Elementary Algebra
- The degree of polynomial p(x) = x3 + 1 + 2x = 6x + 1/x is ?
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x3 + 1 + 2x = 6x + 1/x
x3 + 1 + 2x = (6x2 + 1) / x
(x3 + 1 + 2x)x = 6x22 + 1Correct Option: B
x3 + 1 + 2x = 6x + 1/x
x3 + 1 + 2x = (6x2 + 1) / x
(x3 + 1 + 2x)x = 6x22 + 1
x4 + x + 2x2 - 6x2 - 1 = 0
x4 - 4x2 + x - 1 = 0
Degree of polynomial is highest exponent degree term i. e., 4.
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If √0.03 x 0.3 a = 0.03 x 0.3 x √ b then value of a is b
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According to given question,
√0.03 x 0.3a = 0.03 x 0.3 √b
On squaring both sides, We will get
0.03 × 0.3 × a = 0.09 × 0.09 × bCorrect Option: B
According to given question,
√0.03 x 0.3a = 0.03 x 0.3 √b
On squaring both sides, We will get
0.03 × 0.3 × a = 0.09 × 0.09 × b⇒ a = 0.09 x 0.09 = 0.9 b 0.03 x 0.3
- A piece of cloth cost ₹ 120. If the piece, then was 2 m longer and each metre of cloth costs ₹ 2 less than cost of the piece of cloth would have remained unchanged. What is the original rate per metre of the cloth ?
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Let the length of the piece be L m.
Then,rate per metre = ₹ 120/L
New length = (L + 2) m
Since, the cost remains same.
∴ New rate per metre =Rs.120/(L + 2)
According to the given condition, 120/L - 120/(L + 2) = 2Correct Option: A
Let the length of the piece be L m.
Then,rate per metre = ₹ 120/L
New length = (L + 2) m
Since, the cost remains same.
∴ New rate per metre =Rs.120/(L + 2)
According to the given condition, 120/L - 120/(L + 2) = 2
⇒ [120(L + 2) - 120L]/L(L + 2) = 2
⇒ [120L + 240 - 120L] / L(L + 2) = 2
⇒ [120L + 240 -120L] / L(L + 2) = 2
⇒ 240/L(L + 2) = 2
⇒ 240 = 2L(L + 2)
⇒ 120 = L(L + 2) = L2 + 2L
⇒ L2 + 2L - 120 = 0
⇒ L2 + 12L - 10L - 120 = 0
⇒ L(L + 12) - 10 x (L + 12) = 0
⇒ (L + 12)(L - 10) = 0
⇒ L + 12 = 0 or L - 10 = 0
⇒ L = -12 or 10
⇒ L = 10(since, L cannot be negative)
∴ Original rate per metre of cloth = 120/L = 120/10 = ₹ 12
- Area of the triangle formed by the graph of the line 2x – 3y + 6 = 0 along with the coordinate axes is:
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Given in the question ,
Putting x = 0 in line 2x – 3y + 6 = 0
⇒ y = 2
Putting y = 0 in 2x + 3y + 6 = 0
⇒ x = – 3Area of ∆ OAB = 1 x OB x OA = 1 2 2 
Correct Option: C
Given in the question ,
Putting x = 0 in line 2x – 3y + 6 = 0
⇒ y = 2
Putting y = 0 in 2x + 3y + 6 = 0
⇒ x = – 3Area of ∆ OAB = 1 x OB x OA = 1 x 3 x 2 = 3 sq. units. 2 2 
- The sum of the squares of two numbers is 234 and the square of their difference is 144. Find the product of the two numbers ?
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Let the two numbers be x and y.
Then, x2 + y2 = 234 ...(i)
and (x - y)2 = 144 ...(ii)
Now, (x - y)2 = 144
⇒ x2 + y2 - 2xy = 144
⇒ 234 - 2xy = 144 [using Eq.(i)]
Correct Option: D
Let the two numbers be x and y.
Then, x2 + y2 = 234 ...(i)
and (x - y)2 = 144 ...(ii)
Now, (x - y)2 = 144
⇒ x2 + y2 - 2xy = 144
⇒ 234 - 2xy = 144 [using Eq.(i)]
On substituting the value of x2 + y2 from Eq.(i) in Eq.(ii),
we get
2xy = 90
⇒ xy = 45
So, the product of the two numbers is 45.
