On the set of all colleges in a state, a relation R is defined such that two colleges are related if they belong to the same district. Find the properties satisfied by R.
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Let R be the relation in the set Z of integers given by R={(a,b):2 divides a-b}. Show that the relation R transitive ? Write the equivalence class [0]
Let 2 divides `(a-b)` and 2 divides `(b-c)` : where `a,b,c, in Z` So 2 divides `[(a-b)+(b-c)]` 2divides `(a-c)` : Yes relation R is transitive `[0]={0,+-2,+-4,+-6,....}`
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Two thin prisms are combined such that they neither produce any average deviation nor do they cause any dispersion when white light is incident on the
Correct Answer - `0.04`
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A boy has a collection of blue and green marbles. The number of blue marbles belong to the set `{2,3,4,…..,13}`. If two marbles are chosen simultaneou
Correct Answer - A::B::C `(a,b,c)` Let the no. of blue marbles is `a` and no. of green marbles is `b` . `:.(ab)/("^(a+b)C_(2))=(1)/(2)` `implies(a+b)(a+b-1)=4ab` `impliesb^(2)-(2a+1)b+a^(2)-a=0` but `b in R implies D=(2a+1)^(2)-4(a^(2)-a)=8a+1` `:....
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`C_(4)` plants are spacial, They have special type of (A)_____ they tolerate (B)____,they show a response to (C)______, they lack a process called (D)
Correct Answer - A-leaf anatomy B-Higher temperature C-High light intensities D-Photorespiration E-productivity f biomass
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Which of the following sets in an finite/infinite set ? `(i)` Set of divisors of `24` `(ii)` Set of all real number which lie between `1` and `2` `(ii
Correct Answer - `(i)` Finite `(ii)` Infinite `(iii)` Finite `(iv)` Finite
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Which of the following are examples of the null set ? (i) Set of odd numbers divisible by 2. (ii) Set of even prime numbers. (iii) `A={x:x in N,1 lt x
Correct Answer - (i),(iv),(v),(vi)
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State whether the given set is finite or infinite. (i) ` A=` Set of all triangles in a plane. (ii) `B=` set of all points on the circumference (iii) `
Correct Answer - (i) infinte (ii) infinte (iii) infinite (iv) finte (v) infinite (vi) infinte (vii) infinite (viii) finite (ix) infinte (x) infinte (xi) infinite
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Rewrite the following statements using set notation : (i) a is an element of set A. (ii) b is not a element of A. A is a empty set and B is a nonemept
Correct Answer - (i) `a in A ` (ii) `b lin A` (iii) `A=phi and Bne phi` `n (A)=6` (v) `0 in W "but" 0 lin N`
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Places A and B are 160 km apart on a highway. One car starts from A and another from B at the same time. If they travel in the same direction, they me
Correct Answer - 50 kmph, 30 kmph
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Three ducks and two ducklings weigh 32 kg. Four ducks and three ducklings weigh 44 kg. All ducks weigh the same and all ducklings weigh the same
The correct option is (A) 20 kg. Lets weight of Duck = D and weight of duckling = d. 3D + 2d = 32 4D + 3d = 44 multiply first by 3, second by 2 9D...
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