VITEEE Maths Test - 2 - JEE MCQ

Solution:

• Let the integer be x.


• The difference of the integer and its cube is x - x^3.


• For this difference to be divisible by a number, the number should divide the difference without leaving a remainder.


• We need to find a number which divides x - x^3 without leaving a remainder.


• Factoring out x from x - x^3 gives x(1 - x^2).


• Further factoring 1 - x^2 gives (1 - x)(1 + x).


• Therefore, the difference x - x^3 = x(1 - x)(1 + x).


• The number that divides x - x^3 without leaving a remainder is the common factor of x, 1 - x, and 1 + x.


• The common factor of x, 1 - x, and 1 + x is 1.


• Therefore, the difference of an integer and its cube is divisible by 1, which means it is divisible by any integer including 4, 6, 10, and 9.


• However, the smallest number among the given options that divides x - x^3 without leaving a remainder is 6.


• Hence, the correct answer is B: 6.


 

Given, A + B + C = 180
So, A + B = 180 - C
Taking tan on both sides we get,
⇒ tan(A+B) = tan(180-C)
⇒ 
⇒ tanA + tanB = -tanC(1 - tanA tanB)
⇒ tanA + tanB = - tanC + tanA tanB tanC
⇒ tanA + tanB + tanC = tanA tanB tanC

y² = 5x + 4y + 1
or y² - 4y = 5x + 1
or y² - 2.2.y + (2)² - (2)² = 5x + 1
or (y - 2)² = 5x + 5
or (y - 2)² = 5(x + 1)
Length of the latus rectum = 5

To find f(1) from the function f(x) = 2x - 3 when x ≤ 2, follow these steps:

• Substitute x = 1 into the function: f(1) = 2(1) - 3.
• Calculate the value: 2 - 3 = -1.

Now, calculate f(2):

• Use the same function with x = 2: f(2) = 2(2) - 3.
• Compute the result: 4 - 3 = 1.

We found f(1) = -1 and f(2) = 1.

Therefore, f(1) is equal to -f(2).

Given, A = (10i + 3j​)
B = (12i - 5j)​
C = (ai + 11j​)
AB = 2i - 8j​
AC = (a - 10)i + 8j​
AB and AC are collinear
⇒ 2/(a - 10) = -8/8
⇒ 2 = 10 - a
⇒ a = 8

Explanation:

• To compare two complex numbers, we first compare their real parts. If the real parts are equal, then we compare the imaginary parts.


• In this case, the real parts are 5 and 6. Since 5 is less than 6, we can say that 5 + 3i is less than 6 + 4i.


• Therefore, the correct answer is option D: 5 + 3i < 6 + 4i.

 

If inverse will not exist then |A|=0 x² − 11x + 29 = 0

α + β = 2
αβ = 2
(α + β)² = 2²
α² + β² +2αβ = 4
α² + β² +2(2) = 4
α² + β² + 4 = 4
α² + β² = 0