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If a plane passes through intersection of planes 2x-y-4 = 0 and y+2z-4 = 0 and also passes through the point (1, 1, 0). Then the equation of the plane is

A) x-y-z = 0B) 2x-z = 0C) x+2z-1 = 0D) x-z-1 = 0Solution:Required equation of the plane is (2x-y-4)+λ(y+2z-4) = 0Given it pass through... View Article

The perpendicular distance of point ( 2,-1,4) from the line [latex]frac{x+3}{10}=frac{y-2}{-7}=frac{z}{1}[/latex] lies between

A) (2, 3)B) (3, 4)C) (4, 5)D) (1, 2)Solution: Let A be (2,-1,4).Direction ratio of AB = (10λ-5, -7λ+3, λ-4)Drs of given line = (10, -7,... View Article

A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate axes will lie only in

A) 1st, 2nd and 4th quadrantsB) 1st and 2nd quadrantsC) 4th quadrantsD) 1st quadrantsSolution:3x+5y = 15 is the equation of the straight line.If... View Article

Let vertices of the triangle ABC is A(0, 0), B(0, 1) and C(x, y) and perimeter is 4 then locus of ‘C’ is

A) 9x2 + 8y2+8y = 16B) 8x2 + 9y2+9y = 16C) 9x2 + 8y2-8y = 16D) 8x2 + 9y2-9x = 16Solution: Given AB+AC+BC = 41+ = 4√(x2+y2)2 =... View Article

Let f:[0,2] -> R be a twice differentiable functions such that f’’(x) >0 for all x ∈ (0,2). If f(x) = f(x)+f(2-x). then f is:

A) Increasing in (0, 1) and decreasing in (1, 2)B) Decreasing in (0, 1) and increasing in (1, 2)C) Increasing in (0, 2)D) Decreasing in (0,... View Article

Let S₁ is set of minima and S₂is set of maxima for the curve y = 9x⁴+12x³-36x²-25 then

A) S1 = {-2,-1} S2 = {0}B) S1 = {-2,1} S2 = {0}C) S1 = {-2,1} S2 = {-1}D) S1 = {-2,2} S2 = {0}Solution:y = 9x4+12x3-36x2-25dy/dx = 36x3 +... View Article

Let [latex]2y={{\left[ {{\cot }^{-1}}\left( \frac{\sqrt{3}\cos x+\sin x}{\cos x-\sqrt{3}\sin x} \right) \right]}^{2}}[/latex] then [latex]\frac{dy}{dx}=[/latex]

A) x-(π/6)B) x+(π/6)C) 2x-(π/6)D) 2x-(π/3)Solution: 2y = [(π/2) -(π/3)+x]22y = [(π/6)-x]2Differentiating we get,2 dy/dx =... View Article

Find the value of ‘c’ for which the following equations have non-trivial solutions: cx-y-z = 0, -cx+y-cz = 0 and x+y-cz = 0.

A) 1/2B) -1C) 2D) 0Solution:For non trivial solutions, c(-c+c) +1(c2+c)-1(-c-1) = 0c2+c+c+1 = 0(c+1)2 = 0c+1 = 0c = -1Answer: B... View Article

If f(x) = log((1-x)/(1+x)) then f(2x/1+x²) is equal to

A) f(x)B) 2f(x)C) -2f(x)D) [f(x)]2Solution:f(x) = = 2 f(x)Answer: B... View Article

Let y = y(x) be the solution of the differential equation, (x²+1)²dy/dx + 2x(x²+1)y = 1 such that y(0) = 0. If √a y(1) = π/32, then the value of a is:

A) 1/2B) 1/4C) 1/16D) 1Solution:(x2+1)2dy/dx + 2x(x2+1)y = 1 dy/dx +Py = QP = 2x/x2+1Q = 1/(x2+1)2 I.F = = 1+x2 The general solution of linear... View Article

If α and β are the roots of x²-2x+2 = 0 then the minimum value of n such that (α/β)ⁿ = 1

A) 4B) 3C) 2D) 5Solution:x2-2x+2 = 0x2-2x+1+1 = 0 (x-1)2 = -1(x-1) = ±ix = 1+i or 1-iLet α = 1+iβ = 1-i(α/β) =... View Article

If mean and variance of 7 variates are 8 and 16 respectively and five of them are 2, 4, 10, 12, 14 then the product of remaining two variates is

A) 49B) 48C) 45D) 40Solution:Let the remaining two variates be x and yGiven mean = 8(x+y+2+4+10+12+14)/7 = 8x+y+42 = 56x+y = 14 ..(1)Given... View Article

Sum of natural numbers between 100 and 200 whose HCF with 91 should be more than 1.

A) 1121B) 3210C) 3121D) 1520Solution:Given numbers: 101, 102, 103, … 198, 19991=13 × 7HCF of 91 and a number is more than 1 means the number... View Article

The sum of the series 2. 20C₀ + 5.20C₁+8.20C₂+62.20C₂₀ is equal to

A) 16.222B) 8.222C) 8.221D) 16.221Solution:2. 20C0 + 5.20C1+8.20C2+62.20C20= = 60.219+2.220= 221(15+1)= 221.16Answer: D... View Article

Let g(x) is equal to ln x and f(x) is equal to (1-xcos x) by (1+xcos x) then solve the integral.

A) ln 1 B) ln 2 C) ln e D) ln 4 Solution: g(f(x)) = = I = = ..(1) We have I = ..(2) Add (1) and (2) 2I = = Because... View Article

How many 9 digit numbers can be formed by using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 such that odd numbers occur at even places.

A) 160B) 175C) 180D) 220Solution: Even places = 4Odd numbers = 3Even numbers = 6Therefore number of numbers = Answer: C... View Article

[latex]\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin^{2} x}{\sqrt{2}-\sqrt{1+\cos x}}=[/latex]

A) √2B) 2C) 4D) 4√2Solution:Rationalise the denominator = (4/2) √2+√(1+1)= 4√2Answer: D... View Article

Shortest distance between the curves y² = x-2 and y = x is

A) greater than 4B) less than 2C) greater than 3D) greater than 2Solution:y2 = x-2Differentiating we get,2y (dy/dx) = 1(dy/dx) = 1/2ySlope of the... View Article

[latex]A=\left[ \begin{matrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \\ \end{matrix} \right][/latex]and [latex]{{A}^{32}}=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right][/latex]. then α may be

A) 0B) π/32C) π/64D) π/16Solution:A = cos 32α = 0 and sin 32α = 1 32α = π/2α = π/64Answer: C... View Article

“If you are born in India then you are citizen of India” contrapositive of this statement is

A) If you are born in India then you are not citizen of IndiaB) If you are not citizen of India then you are not born in IndiaC) If you are... View Article