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Let x be a vector in the plane containing vectors

Let x be a vector in the plane containing vectors a = 2i – j + k and b =... View Article

Let f : [–3, 1]→ R be given as

Let f : [–3, 1]→ R be given as \(\begin{array}{l}f(x)=\left\{\begin{matrix} min[(x+6,x^{2})], &-3\leq x\leq 0 \\ max[\sqrt{x},x^{2}],&0\leq x\leq 1 \end{matrix}\right.\end{array} \)... View Article

Let I_n = ∫₁^e x¹⁹ (log |x|)ⁿ dx, where n ∈ N.

Let In = ∫1e x19 (log |x|)n dx, where n ∈ N. If 20 (I10) = αI9 + βI8, for... View Article

Let f : [–1,1] → R be defined as f (x) = ax² + bx + c

Let f : [–1,1] → R be defined as f (x) = ax2 + bx + c for all x... View Article

Let A = [latex]\begin{bmatrix} a &b \\ c&d \end{bmatrix}[/latex] and B= [latex]\begin{bmatrix} \alpha \\ \beta \end{bmatrix}\neq \begin{bmatrix} 0\\ 0 \end{bmatrix}[/latex] such that AB = B and a + d = 2021, then the value of ad-bc is equal to

Let A = \(\begin{array}{l}\begin{bmatrix} a &b \\ c&d \end{bmatrix}\end{array} \) and B= \(\begin{array}{l}\begin{bmatrix} \alpha \\ \beta \end{bmatrix}\neq \begin{bmatrix} 0\\ 0... View Article

Let the coefficients of third, fourth and fifth terms in the expansion

Let the coefficients of third, fourth and fifth terms in the expansion of [x + (a / x2)]n, x ≠... View Article

The number of solutions of the equation sin^-1 [x² + (1 / 3)] + cos^-1 [x² – (2 / 3)] = x², for x ∈ [- 1, 1], and [x] denotes the greatest integer less than or equal to x, is:

a. 0 b. 2 c. 4 d. Infinite Answer: (a) There are three cases possible for x ∈ [– 1,... View Article

Two tangents are drawn from a point P to the circle

Two tangents are drawn from a point P to the circle x2 + y2 – 2x – 4y + 4... View Article

The value of ∑_r=0⁶ (⁶C_r . ⁶C_6-r) is equal to

a. 1124 b. 924 c. 1324 d. 1024 Answer: (b) ∑r=06 (6Cr . 6C6-r) = 6C0.6C6 + 6C1.6C5 + …….... View Article

The value of lim_x→∞[r] + [2r] + ……. [nr] / [n²], where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to

a. 0 b. r c. r / 2 d. 2r Answer: (c) We know that r ≤ [r] < r... View Article

If the sides AB, BC, and CA of a triangle ABC have, 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices is equal to:

a. 360 b. 240 c. 333 d. 364 Answer: (c) Total number of triangles = 3C1 × 5C1 × 6C1... View Article

Let S₁, S₂ and S₃ be three sets defined

Let S1, S2 and S3 be three sets defined as S1 = {z ∈ C : |z – 1| ≤ √2},... View Article

If the curve y = y(x) is the solution of the differential equation

If the curve y = y(x) is the solution of the differential equation 2 (x2 + x5/4) dy – y... View Article

The value of the limit lim_θ→0 [tan (π cos² θ)] / [sin (2π sin² θ)] is equal to

a. – 1 / 2 b. – 1 / 4 c. 0 d. 1 / 4 Answer: (a) Given, limθ→0... View Article

Let y = y (x) be the solution of the differential equation cosx (3 sinx + cosx + 3) dy = (1 + y sinx (3 sinx + cosx + 3)) dx, 0 ≤ x ≤ π / 2, y(0) = 0. Then, y (π / 3) is equal to

a. 2 loge [(2√3 + 10) / 11] b. 2 loge [(√3 + 7) / 2] c. 2 loge [(3√3... View Article

Let L be a tangent line to the parabola y² = 4x – 20 at (6, 2). If L is also a tangent to the ellipse (x² / 2) + (y² / b) = 1, then the value of b is equal to:

a. 20 b. 14 c. 16 d. 11 Answer: (b) Parabola y2 = 4x – 20 Tangent at P (6,... View Article

Let O be the origin. Let OP = xi + yj – k and OQ = – i + 2j + 3xk

Let O be the origin. Let OP = xi + yj – k and OQ = – i + 2j... View Article

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