NATA Mock Test - 2 - JEE MCQ

Let the equation of the circle is

(x-1)² + (y-k)²  = k²

It passes through (2, 3)

⇒ (2-1)² + (3-k)² = k²

⇒ 1+9+k²-6k = k²

⇒ 10-6k=0

⇒ k=-10/-6

⇒ k = 5/3

⇒ diameter = 10/3

Let A=iⁱ

⇒ log A = i log i

∵ e^{i θ} = cos θ + i sin θ

∴ e^iπ/2 = i

∴ i . π/2 = log i

∴ log A = i · i π/ 2 = - π / 2

⇒ A = e^-π/2

Let the third vertex C be (x₁ , y₁) since O(0, 0) is the orthocenter

m_CO × m_AB = – 1

⇒ y 1 - 0 x 1 - 0 · 3 - - 1 - 2 - 5 = - 1

⇒ y 1 x 1 · 4 7 = 1

⇒ 7 x 1 = 4 y 1

Also mBO × mAC = – 1

⇒ 3 - 2 × y 1 + 1 x 1 - 5 = - 1

⇒ 3 y 1 + 3 = 2 x 1 - 1 0

⇒ 3 × 7 4 x 1 + 3 = 2 x 1 - 1 0

⇒ x₁ = – 4

y₁ = – 7

Hence, the third vertex is (– 4, – 7)

f(x) = eax + e- ax

But a < 0

∴ e ax - e - ax > 0

⇒ e ax > e - ax

⇒ ax > - ax ⇒ 2 ax > 0

∴ ax > 0, then x < 0 (∴ a < 0)

A three-digit number is formed by choosing a digit for each of the hundreds, tens, and units places.

Since 0 cannot be used and 1, 7, 8, and 9 are the only available digits, each place (hundreds, tens, and units) must be filled by one of these four digits.

Thus, we have:

• 4 choices for the hundreds place (1, 7, 8, 9)
• 4 choices for the tens place (1, 7, 8, 9)
• 4 choices for the units place (1, 7, 8, 9)

The total number of different three-digit numbers that can be formed is calculated by multiplying the number of choices for each place:

4 × 4 × 4 = 64 

Therefore, the correct answer is: 64

1,2,3,4,5

Number of given digits (=5) Number of Digits number

to be formed (=5) Number of such numbers

Hence, speed after one revolution

Comparing vx = ky²

vy = kx

and slope

By conservation of angular momentum

and average force on third particle

x ∝ y², path is parabolic.

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The Statue of Liberty is a colossal neoclassical sculpture on Liberty Island in New York Harbor in New York, in the United States. The copper statue, a gift from the people of France to the people of the United States, was designed by French sculptor Frédéric Auguste Bartholdi and its metal framework was built by Gustave Eiffel. The statue was dedicated on October 28, 1886.

If a colour is made darker by adding black, the result is called a Shade

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LIC Building is a 15-storied building in Chennai, India, serving as the southern regional headquarters of the Life Insurance Corporation of India

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TEOTIHUACAN is an ancient Mesoamerican city located in a sub-valley of the Valley of Mexico, located in the State of Mexico 40 kilometres (25 mi) northeast of modern-day Mexico City, known today as the site of many of the most architecturally significant Mesoamerican pyramids built in the pre-Columbian Americas.