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Let a₁, a₂, …, a_n be a given A.P. whose common difference is an integer

Let a1, a2, …, an be a given A.P. whose common difference is an integer and Sn = a1+a2+ ….... View Article

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 1/2.

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is... View Article

Let [latex]\bigcup_{i=1}^{50}X_{i}= \bigcup_{i=1}^{n}Y_{i}= T[/latex] where each X_i contains 10 elements and each Y_i contains 5 elements.

Let \(\begin{array}{l}\bigcup_{i=1}^{50}X_{i}= \bigcup_{i=1}^{n}Y_{i}= T\end{array} \) where each Xi contains 10 elements and each Yi contains 5 elements. If each element... View Article

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30⁰.

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 300.... View Article

Let λ ≠ 0 be in R. If α and β are the roots of the equation

Let λ ≠ 0 be in R. If α and β are the roots of the equation, x2-x+2λ = 0... View Article

The solution of the differential equation (dy/dx)-((y+3x)/log_e(y+3x)) + 3 = 0 is: (where c is a constant of integration)

a) x-loge(y+3x) = C b) x-(1/2)(loge(y+3x))2 = C c) x-2loge(y+3x) = C d) y+3x-(1/2)(logex)2 = C Solution: (dy/dx)-((y+3x)/ln(y+3x))+3 = 0... View Article

The function f(x) =

The function a) both continuous and differentiable on R-{-1} b) continuous on R-{-1} and differentiable on R-{-1,1} c) continuous on... View Article

If for some positive integer n, the coefficients of three consecutive terms

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1+x)n+5 are in... View Article

In a game two players A and B take turns in throwing a pair of fair dice

In a game two players A and B take turns in throwing a pair of fair dice starting with player... View Article

If the system of equations

If the system of equations x+y+z = 2 2x+4y–z = 6 3x+2y+ λz = μ has infinitely many solutions, then... View Article

The integral [latex]int_{frac{pi }{6}}^{frac{pi }{3}}tan ^{3}x.sin ^{2}3x(2sec ^{2}x.sin ^{2}3x+3tan x.sin 6x)dx[/latex] is equal to

a) 9/2 b) -1/18 c) -1/9 d) 7/18 Solution: = (1/2)[9×0-(1/3)×(1/3)×1] = -1/18 Answer: b

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, y = x²-1 below the x-axis, is

a) 2/3√3 b) 4/3 c) 1/3√3 d) 4/3√3 Solution: Area = 2a(a2-1) A = 2a3-2a dA/da = 6a2-2 = 0... View Article

If the perpendicular bisector of the line segment joining the points P(1 , 4) and Q(k, 3) has y-intercept equal to -4, then a value of k is

a) -2 b) √15 c) √14 d) -4 Solution: mPQ = (4-3)/(1-k) ⇒ \(\begin{array}{l}m_{\perp}\end{array} \) = k-1 Midpoint of PQ... View Article

Contrapositive of the statement

Contrapositive of the statement : ‘If a function f is differentiable at a, then it is also continuous at a’,... View Article

Let f: (0, ∞)→ (0, ∞) be a differentiable function such that f(1) = e and [latex]lim_{tto x}frac{t^{2}f^{2}(x)-x^{2}f^{2}(t)}{t-x}=0[/latex].

Let f: (0, ∞)→ (0, ∞) be a differentiable function such that f(1) = e and \(\begin{array}{l}\lim_{t\to x}\frac{t^{2}f^{2}(x)-x^{2}f^{2}(t)}{t-x}=0\end{array} \). If... View Article

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