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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... View Article

WSDL Full Form

What Is The Full Form Of WSDL? The full form of WSDL is Web Services Description Language. WSDL is an... 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

\(\begin{array}{l}\sqrt{3}\left | \vec{a}+\vec{b}\right |+\left |\vec{a}-\vec{b} \right |\end{array} \) = √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... 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) 5050/5049 2) 5050/5051 3) 5051/5050 4) 5049/5050 I2 = \(\begin{array}{l}I_{1}-0+int_{0}^{1}frac{(1-x^{50})^{101}}{-5050}dx\end{array} \) I2 = I1-I2/5050 (5051/5050)I2 = I1 I2 =... 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)/2 2) 2a(t1+t2)+b 3) (t2-t1)/2 4) a(t2-t1)+b f’(t) = Vav = f(t2)-f(t1)/(t2-t1) = [a(t22-t12)+b(t2-t1)]/(t2-t1) = a(t1+t2)+b = 2at+b t... View Article

Find the the standard deviation of n observations

If \(\begin{array}{l}\sum_{i=1}^{n}\left(x_{i}-a\right)=n\end{array} \) and \(\begin{array}{l}\sum_{i=1}^{n}\left(x_{i}-a\right)^{2}=n a\end{array} \) , (n, a>1) then the standard deviation of n observations x1, x2, x3…xn... View Article

Solve the given limit problem

\(\begin{array}{l}\lim _{x \rightarrow 1}\left(\frac{\int_{0}^{(x-1)^{2}} t \cos \left(t^{2}\right) d t}{(x-1) \sin (x-1)}\right)\end{array} \) 1) is equal to 1 2) is equal... 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)... View Article

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

1) 5/8 2) 1/8 3) 7/8 4) 3/8 {3200/8} = {9100/8} = {(8+1)100/8} {(100C0 1100+100C1 (8)199+100C2 (82)198+…100C100 8100)/8} = {(100C0... 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) 2/3 2) 1/9 3) 1/3 4) 4/9 f(x + y) = f(x) f(y) Put x = 1, y =... 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) 10/99 2) 5/33 3) 15/101 4) 5/101 Case-1 E, O, E, O, E, O, E, O, E, O, E... View Article

A ray of light coming from the point (2, 2√3) is incident at an angle 30⁰ on the line x =1 at the point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB passes through the point:

1) (4,-√3) 2) (3, -1/√3) 3) (3,-√3) 4) (4, -√3/2) Equation of line P’B passing through (0, 2√3) (y-y1) =... View Article

Let m and M be respectively the minimum and maximum values of …

Let m and M be respectively the minimum and maximum values of \(\begin{array}{l}\begin{vmatrix} \cos ^{2}x& 1+\sin ^{2}x& \sin 2x\\ 1+\cos... View Article

The values of λ and μ for which the system of linear equations:x+y+z = 2, x+2y+3z = 5 and x+3y+λz = μ has infinitely many solutions are, respectively:

1) 6 and 8 2) 5 and 8 3) 5 and 7 4) 4 and 9 x+y+z = 2 x+2y+3z... View Article

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

1) 2! 3! 4! 2) (3!)3(4!) 3) 3!(4!)3 4) (3!)2(4!) Total numbers in three families = 3+3+4 = 10 So... View Article

Let a, b, c, d and p be any non zero distinct real numbers such that (a²+b²+c²)p²-2(ab+bc+cd)p +(b² +c²+d²) = 0. Then:

1) a, c, p are in G.P. 2) a, b, c, d are in G.P. 3) a, b, c, d... View Article

The shortest distance between the lines (x-1)/0 = (y+1)/-1 = z/1 and x+y+z+1 = 0, 2x-y+z+3 = 0 is:

1) 1 2) 1/√2 3) 1/√3 4) ½ Plane through line of intersection is x+y+z+1+λ(2x-y+z+3) = 0 It should be... View Article

The area (in sq. units) of the region A = {(x, y): |x|+|y| ≤ 1, 2y²|x|}

1) 1/6 2) 5/6 3) 1/3 4) 7/6 Total area = \(\begin{array}{l}4 \int_{0}^{1 / 2}\left[(1-x)-\left(\sqrt{\frac{x}{2}}\right)\right] d x\end{array} \) = \(\begin{array}{l}4\left[x-\frac{x^{2}}{2}-\frac{1}{\sqrt{2}}... View Article

Let L₁ be a tangent to the parabola y² = 4(x+1) and L₂ be a tangent to the parabola y² = 8(x+2) such that L₁ and L₂ intersect at right angles. Then L₁ and L₂meet on the straight line:

1) x+2y = 0 2) x+2 = 0 3) 2x+1 = 0 4) x+3 = 0 Let t1 tangent of... View Article

The general solution of the differential equation √(1+x²+y²+x²y²)+xy(dy/dx) = 0(where C is a constant of integration)

1) \(\begin{array}{l}\sqrt{1+y^{2}}+\sqrt{1+x^{2}}= \frac{1}{2}log_{e}\left ( \frac{\sqrt{1+x^{2}}-1}{\sqrt{1+x^{2}}+1} \right )+c\end{array} \) 2) \(\begin{array}{l}\sqrt{1+y^{2}}-\sqrt{1+x^{2}}= \frac{1}{2}log_{e}\left ( \frac{\sqrt{1+x^{2}}-1}{\sqrt{1+x^{2}}+1} \right )+c\end{array} \) 3) \(\begin{array}{l}\sqrt{1+y^{2}}+\sqrt{1+x^{2}}= \frac{1}{2}log_{e}\left (... View Article

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