Class 11th

The value of ((1+sin(2π/9)+icos(2π/9))/(1+sin(2π/9)-icos(2π/9)))³ is

Let P(h,k) be a point on the curve y = x² + 7x + 2, nearest to the line, y = 3x - 3. Then the equation of the normal to the curve at P is

The statement that is not true about ozone is:

Let α > 0, β > 0 be such that α³ + β² = 4. If the maximum value of the term independent of x in the binomial expansion of (αx¹/⁹ + βx⁻¹/⁶)¹⁰ is 10k, then k is equal to

If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the following series (x+y) + (x²+xy+y²) + (x³+x²y+xy²+y³) + . is

If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the following series (x+y) + (x²+xy+y²) + (x³+x²y+xy²+y³) + . is

If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the following series (x+y) + (x²+xy+y²) + (x³+x²y+xy²+y³) + . is

The elevation of boiling point of 0.10 m aqueous CrCl₃·xNH₃ solution is two times that of 0.05 m aqueous CaCl₂ solution. The value of x is [numerical value]. [Assume 100% ionisation of the complex and CaCl₂, coordination number of Cr as 6, and that all NH₃ molecules are present inside the coordination sphere]

In Carius method of estimation of halogen, 0.172 g of an organic compound showed presence of 0.08 g of bromine. Which of these is the correct structure of the compound?

Potassium chlorate is prepared by the electrolysis of KCl in basic solution 6OH⁻+Cl⁻→ClO₃⁻+3H₂O+6e⁻. If only 60% of the current is utilized in the reaction, the time (rounded to the nearest hour) required to produce 10 g of KClO₃ using a current of 2 A is [numerical value] (Given: F=96,500 Cmol⁻¹; molar mass of KClO₃=122 g mol⁻¹)