Q73.Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and α(> 0), and the mean and standard deviation of marks of class B of n students be respectively 55 and 30 −α. If the mean and variance of the marks of the combined class of 100 + n students are respectively 50 and 350 , then the sum of variances of classes A and B is (1) 500 (2) 450 (3) 650 (4) 900
What This Question Tests
This question tests the understanding of formulas for mean and variance of combined data sets, requiring careful substitution and algebraic manipulation to solve for unknown parameters and then calculate the sum of variances.
Concepts Tested
Formulas Used
Mean_combined = (n1*mean1 + n2*mean2) / (n1+n2)
Variance_combined = (n1*var1 + n2*var2 + n1*d1^2 + n2*d2^2) / (n1+n2)
📚 NCERT Sections This Tests
13.5 — The Q Value Of A Nuclear Reaction A + B ® C + D Is Defined By
Physics Class 12 · Chapter 13
13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
13.2 — Obtain The Binding Energy Of The Nuclei 5626Fe And 20983 Bi In Units Of
Physics Class 12 · Chapter 13
13.2 Obtain the binding energy of the nuclei 5626Fe and 20983 Bi in units of MeV from the following data: m ( 5626Fe ) = 55.934939 u m ( 20983 Bi ) = 208.980388 u
9.6 — A Prism Is Made Of Glass Of Unknown Refractive Index. A Parallel
Physics Class 12 · Chapter 9
9.6 A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be 40°. What is the refractive index of the material of the prism? The refracting angle of the prism is 60°. If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light.
📋 Question Details
- Chapter
- Statistics
- Topic
- Mean and variance of combined data
- Year
- 2023
- Shift
- 31 Jan Shift 2
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 15: Statistics
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