Class 11th

Complete combustion of 3 g of ethane gives x*10²² molecules of water. The value of x is _____. (Round off to the nearest integer).
[ Use : NA = 6.023 *10²³; Atomic masses in u: C:12.0,O:16.0; H:1.0]

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be 1/2 and probability of occurrence of 0 at the odd place be 1/3. Then the probability that '10' is followed by 01 is equal to:

If the curve y=y(x) is the solution of the differential equation 2(x² + x⁵/⁴)dy - y(x + x¹/⁴)dx = 2x⁹/⁴dx, x > 0 which passes through the point (1, 1 - (4/3)logₑ2), then the value of y(16) is equal to:

_____ grams of 3-Hydroxy propanal (MW = 74) must be dehydrated to produce 7.8g of acrolein (MW = 56) (C?H?O) if the percentage yield is 64. (Round off to the nearest integer).
[Given: Atomic masses: C: 12.0u, H:1.0u, O:16.0u]

AX is a covalent diatomic molecule where A and X are second row elements of periodic table. Based on molecular orbital theory, the bond order of AX is 2.5. The total number of electrons in AX is _____. (Round off to the nearest integer).

Let O be the origin. Let OP = xi + yj - k and OQ = -i + 2j + 3xk, x, y ∈ R, x > 0, be such that |PQ| = √20 and the vector OP is perpendicular to OQ. If OR = 3i + zj - 7k, z ∈ R, is coplanar with OP and OQ, then the value of x² + y² + z² is equal to:

The number of ionisable hydrogens present in the product obtained from a reaction of phosphorus trichloride and phosphonic acid is:

Let S₁, S₂, and S₃ be three sets defined as
S₁ = { z∈C : |z−1| ≤ √2}
S₂ = {z∈C : Re((1-i)z) ≥ 1}
S₃ = {z∈C : Im(z) ≤ 1}
Then the set S₁ ∩ S₂ ∩ S₃

Reaction of Grignard reagent, C?H?MgBr with C?H?O followed by hydrolysis gives compound "A” which reacts instantly with Lucas reagent to give compound B, C?H?Cl. The compound B is:

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is ______.