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The correct observation in the following reactions is:

The correct observation in the following reactions is:1) Formation of red colour2) Formation of blue colour3) Formation of violet colour4) Gives... View Article

Simplified absorption spectra of three complexes…

Simplified absorption spectra of three complexes ((i), (ii) and (iii)) of Mn+ ion are provided below; their λmax values are marked as A, B and C... View Article

The shape/structure of [XeF₅]^– and XeO₃F₂, respectively, are :

1) Pentagonal planar and trigonal bipyramidal2) Trigonal bipyramidal and trigonal bipyramidal3) Octahedral and square pyramidal4) Trigonal... View Article

Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m×n is

A and B are two sets having m, n element respectivelyNo. of subsets of A = 2mNo. of subsets of B = 2n2m = 2n +1122m -2n = 1122n (2m-n-1) =... View Article

The angle of elevation of the top of a hill from a point on the horizontal plane …

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 450. After... View Article

Let f : R → R be defined as

Let f : R → R be defined as The value of λ for which f''(0) exists, is Solution: If f’’(0) exists thenf’’(0+) =... View Article

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point A such that MD²+MC² is minimum is:

(MD)2 = x2+82 = x2+64(MC)2 = (10-x)2 +(11)2 = (x-10)2+121f(x) = (MD)2+(MC)2 = x2+64 +(x-10)2+(121)Differentiatef'(x) = 02x+2(x-10) = 04x =... View Article

FDD Full Form

The full form of FDD is Feature-Driven Development. FDD is a framework for developing software that uses an agile model to progress, organize,... View Article

IEEE Full Form

The full form of IEEE is the Institute of Electrical and Electronics Engineers. IEEE is a technical professional society dedicated to advancing... View Article

Aspirational Model: Inspiration for the World: RSTV – Big Picture

Rajya Sabha TV programs and discussions are very insightful and informative from a UPSC perspective. In this article, we provide a gist of the... View Article

WSDL Full Form

The full form of WSDL is Web Services Description Language. WSDL is an XML-based file that describes a web service to the client application,... View Article

If [latex]\vec{a}[/latex] and [latex]\vec{b}[/latex] are unit vectors, then the greatest value of [latex]\sqrt{3}\left | \vec{a}+\vec{b}\right |+\left |\vec{a}-\vec{b} \right |[/latex] is

= √3(√(2+2cosθ)+√(2-2cosθ)= √6(√(1+cosθ)+√2(1-cosθ)= √6(√(1+2cos2 (θ/2)-1)+√2(√(1-1+2sin2 θ/2)= √6(√(2cos2θ/2)+√2(√(2sin2θ/2)){ greatest value... View Article

If [latex]I_{1}=\int_{0}^{1}(1-x^{50})^{100}dx[/latex] and [latex]I_{2}=\int_{0}^{1}(1-x^{50})^{101}dx[/latex] such that I₂ = αI₁ then α equals to:

1) 5050/50492) 5050/50513) 5051/50504) 5049/5050 I2 = I2 = I1-I2/5050(5051/5050)I2 = I1 I2 = (5050/5051)I1 α = 5050/5051Answer: (2)... View Article

The position of a moving car at time t is given by f(t) = at²+bt+c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t₁, t₂] is attained at the point :

1) (t1+t2)/22) 2a(t1+t2)+b3) (t2-t1)/24) a(t2-t1)+bf’(t) = Vav = f(t2)-f(t1)/(t2-t1)= [a(t22-t12)+b(t2-t1)]/(t2-t1)= a(t1+t2)+b= 2at+bt =... View Article

Find the the standard deviation of n observations

If , (n, a>1) then the standard deviation of n observations x1, x2, x3…xn is:1) n√(a-1)2) √(na-1)3) a-14) √(a-1) Solution:S.D = Answer: (4)... View Article

Solve the given limit problem

On taking limit= 0/(1+1)= 0Answer: Bouns... View Article

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse (x²/4)+(y²/2) = 1 from any of its foci ?

1) (-1,√3)2) (-2, √3)3) (-1, √2)4) (1,2)Let foot of perpendicular is (h,k) (x2/4)+(y2/2) = 1 (Given)a = 2, b = √2e = √(1-2/4)= 1/√2So focus... View Article

If {p} denotes the fractional part of the number p, then {3²⁰⁰/8} is equal to:

1) 5/82) 1/83) 7/84) 3/8{3200/8} = {9100/8} = {(8+1)100/8}{(100C0 1100+100C1 (8)199+100C2 (82)198+…100C100 8100)/8}= {(100C0 1100+8k)/8}=... View Article

If f(x + y) = f(x) f(y) and [latex]sum_{x=1}^{infty }f(x)=2[/latex] x, y ∈N, where N is the set of all natural number, then the value of f(4)/f(2) is:

1) 2/32) 1/93) 1/34) 4/9f(x + y) = f(x) f(y)Put x = 1, y = 1f(2) = (f(1))2 Put x = 2, y = 1f(3) = f(2). f(1) = f((1))3 Put x = 2, y = 2f(4) =... View Article

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:

1) 10/992) 5/333) 15/1014) 5/101Case-1E, O, E, O, E, O, E, O, E, O, E2b = a+c → Even⇒ Both a and c should be either even or odd.P =... View Article