Ncert Solutions Maths class 11th

. The number of real roots of the equation e⁴ˣ + e³ˣ – 4e²ˣ – eˣ + 1 = 0 is equal to………….

Which of the following is the negation of the statement “for all M > 0, there exists x ∈ S such that x ≥ M”?

Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals of the parallelogram is 11x + 7y = 9, then other diagonal passes through the point:

For real numbers α and β ≠ 0, if the point of intersection of the straight lines (x-α)/1 = (y-1)/2 = (z-1)/3 and (x-4)/β = (y-6)/3 = (z-7)/3 lies on the plane x+2y-z = 8, then α - β is equal to:

The value of limₓ→₀ x/(√1-sinx - √1+sinx) is equal to :

Let C be the set of all complex numbers. Let S₁ = {z∈ C:|z-2|≤1} and S₂ = {z∈ C: z(1+i)+z̄(1-i) ≥ 4}. Then, the maximum value of |z - 5/2|² for z ∈ S₁ ∩ S₂ is equal to:

Let α = maxₓ∈ᵣ{8²sin³ˣ 4⁴cos³ˣ} and β = minₓ∈ᵣ{8²sin³ˣ 4⁴cos³ˣ}. If 8x² + bx + c = 0 is a quadratic equation whose roots are α¹/⁵ and β¹/⁵, then the value of c – b is equal to :

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept 6√5 on the x-axis. Then the radius of the circle C is equal to :

The point P(a,b) undergoes the following three transformations successively :
(a) reflection about the line y = x
(b) translation through 2 units along the positive direction of x-axis.
(c) rotation through angle π/4 about the origin in the anti-clockwise direction.
If the co-ordinates of the final position of the point P are (-1/√2, 7/√2), then the value of 2a + b is equal to :

Let f : [0,∞) → be a function defined by f(x) = { max{sint: 0≤ t ≤x}, 0≤x≤π, 2 + cos x, x > π
Then which of the following is true?