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Let z be a complex number find the value of |z+3i|

Let z be a complex number such that Answer: (b)... View Article

If the matrices A is given, B = adj A and C = 3A, then …

If the matrices A = = 13 + 1 - 8= 6B = adj(A) ǀadj Bǀ = ǀadj (adj A)ǀ = ǀAǀ4 = 64 ǀCǀ = ǀ3Aǀ = 33ǀAǀ = 33 × 6 = 64/(33×6)= 8Answer: (c)... View Article

If f(x) is continuous at x = 0 then a + 2b is equal to:

If f(x) = is continuous at x = 0 then a + 2b is equal to:a) -2b) 1c) 0d) 1Solution:f(x) is continuous at x = 0 a + 3 = 1 a = -2a + 2b = 0Answer: (c)... View Article

Let z be those complex number which satisfies |z + 5| ≤ 4 and z (1 + i) + [latex]bar{z}[/latex] (1 – i) ≥ – 10, i = √-1. If the maximum value of |z + 1|² is ɑ + β√2, then the value of ɑ + β is

Solution:Answer: 48Given, |z + 5| ≤ 4(x + 5)2 + y2 ≤ 16Also, z (1 + i) + (1 - i) ≥ - 10x - y ≥ - 5 ---- (2)From (1) and... View Article

Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, – 3) and (4, – 2 √2), and given that a – 2√2b = 3, then (a² + b² + ab) is equal to

Solution:Answer: 9Let the equation of normal is Y - y = (- 1 / m) (X - x), where m = dy / dxAs it passes through (a, b)b - y = (- 1 / m) (a - x)... View Article

If the arithmetic mean and the geometric mean of the p^th and q^th terms of the sequence – 16, 8, – 4, 2, … satisfy the equation 4x² – 9x + 5 = 0, then p + q is equal to

Solution:Answer: 10Given, 4x2 - 9x + 5 = 0(x - 1) (4x - 5) = 0AM = 5 / 4, GM = 1 (AM ≥ GM)Again for the series, - 16, 8, - 4, 2, …pth... View Article

For some real numbers α and β, then β -ɑ is equal to

If the matrix for some real numbers ɑ and β, then β -ɑ is equal to_________.Solution:Answer: 4... View Article

Let L be a common tangent line to the curves 4x² + 9y² = 36 and (2x)² + (2y)² = 31. Then the square of the slope of the line L is

Solution:Answer: 3E : (x2 / 9) + (y2 / 4) = 1C : x2 + y2 = 31 / 4The equation of the tangent to the ellipse is y = mx ± √(9m2 + 4)... View Article

In I_m,n = ∫₀¹ x^m-1

In Im,n = ∫01 xm-1 (1 - x)n-1 dx, for m, n ≥ 1 and ∫01 [xm-1 + xn-1] / [(1 + x)m+n] dx = ɑIm,n, ɑ belongs to R, then ɑ =Solution:Answer: 1... View Article

Let X₁, X₂, …. X₁₈ be eighteen observation such that ∑_i=1¹⁸ (X_i – ɑ) = 36 and

Answer: 4 Solution: Given, ∑i=118 (Xi - ɑ) = 36 ∑xi - 18ɑ = 36 ∑xi = 18 (ɑ + 2) ---- (1) ∑i=118 (Xi - β)2 = 90 ∑xi2 + 18β2 - 2β ∑xi = 90... View Article

Let ɑ and β be two real numbers such that ɑ + β = 1 and ɑ β = – 1.

Let ɑ and β be two real numbers such that ɑ + β = 1 and ɑ β = - 1. Let Pn = (ɑ)n + (β)n, Pn-1 = 11 and Pn+1 = 29 for some... View Article

The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is

Answer: 1000 Since the required number has G.C.D with 18 as 3. It must be an odd multiple of ‘3’ but not a multiple of... View Article

The triangle of the maximum area that can be inscribed in a given circle of radius ‘r’ is:

a. A right-angle triangle having two of its sides of length 2r and r.b. An equilateral triangle of height 2r / 3.c. isosceles triangle with base... View Article

Let f (x) = ∫₀^x e^t f (t) dt + e^x be a differentiable function for all x ∈ R. Then f (x) equals

a. 2eex-1 - 1b. e(e^x-1)c. 2ee^x - 1d. ee^x - 1Solution:Answer: (a)Given, f (x) = ∫0x et f (t) dt + ex ---- (1)f’ (x) = ex . f (x) + ex... View Article

Let f (x) = sin^-1 x and g (x) = [x² – x – 2] / [2x² – x – 6]. If g (2) = lim_x→2g (x), then then the domain of the function fog is:

a. (- ∞, - 2] ⋃ [- 4 / 3, ∞]b. (- ∞, - 1] ⋃ [2, ∞)c. (- ∞, - 2] ⋃ [- 1, ∞]d. (- ∞, 2] ⋃ [- 3 / 2,... View Article

If vectors a₁ = xi – j + k and a₂ = i + yj + zk are collinear, then a possible unit vector parallel to the vector xi + yj + zk is

a. (1 / √2) (- j + k)b. (1 / √2) (i - j)c. (1 / √3) (i - j + k)d. (1 / √3) (i + j - k)Solution:Answer: (3)(x / 1) = - 1 /... View Article

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