For transitive,  if l₁ R l₂ and l₂ R l₃
⇒ l₁ R l₂  and l₂ R l₃  does not imply that l₁ ⊥ l₃ hence not transitive.

α + β = -a,αβ = -b;γ+δ = -a,γδ = b
(α² + aα + b) (β² + aβ +b) = 4b²

Now, for n = 1, 2*4⁽²⁺¹⁾ + 3⁽³⁺¹⁾ = 2*4³ + 3⁴ 
= 2*64 + 81 = 128 + 81 = 209, for n = 2,  2*4⁵ + 3⁷ 
= 8*256 + 2187
= 2048 + 2187 = 4235 
Note that the H.C.F. of 209 and 4235 is 11. 
So, 2*4⁽²ⁿ⁺¹⁾ + 3⁽³ⁿ⁺¹⁾ is divisible by 11. 
Hence, λ is 11

Total No. of ways = ⁶C₃
No. of favorable ways = 2

Step-by-step explanation:

Set of rational numbers { x: x=p/q where p and q are integers and q≠0}.
Set of real numbers is not a subset of X. Set of natural numbers, whole numbers, integers are subset of X.

cos 2θ = 2cos²θ - 1
= 2(1/√5)² - 1
= 2/5 - 1
= -3/5

Let z = 0 + ib, where b < 0. Then z is represented by a point on the negative direction of y-axis. 

Co-efficient of x⁵ in (1+x²)⁵ (1+x)⁴
= {⁵C₀ (1)⁰ + ⁵C₁ (1)x² + ⁵C₂ (1)(x2)2 + ⁵C₃ (1)(x²)³ + ⁵C₄ (1)(x²)⁴ + ⁵C₅ (1)(x²)⁵} * {4C0 (1) + 4C1 (x) + 4C2 (x)2 + 4C3 (x)3 + 4C4 (x)4}
= {⁵C₂(x)⁴ * ⁴C₁(x) + ⁵C₁(x)⁴ + ⁵C₁(x)² * ⁴C₃(x)³} 
∴ coefficient of x5
=> (5×4)/(2×1) × 4)x⁵ + (5×4)x⁵
⇒(10×4+20)x⁵
⇒ 60x⁵

In any traingle The sum of 3 sides of a traingle is equal to 180°

Given 

A=72°

B=48°

A+B+C=180°

72°+48°+C=180°

C=180°-120°

C=60°