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If θ is the fundamental period of the function f(x) = sin99x + sin99(x + 2π/3) + sin99(x + 4π/3), then the complex number z = r(cosθ + isinθ) lies in the quadrant??? I m getting θ= 2π/3 and hence the ans should be 2... ...
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1) If (1-x)n = C0 - C1x + C2x2 -..... + (-1)nCnxn, then the value of C0 - C1 + C2 - .... + C100 is, where n>102 a) 0 b) nC101 c) n-1C101 d) 2nC100 ...
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1) Straight lines are drawn by jining 'm' points on a straght lne to 'n' points on another line. Excluding the given points(m+n), find the number of intersection points if no two drawn are parallel and no three are concurrent ...
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Show that \sum_{k=0}^{n}{C(n,k)sinkx cos(n-k)x} = 2^{n-1}sinnx ...
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1) The half-time of first order decomposition of nitramide is 2.1hr at 15°C NH2NO2(aq) → N2O(g) + H2O(l) If 6.2g of NH2NO2 is allowed to decompose, calculate a) time taken for NH2NO2 to decompose 99%. b) volume of dry N2O ...
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Why are oxides with lower oxidation number of metals are basic while those with higher oxidation numbers are acidic in case of d-block elements? ...
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1) At 0°C and 1atm pressure the densities of air, oxygen and nitrogen are 1.293, 1.429 and 1.251 kg/m3. Calculate the percentage of nitrogen in air, assuming these two gases to be present only. (it seems an easy one but stil ...
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1) The atomic mass of iodine is 127g/mol. A standing wave in iodine vapour at 400K has nodes that are 6.77 cm apart when the frequency is 1000Hz. At this temperature, is iodine vapour mono-atomic or diatomic? ...
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1) Let f: R→ R satisfy xf(x) = [x] f ({x}) + {x} f ([x]), (brackets have their usual meaning). Find f(x). ...
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Prove that for n ≥ 6, the equation 1/x12 + 1/x22 + 1/x32 + .... + 1/x2n = 1 has integral solutions. ...
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1) If f : R→R is a continuous and differentiable function such that \int_{-1}^{x}{f(t)dt} + f'''(3) \int_{x}^{0}{dt} = \int_{1}^{x}{t^{3}dt} - f'(1) \int_{x}^{2}{t^{2}dt} + f''(2) \int_{3}^{x}{tdt} , then find the value of ...
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Passage For x ε (0 , Π/4), Let Sn = \sum_{r=1}^{2n}{sin(sin^{-1}x^{3r-2}}) Cn = \sum_{r=1}^{2n}{cos(cos^{-1}x^{3r-1}}) Tn = \sum_{r=1}^{2n}{tan(tan^{-1}x^{3r}}) 1) The correct order of Sn, Cn, Tn is 2) The value of \lim_{n\ ...
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1) The time period of a particle in SHM is equal to the smallest time between the particle acquiring a particular velocity v. The value of v is (a) vmax (b) 0 (c) between 0 and vmax (i think this value can be anything) 2) Two ...
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Q) Find f(x) if \int_{1}^{xy}{f(t)dt} = y \int_{1}^{x}{f(t)dt} + x \int_{1}^{y}{f(t)dt} ...
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Consider the polynomial f(x) = ax2+bx+c. If f(0) = 0 and f(2) = 2, find the minimum value of \int_{0}^{2}{\left|f'(x) \right|}dx equals?? i get 2a+b=1 (simple), but how to get the value of -b/2a?? ...
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Q) \int ( \frac{1}{\sqrt[3]{x} + \sqrt[4]{x}} + \frac{ln( 1 + \sqrt[6]{x}}{\sqrt[3]{x} + \sqrt[]{x}} ) dx ...
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Can anyone plz explain the use of complex numbers ( de-moivre's theorem) in finding out the integral of type ∫sinmxcosnxdx , where both m,n are positive integers. ...
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WHAT ARE THE PINKED POSTS ???? aur yeh pink hote kaise hain??? ...
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1) If t be a real number satisfying the equation 2t3 - 9t2 + 30 - a, then find the values of the parameter 'a' for which the equation x + 1/x = t gives six real and distinct values of x. ...
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σ-bond is stronger than a Π-bond..... hence when electrons are filled in the molecular orbitals σ2px should be filled before Π2py (or 2pz), (as in case of molecules with no. of electrons ≥ 15).... but for molecules with ...
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P(x) be a polynomial of at most degree 5 which leaves remainders -1 and 1 upon division by (x-1)3 and (x+1)3 respectively. 1) Number of real roots of P(x) = 0 (a) 1 (b) 3 (c) 5 (d) 2 2) The maximum value of y=P''(x) can be ob ...
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Q) y ≥ √(1-x2), max( !x!, !y!) ≤ 4 The slope of a family of lines is defined as m(t) = -sin2t + sint + 1, where (t, 2t+0.4) lies inside the region R. 1) The maxmvalue of the slope of any member of family is for t = (a) ...
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"My dream has begun with a teacher who believes in me, who tugs and pushes and leads me to the next plateau, sometimes poking me with a sharp stick called truth." HAPPY TEACHER'S DAY TO ALL.... ...
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CONCEPT :- For a system to be in equilibrium, the torques acting on it must balance. This is true when we take torques about any point on the system or outside it. DOUBT :- Does the above statement hold when the system is in ...
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Q) Why is Wurtz reaction not given by tert. alkyl halides? ...
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Among the following which pair of quadratic equations have the same nature of roots? a) 13x2+41x+37 and 912+67x+13 b) 11x2+23x+25 and 59x2+45x+11 c) 31x2+14x+7 and 52x2+76x+31 d) all Finding out the discriminant is a tedious ...
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Q) Henry's Law constant for CO2 is 1.67* 108 Pa at 298K. Calculate the quantity of CO2 in 500mL of soda water when packed under 2.5atm CO2 pressure at 298K. (Is th answer 0.0024g??) ...
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\lim_{n\rightarrow \propto } \frac{\left[1^{3}x \right]+\frac{1}{2}\left[2^{3}x \right]+\frac{1}{3}\left[3^{3}x \right]+......+\frac{1}{n}\left[n^{3}x \right]}{1^{2}+2^{2}+3^{2}+...+n^{2}} , where [.] denotes greatest integer ...
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Q) 2.6g sample of pyrolusite was boiled with 65ml of N oxalic acid and excess of dil. H2SO4. The liquid was then filtered and the residue washed. The filtrate and the washing were mixed and made upto 500ml. 100ml of this soln ...
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Q) Which of the following statements is/are false? a) If two particles are neither approaching nor separating from each other, then their relative velocity is zero. b) Four dogs are running along a line in same direction, suc ...
