Archives

If (2 + sinx) (dy/dx) + (y + 1) cosx = 0 and y(0) = 1, then y(π/2) is equal to

1) -2/32) -1/33) 4/34) 1/3Solution:Answer: (4) (2 + sinx) (dy/dx) + (y + 1) cos x = 0y(0) = 1, y(π / 2) = ?(1/(y + 1)) dy + (cos x/[2 +... View Article

The area (in sq. units) of the region {(x, y) : x ≥ 0, x + y ≤ 3, x²≤ 4y and y ≤ 1 + x} is :

1) 3 / 22) 7 / 33) 5 / 24) 59 / 12Solution:Answer: (3) Area of the shaded region= sq units... View Article

The integral [latex]int_{frac{pi}{4}}^{frac{3pi}{4}}frac{dx}{1+cosx}[/latex] is equal to:

1) 22) 43) −14) −2Solution:Answer: (1)... View Article

Let I_n = ∫tanⁿ x dx, (n > 1). If I₄+ I₆= a tan⁵ x + bx⁵+ C, where C is a constant of integration, then the ordered pair (a, b) is equal to

1) (1/5, 0)2) (1/5, -1)3) (-1/5, 0)4) (-1/5, 1)Solution:Answer: (1) In = ∫tann x dx, (n > 1)I4 + I6 = ∫(tan4 x + tan6 x) dx= ∫tan4 x sec2 x... View Article

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is

1) 102) 253) 304) 12.5Solution:Answer: (2) 2r + θr = 20 ---- (i)A = Area = (θ / 2π) * (πr2) = (θr2 / 2) ---- (ii)A = (r2 / 2) ([20 - 2r]... View Article

The normal to the curve y (x − 2) (x − 3) = x + 6 at the point where the curve intersects the y-axis passes through the point

1) (1/2, 1/2)2) (1/2, -1/3)3) (1/2, 1/3)4) (-1/2, -1/2)Solution:Answer: (1) y (x - 2) (x - 3) = x + 6At y-axis, x = 0, y = 1Now, on... View Article

If for x ∈ (0, (1 / 4)), the derivative of tan^-1 (6x√x / (1 – 9x³)) is √x . g(x), then g(x) equals:

1) (3x√x / (1 - 9x3))2) (3x/(1 - 9x3))3) (3/(1 + 9x3))4) (9/(1 + 9x3))Solution:Answer: (4) f (x) = 2 tan-1 (3x√x) for x ∈ (0, (1/4))f ‘ (x)... View Article

[latex]\lim_{x\rightarrow \pi/2}\frac{cotx-cosx}{(\pi-2x)^{3}}[/latex] equals:

1) 1 / 162) 1 / 83) 1 / 44) 1 / 24Solution:Answer: (1)... View Article

Let a, b, c ∈ R. If f (x) = ax²+ bx + c is such that a + b + c = 3 and f (x + y) = f (x) + f (y) + xy, ∀ x, y ∈ R, then [latex]sum_{n=1}^{10}[/latex] f (n) = is equal to

1) 1652) 1903) 2554) 330Solution:Answer: (4)As f (x + y) = f (x) + f (y) + xyGiven, f (1) = 3Putting, x = y = 1⇒ f (2) = 2 f (1) + 1 =... View Article

For any three positive real numbers a, b and c, 9 (25a²+ b²) + 25 (c² − 3ac) = 15b (3a + c). Then :

1) b, c and a are in A.P.2) a, b and c are in A.P.3) a, b and c are in G.P.4) b, c and a are in G.P.Solution:Answer: (1) 9 (25a2 + b2) + 25 (c2... View Article

The value of (²¹C₁ – ¹⁰C₁) + (²¹C₂ – ¹⁰C₂) + (²¹C₃ – ¹⁰C₃) + (²¹C₄ – ¹⁰C₄) + … (²¹C₁₀ – ¹⁰C₁₀) is

1) 221 − 210 2) 220 − 293) 220 − 2104) 221 − 211Solution:Answer: (3) 21C1 + 21C2 + …… 21C10 = (1 / 2) (21C0 + 21C1 + ….. 21C21) - 1= 220 - 110C1... View Article

If S is the set of distinct values of ‘b’ for which the following system of linear equations

If S is the set of distinct values of ‘b’ for which the following system of linear equationsx + y + z = 1x + ay + z = 1ax + by + z = 0has no... View Article

The adj (3A² + 12A) is equal to

Ifthen adj (3A2 + 12A) is equal to : Solution:Answer: (1) = (2 – 2λ – λ + λ2) – 12f (λ) = λ2 - 3λ - 10∵ A satisfies f (λ).A2 - 3A - 10I = 0A2... View Article

Let ω be a complex number such that 2ω + 1 = z….

Let ω be a complex number such that 2ω + 1 = z where z = √-3. If then k is equal to,1) z2) −13) 14) − zSolution:Answer: (4)2ω + 1 = z, z = √3iω... View Article

If, for a positive integer n, the quadratic equation,

If, for a positive integer n, the quadratic equation,has two consecutive integral solutions, then n is equal to: 1) 92) 103) 114)... View Article

The function f : R → [(-1/2), (1/2)] is defined as f(x) = [x]/[1 + x²], is:

1) injective but not surjective.2) surjective but not injective.3) neither injective nor surjective.4) invertible.Solution:Answer: (2) f(x) =... View Article

If α = cos^-1(3/5), β = tan^-1 (1/3), where 0<α, β < π/2, then α-β is equal to:

A) tan-1(9/5√10)B) sin-1(9/5√10)C) tan-1(9/15)D) cos-1(9/5√10)Solution:α = cos-1(3/5) = tan-1(4/3)β = tan-1... View Article

Find the magnitude of projection of vector [latex]2hat{i}+3hat{j}+hat{k}[/latex] on a vector which is perpendicular to the plane containing vectors [latex]hat{i}+hat{j}+hat{k}[/latex] and [latex]hat{i}+2hat{j}+3hat{k}[/latex]

A) √3/2B) √(3/2)C) 3√6D) √6Solution:The vector perpendicular to given vectors is = 2-6+1/√6= 3/√6= √(3/2)Answer: B... View Article

If the tangents on the ellipse 4x²+y² = 8 at the points (1,2) and (a,b) areperpendicular to each other, then a² is equal to

A) 2/17B) 64/17C) 128/17D) 4/17Solution:The equation of the ellipse 4x2+y2 = 8dy/dx = -4x/yThe tangent at (1,2) and (a,b) are... View Article

The sum of the solutions of the equation |√x-2|+√x(√x-4)+2 = 0, (x>0) is equal to

A) 4B) 10C) 9D) 12Solution:Given equation is |√x-2|+√x(√x-4)+2 = 0, (x>0)Put √x = t|t-2|+t(t-4)+2 = 0If t ≥2t-2+t2-4t+2 = 0t2-3t = 0t(t-3) =... View Article