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If the system of equations x-2y+3z = 9

If the system of equations x-2y+3z = 9 2x+y+z = b x-7y+az = 24, has infinitely many solutions, then a-b... View Article

If the equation of a plane P, passing through the intersection of the planes

If the equation of a plane P, passing through the intersection of the planes, x+4y-z+7 = 0 and 3x+y+5z =... View Article

Suppose a differentiable function f(x) satisfies the identity f(x+y) = f(x)+f(y)+xy²+x²y,for all real x and y.

Suppose a differentiable function f(x) satisfies the identity f(x+y) = f(x)+f(y)+xy2+x2y,for all real x and y. If \(\begin{array}{l}\lim_{x\to0}\frac{f(x)}{x}=1\end{array} \) then... View Article

If (a+√2b cos x)( a-√2b cos y) = a²-b², where a>b>0, then dy/dx at (π/4, π/4) is

If (a+√2b cos x)( a-√2b cos y) = a2-b2, where a>b>0, then dy/dx at (π/4, π/4) is: a) (a+b)/(a-b) b)... View Article

Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground.

Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with... View Article

Given the following two statements.

Given the following two statements (S1): (q˅p)→(p ↔ ~q) is a tautology. (S2): ~q ˄ (~p ↔ q) is a... View Article

A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B.

A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If... View Article

The mean and variance of 8 observations are 10 and 13.5, respectively.

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7,... View Article

If A = [latex]\begin{bmatrix} \cos \theta & i\sin \theta \\ i\sin \theta & \cos \theta \end{bmatrix}[/latex], (θ = π/24) and A⁵ = [latex]\begin{bmatrix} a & b\\ c& d \end{bmatrix}[/latex], where i = √-1,

If A = \(\begin{array}{l}\begin{bmatrix} \cos \theta & i\sin \theta \\ i\sin \theta & \cos \theta \end{bmatrix}\end{array} \), (θ = π/24)... View Article

Let u = (2z+i)/(z-ki), z = x+iy and k>0.

Let u = (2z+i)/(z-ki), z = x+iy and k>0. If the curve represented by Re(u) +Im(u) =1 intersects the y-axis... View Article

Let α and β be the roots of x²-3x+p = 0 and 1/γ and 1/δ be the roots of x²-6x+q = 0.

Let α and β be the roots of x2-3x+p = 0 and 1/γ and 1/δ be the roots of x2-6x+q... View Article

Let f be a twice differentiable function on (1,6). If f(2) = 8, f’(2) = 5, f’(x) ≥1 and f’’(x) ≥4, for all x ∈ (1,6), then:

a) f(5)+f’(5) ≥28 b) f’(5)+f’’(5) ≤20 c) f(5) ≤10 d) f(5)+f’(5) ≤26 Solution: f(2) = 8, f’(2) = 5, f’(x)... View Article

A triangle ABC lying in the first quadrant has two vertices as A(1,2) and B(3,1).

A triangle ABC lying in the first quadrant has two vertices as A(1,2) and B(3,1). If BAC = 900 and... View Article

Let x₀ be the point of local maxima of f(x) = [latex]vec{a}.(vec{b}times vec{c})[/latex]

Let x0 be the point of local maxima of f(x) = \(\begin{array}{l}\vec{a}.(\vec{b}\times \vec{c})\end{array} \) where \(\begin{array}{l}\vec{a}= x\hat{i}-2\hat{j}+3\hat{k}\end{array} \), \(\begin{array}{l}\vec{b}= -2\hat{i}+x\hat{j}-\hat{k}\end{array}... View Article

Let f(x)= |x-2| and g(x) = f(f(x)) ,x∈0,4]. Then [latex]int_{0}^{3}(g(x)-f(x))dx[/latex] is equal to

a) 1/2 b) 0 c) 1 d) 3/2 Solution: f(x) = |x-2| = \(\begin{array}{l}\left\{\begin{matrix} x-2, & x\geq 2\\ 2-x, &... View Article

The integral [latex]int left ( frac{x}{xsin x+cos x} right )^{2}dx[/latex] is equal to: (where C is a constant of integration)

a) tan x-(x sec x/(x sin x+cos x))+C b) sec x-(x tan x/(x sin x+cos x))+C c) sec x+(x tan... View Article

Let P(3, 3) be a point on the hyperbola, (x²/a²)-(y²/b²) = 1. If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair (a², e²) is equal to

a) (9, 3) b) (9/2, 2) c) (9/2, 3) d) (3/2, 2) Solution: (x2/a2)-(y2/b2) = 1 Point P(3, 3) on... View Article

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