Mathematics (Urdu) - ریاضی - For Class SSC - Part 1 (Science Group) - Solved Model papers 2020 -2021- AS PER CONDENSED SYLLABUS

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Mathematics (Urdu) - ریاضی
For Class SSC - Part 1 (Science Groups)
Solved Model papers 2020 -2021
As Per condensed Syllabus

SECTION "B"

(Short Answer Question)

Q.2: If S = {10, 20, 30, 40}, then find P (S)
Solution:-
|P (S)| = 2ⁿ = 2⁴ = 2 x 2 x 2 x 2 = 16 (where 'n' is number of elements in set S.)
(Hence, Set S has 16 subsets or power sets.)
|P (S)| = { { }, {10}, {20}, {30}, {40}, {10, 20}, {10, 30}, (10, 40), {20, 30}, {20, 40}, {30, 40}, {10, 20, 30), {10, 20, 40}, {10, 30, 40}, {20, 30, 40}, {10, 20, 30, 40} } Ans.

Q.3: If A = {a, b, c, d} and B = {b, d, e, f}, then
Prove that (AUB) - (A∩B) = (A ∆ B)
Solution:
Taking R.H.S:
AΔB = {a, b, c, d} Δ {b, d, e, f}
(By selecting uncommon members among both sets)
We get AΔB = {a, c, e, f} ....... (1)

Taking L.H.S:
AUB = {a, b, c, d} U {b, d, e, f}
AUB = (a, b, c, d, e, f)

A∩B = {a, b, c, d} ∩ {b, d, e, f}
A∩B = (b, d)
AUB - A∩B = (a, b, c, d, e, f) - (b, d)
We get AUB - A∩B = ({a, c, e, f} ....... (2)
By (1) and (2)

AΔB = AUB - A∩B Hence Proved

Q.4: Find the value of a²+b²+c² when a+b+c = √ 17 and ab+bc+ca = 2.
Solution:
Given that:
(a+b+c) = √ 17
By squaring on both side
(a+b+c)² = (√ 17)²
From Formula:

 (a+b+c)² = a²+b²+c² + 2ab + 2bc + 2ca 

(a+b+c)² = a²+b²+c² + 2ab + 2bc + 2ca = 17
(a+b+c)² = a²+b²+c² + 2 (ab + bc + ca) = 17
(a+b+c)² = a²+b²+c² + 2 (2) = 17
(a+b+c)² = a²+b²+c² + 4 = 17
(a+b+c)² = a²+b²+c² = 17 - 4

(a+b+c)² = a²+b²+c² = 13 ANSWER

Q.4: Find the value of 85.7 x 2.47 / 8.89 with the help of logarithmic table.