JEE Main Practice Test- 26 - JEE MCQ

If ω is a cube root of unity ,then
(1 - ω + ω²)⁵ + (1 + ω - ω²) is equal to

If z = -2/(1 + √3i),then the value of arg (z) is

The solution of the differential equation cos x sin y dx + sin x cos y dy =0 is

The value of f(0) so that f (x)    is continuous at x = 0 is

If m and n are integers, then what is the value of sin m x sin n x d x . If m ≠ n

The solution of the equation xdy-ydx=0 is

If y=sec⁻¹[(x+1)/(x-1)]+sin⁻¹[(x-1)/(x+1)], (dy/dx)=

Tangents are drawn from a point P(3,4) to the ellipse (x²/9) + (y²/16) = 1 touching the ellipse in the points Q and R. The angle between PQ and PR is

Which statement is logically equivalent to "If Yoda cannot use a lightsaber, then he cannot help Luke win the battle."

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): Let f(x) and g(x) be two polynomials all of whose coefficients are rational numbers . Suppose f(x) and g(x) have a common irrational root, then g(x) = r f(x) for some rational number.
Reason(R): The common root of the equations ax² + bx + c = 0 and a'x² + b'x + c' = 0 is  

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A):
Reason(R):  

If each element of a 3 x 3 matrix is multiplie by 3, then the determinant of the newly formed matrix is

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A):α₁,α₂,α₃,α₄ are roots of 2x⁴ - 2x³ + 9x² - x + 12 = 0, then the value of   is 21.
Reason(R): 2(x-α₁) (x-α₂)(x-α₃) x  (x-α₄) = 2x⁴ - 2x³ + 3x² - x + 12. Put x = 3 i on both sides and take modulus of both sides

The line 4x + 6y + 9 = 0 touches the parabola y² = 4 x at the point

If A = [(x,y) : x² + y² = 25] and B = [(x,y) : x² + 9y² = 144] and A ∩ B contains

A random variable X has the following distribution
x                  1    2   3  4
P ( X = x)     c  2c 3c 4c
The value of c is

The plane XOZ divides the join of (1,-1,5) and (2,3,4) in the ratio λ:1,then λ is

The angle between the vectors
î - ĵ + k̂ and î + 2ĵ + k̂ is

 are non− coplanar, then the sum