Algebra - Study Mode
[#281] If a ⊕ b = (a × b) + b, then 5 ⊕ 7 equals to?
Correct Answer
(C) 42
Explanation
Solution: $$eqalign{
& a oplus b = left( {a imes b}
ight) + b cr
& Rightarrow 5 oplus 7 cr
& = left( {5 imes 7}
ight) + 7 cr
& = 35 + 7 cr
& = 42 cr} $$
[#282] Given that 10 0.48 = x, 10 0.70 = y and x z = y 2 , then the value of z is close to?
Correct Answer
(C) 2.9
Explanation
Solution: $$eqalign{
& {10^{0.48}} = x{ ext{ }} cr
& {10^{0.70}} = y{ ext{ }} cr
& { ext{and }}{x^z} = {y^2} cr
& herefore {left( {{{10}^{0.48}}}
ight)^z} = {left( {{{10}^{0.70}}}
ight)^2} cr
& Rightarrow {10^{0.48z}} = {10^{1.40}} cr} $$ If a x = a y , if base equal power are equal : (x = y) $$eqalign{
& herefore 0.48z = 1.40 cr
& Rightarrow z = frac{{140}}{{48}} cr
& Rightarrow z = frac{{35}}{{12}} cr
& Rightarrow z = 2.9 cr} $$
[#283] If 47.2506 = 4A + 7B + 2C + $$frac{5}{{ ext{D}}}$$ + 6E, then the value of 5A + 3B + 6C + D + 3E is?
Correct Answer
(C) 153.6003
Explanation
Solution: Given 47.2506 = 4A + 7B + 2C + $$frac{5}{{ ext{D}}}$$ + 6E . . . . . . . . (1) Now, we can write 47.2506 = 40 + 7 + 0.2 + 0.05 + 0.0006 . . . . . . . . (2) Comparing (1) and (2) we get 4A = 40 ⇒ A = 10 $7B = 7 ⇒ B = 1 2C = 0.2 ⇒ C = 0.1 $$frac{5}{{ ext{D}}}$$ = 0.05 ⇒ D = $$frac{5}{{0.05}}$$ = 100 and, 6E = 0.0006 ⇒ E = 0.0001 So velue of 5A + 3B + 6C + D + 3E = (5 × 10) + (3 × 1) + (6 × 0.1) + 100 + (3 × 0.0001) = 50 + 3 + 0.6 + 100 + 0.0003 = 153.6003
[#284] If x * y = x 2 + y 2 - xy, then the value of 9 * 11 is?
Correct Answer
(B) 103
Explanation
Solution: $$eqalign{
& x*y = {x^2} + {y^2} - xy cr
& { ext{ }}9*11 = {left( 9
ight)^2} + {left( {11}
ight)^2} - 11 imes 9 cr
& Rightarrow 9*11 = 81 + 121 - 99 cr
& Rightarrow 9*11 = 103 cr} $$
[#285] If $${3^{x + 3}} + 7 = 250{ ext{,}}$$ xa0xa0 then x is equal to?
Correct Answer
(C) 2
Explanation
Solution: $$eqalign{
& {3^{x + 3}} + 7 = 250 cr
& Rightarrow {3^{x + 3}} = 250 - 7 cr
& Rightarrow {3^{x + 3}} = 243 cr
& Rightarrow {3^{x + 3}} = {3^5} cr
& Rightarrow x + 3 = 5 cr
& Rightarrow x = 2 cr} $$