AWES TGT Maths Mock Test - 4 - AWES TGT/PGT MCQ

India recently overtook Hong Kong as the world’s fourth-largest equity market, boasting a total market value of $4.33 trillion, surpassing Hong Kong’s $4.29 trillion. The leading global stock markets are currently the U.S., China, and Japan. This milestone underscores India’s rising prominence in the global financial arena, propelled by a robust GDP, political stability, foreign investments, and its appeal as an alternative to China. Meanwhile, Hong Kong grapples with challenges like COVID-19 restrictions, regulatory crackdowns, a property crisis, and geopolitical tensions, affecting its attractiveness to investors.

The RBI’s “Finances of Panchayati Raj Institutions (PRIs)” report analyzes data from 2.58 lakh Panchayats for 2020-21 to 2022-23, highlighting key findings. Panchayats heavily rely on grants (95%) due to limited own revenue sources like property taxes. Inter-state variations in devolution impact socio-economic outcomes. Inconsistent data poses challenges in assessing fiscal health. PRIs struggle with local tax revenue generation due to a limited tax base, administrative issues, and unclear guidelines. Revenue sources include Central and State government grants, and PRIs have the authority to impose taxes and fees.

The Bombay Stock Exchange (BSE) as its combined market capitalization reached ₹400-lakh crore for the first time. This reflects the growing valuation and strength of the BSE in the financial market, showcasing a substantial increase from previous milestones like ₹200-lakh crore.

SURYA KIRAN's 17th edition is being held in Pithoragarh, Uttarakhand, emphasizing the enduring collaboration between India and Nepal in military cooperation.

India is set to chair the International Sugar Organisation (ISO) in 2024, underlining its prominent position as the world's largest consumer and second-largest producer of sugar.

Russia's nuclear energy corporation Rosatom has set a record by installing a research reactor pressure vessel in Mountain Meteor at an altitude of about 4,000 meters above sea level in El Alto, Bolivia.

International Day of Human Space Flight is celebrated every year on 12 April. This day is celebrated in honor of Yuri Gagarin, the first man to go into space.  The UN General Assembly had announced the celebration of this day in the year 2011. On April 12, 1961, Yuri Gagarin of the Soviet Union became the first man to travel around the Earth in space.

The US-India Strategic and Partnership Forum (USISPF) has appointed former Revenue Secretary and former Secretary of Economic Affairs Tarun Bajaj as the head of the US-India Tax Forum. A 1988 batch Haryana cadre IAS officer, Tarun Bajaj has served as Revenue Secretary. The US-India Tax Forum was officially launched on February 25, 2020.

In the triarchic theory, three types of intelligence proposed by Robert Sternberg are: Analytical, Creative and Practical.

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

In psychology, individual differences refer to the extent and kind of variations or similarities among people on some of the important psychological aspects such as intelligence, personality, interest, and aptitude.

By the property of transpose , (AB)’ = B’A’.

(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.

f (x) is discontinuous when x² - 3|x| + 2 = 0
⇒ |x|² - 3|x| + 2 = 0 ⇒ |x| = 1, 2

f(0) = a -1 < 0
⇒ a < 1
f(1) = 1 + 2a + 1 a - 1 < 0
⇒ 3a < -1

D > 0 ⇒ 4a² + 4a + 1 - 4a + 4 > 0
⇒ 4a² + 5 > 0
True for all a ∈ R
From equation (i), (ii) and (iii) 

When a is positive, the parabola is opening to the right and since directrix is x=-a, it gives the answer.

Domain of sin^-1x is [-1,1]

Therefore, -1 ≤ log₃(x/3) ≤ 1

3^-1 ≤ x/3 ≤ 3

1 ≤ x ≤ 9

Therefore, the domain of sin^-1[log₃(x/3)] is [1,9]

Clearly function f (x) = 3x² - 2x+1 is increasing when
f ' (x) = 6x – 2 > 0 ⇒ x ∈[1 / 3,∞)

∴ f (x) is incorrectly matched with 

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

A relation R on a non empty set A is said to be symmetric if fx Ry ⇔ yRx, for all x , y ∈ R .

(i) The graph of the function y = cos x is continuous and extends on either side in symmetrical wave form.
(ii) Since the graph of y = cos x intersects the x-axis at the origin and at points where x is an odd multiple of 90°, hence cos x is zero at x = (2n + 1)/π² where n = 0, ±1, ±2, ±3, ±4, ……………... .

I = ∫√(x² + 5x)dx

= ∫√(x² + 5x + 25/4 - 25/4)

= ∫√{(x + 5/2)² - (5/2)²}

={1/2(x+5/2)(√x² + 5x)} - {25/8 log{(x + 5/2)+√x²+ 5x}}

= {(2x + 5)/4 (√x² + 5x)} - {25/8 log{(x + 5/2)+√x²+ 5x}}

Thus, option D is correct...

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°

λx + y - 5 = 0 is the focal chord
Since it passes through (0, 5)
Let h, k be the mid point of all such chord h = 5(t₁ + t₂), 
 
On eliminating t₁, t₂
x² = 10 (y - 5). 

[x(-3x(x+2) - 2x(x-3)]+6[2(x+2)+3(x-3)]-1(4x-9x) = 0

⇒ - 5x³ + 35x - 30 = 0
⇒ (x-1)(x-2)(x+3) = 0 ⇒ x=1,2,-3

Let D – Lost card is diamond
D – Lost card is not diamond.

When one diamond card is lost, the number of diamond cards are 12 out of 51.
No. of ways of choosing 2 from 12 cards ¹²C₂ .
Similarity, choosing 2 diamond cards out of 51 are ⁵¹C₂.
 probability of getting two cards, when one diamond is lost

When the lost and is not diamond, number of diamond cards are 13 out of 51.
No. of ways of choosing 2 cards when one card is lost which is not diamond =