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Let α, β ∈ ℝ be such that the function f(x) = { 2α(x² − 2) + 2βx , x < 1 (α + 3)x + (α − β) , x ≥ 1 } be differentiable at all x ∈ ℝ. Then 34(α + β) is equal to

Let α, β ∈ ℝ be such that the function f(x) = { 2α(x² − 2) + 2βx , x […]

Let a circle of radius 4 pass through the origin O, the points A(−√3 a, 0) and B(0, −√2 b), where a and b are real parameters and ab ≠ 0. Then the locus of the centroid of ΔOAB is a circle of radius

Let a circle of radius 4 pass through the origin O the points A and B then the locus of

X and Y are the number of electrons involved, respectively during the oxidation of I⁻ to I₂ and S²⁻ to S by acidified K₂Cr₂O₇. The value of X + Y is _____ .

Electrons involved in oxidation of iodide and sulphide by acidified potassium dichromate Q. X and Y are the number of

In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at 300 K and 715 mm pressure. The percentage of nitrogen in the organic compound is _____ %. (Aqueous tension at 300 K is 15 mm.)

In Dumas method for estimation of nitrogen percentage calculation numerical question Q. In Dumas method for estimation of nitrogen, 0.50

Electricity is passed through an acidic solution of Cu²⁺ till all the Cu²⁺ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping the total volume of the solution fixed at 200 mL. The total volume of oxygen evolved at STP during the entire process is _____ mL. (Nearest integer) [Given: Cu²⁺(aq) + 2e⁻ → Cu(s) E°red = +0.34 V O₂(g) + 4H⁺ + 4e⁻ → 2H₂O E°red = +1.23 V Molar mass of Cu = 63.54 g mol⁻¹ Molar mass of O₂ = 32 g mol⁻¹ Faraday Constant = 96500 C mol⁻¹ Molar volume at STP = 22.4 L ]

Electricity passed through acidic Cu2 plus solution oxygen evolved numerical question Q. Electricity is passed through an acidic solution of

Consider two Group IV metal ions X²⁺ and Y²⁺. A solution containing 0.01 M X²⁺ and 0.01 M Y²⁺ is saturated with H₂S. The pH at which the metal sulphide YS will form as a precipitate is ____ . (Nearest integer) (Given: Ksp(XS) = 1 × 10⁻²² at 25°C, Ksp(YS) = 4 × 10⁻¹⁶ at 25°C, [H₂S] = 0.1 M in solution, Ka₁ × Ka₂ (H₂S) = 1.0 × 10⁻²¹, log 2 = 0.30, log 3 = 0.48, log 5 = 0.70)

Consider two Group IV metal ions X2 plus and Y2 plus saturated with H2S pH of precipitation question Q. Consider

The hydrogen spectrum consists of several spectral lines in Lyman series (L₁, L₂, L₃ … ; L₁ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series (B₁, B₂, B₃ … ; B₁ has lowest energy among Balmer lines). The energy of L₁ is x times the energy of B₁. The value of x is _____ × 10⁻¹. (Nearest integer)

The hydrogen spectrum consists of several spectral lines in Lyman series and Balmer series energy ratio question Q. The hydrogen

Among the following, the CORRECT combinations are A. IF₃ → T-shaped (sp³d) B. IF₅ → Square pyramidal (sp³d²) C. IF₇ → Pentagonal bipyramidal (sp³d³) D. ClO₄⁻ → Square planar (sp²d) Choose the correct answer from the options given below:

Among the following the correct combinations are IF3 IF5 IF7 and ClO4 minus molecular geometry question Q. Among the following,

Given below are statements about some molecules/ions. Identify the CORRECT statements. A. The dipole moment value of NF₃ is higher than that of NH₃. B. The dipole moment value of BeH₂ is zero. C. The bond order of O₂²⁻ and F₂ is same. D. The formal charge on the central oxygen atom of ozone is −1. E. In NO₂, all the three atoms satisfy the octet rule, hence it is very stable.

Given below are statements about some molecules ions Identify the correct statements Q. Given below are statements about some molecules/ions.

At 27°C in presence of a catalyst, activation energy of a reaction is lowered by 10 kJ mol⁻¹. The logarithm of ratio of k(catalysed) / k(uncatalysed) is…. (Consider that the frequency factor for both the reactions is same)

At 27°C in presence of a catalyst activation energy of a reaction is lowered by 10 kJ mol⁻¹ The logarithm

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