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Maths 1 Marks Question

Polynomials · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 74 questions.

Questions · Page 2 of 2

1 Marks Question

Question 511 Mark
Write the coefficient of x2 in $\sqrt{2} x-1$
Answer
Since $x^2$ is absent in given expression, therefore,
Coefficient of x2 = 0
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Question 521 Mark
Write the coefficient of ${x^2}$ in $\frac{\pi }{2}{x^2} + x$
Answer
$\frac{\pi }{2}{x^2} + x$
The coefficient of ${x^2}$ in the polynomial $\frac{\pi }{2}{x^2} + x$ is $\frac{\pi }{2}$.
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Question 541 Mark
Write the coefficient of ${x^2}$ in 2 + x2 +x
Answer
$2 + {x^2} + x$
The coefficient of ${x^2}$ in the polynomial $2 + {x^2} + x$ is 1.
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Question 551 Mark
Is the expression ${x^{10}} + {y^3} + {t^{50}}$, polynomial in one variable or not? State the reason for your answer.
Answer
${x^{10}} + {y^3} + {t^{50}}$
We can observe that in the polynomial ${x^{10}} + {y^3} + {t^{50}}$, we have x, y and t as the variables and the powers of x, y and t in each term is a whole number.
Therefore, we conclude that ${x^{10}} + {y^3} + {t^{50}}$ is a polynomial but not a polynomial in one variable.
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Question 561 Mark
Is the expression $y + \frac{2}{y}$, polynomial in one variable or not? State the reason for your answer.
Answer
$y + \frac{2}{y}$
We can observe that in the polynomial $y + \frac{2}{y}$ ,we have y as the only variable and the powers of y in each term are not a whole number.
Therefore, we conclude that $y + \frac{2}{y}$ is not a polynomial in one variable.
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Question 571 Mark
Is the expression $3\sqrt t + t\sqrt 2$, polynomial in one variable or not? State the reason for your answer.
Answer
$3\sqrt t + t\sqrt 2$
We can observe that in the polynomial $3\sqrt t + t\sqrt 2 $ we have t as the only variable and the
powers of t in each term are not a whole number.
Therefore, we conclude that $3\sqrt t + t\sqrt 2$  is not a polynomial in one variable.
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Question 581 Mark
Is the expression ${y^2} + \sqrt 2$, polynomial in one variable or not? State the reason for your answer.
Answer
${y^2} + \sqrt 2$
We can observe that in the polynomial ${y^2} + \sqrt 2 $, we have y as the only variable and the powers of y in each term are a whole number.
Therefore, we conclude that ${y^2} + \sqrt 2$  is a polynomial in one variable.
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Question 591 Mark
Is the expression $4{x^2} - 3x + 7{\text{ }}$, polynomial in one variable or not? State the reason for your answer.
Answer
$4{x^2} - 3x + 7{\text{ }}$
We can observe that in the polynomial $4{x^2} - 3x + 7{\text{ }}$
we have x as the only variable and the powers of x in each term are a whole number.
Therefore, we conclude that $4{x^2} - 3x + 7{\text{ }}$ is a polynomial in one variable.
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Question 601 Mark
Find a zero of the polynomial p(x) = 2x + 1
Answer
Finding a zero of p(x), is the same as solving the equation p(x) = 0
Now, 2x + 1 = 0 gives us $x=-\frac{1}{2}$
So, $-\frac{1}{2}$ is a zero of the polynomial 2x + 1 $$ $$ $$
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Question 611 Mark
Check whether –2 and 2 are zeroes of the polynomial x + 2
Answer
We have, p(x) = x + 2
Then p(2) = 2 + 2 = 4, p(–2) = –2 + 2 = 0
Therefore, –2 is a zero of the polynomial x + 2, but 2 is not the zero of the polynomial.
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Question 621 Mark
Find the value of p(t) = 4t4 + 5t3 - t2 + 6 at t = a.
Answer
We have, p(t) = 4t4+ 5t3 - t2 + 6
On putting t = a in p(t), we get,
p(a) = 4 (a)4 + 5 (a)3 - (a)2 + 6
= 4a4 + 5a3 - a2 + 6
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Question 631 Mark
Find the value of q(y) = 3y3 - 4y +$\sqrt{11}$at y = 2.
Answer
We have, q(y) = 3y3 - 4y + $\sqrt{11}$
On put y = 2 in q(y), we get
q(2) = 3(2)3 - 4(2)+$\sqrt{11}$
= 3 $\times$8 - 8 + $\sqrt{11}$
= 24 - 8 + $\sqrt{11}$
= 16 + $\sqrt{11}$
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Question 641 Mark
Find the value of p(x) = 5x2 – 3x + 7 at x =
Answer
The given polynomial is,

p(x) = 5x2 – 3x + 7
The value of the polynomial p(x) at x = 1 is given by p(1) = 5(1)2 – 3(1) + 7 = 5 – 3 + 7 = 9

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Question 651 Mark
Evaluate 9993 using suitable identity.
Answer
We have, (999)3 = (1000 – 1)3
= (1000)3 – (1)3 – 3(1000)(1)(1000 – 1)
= 1000000000 – 1 – 2997000
= 997002999
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Question 661 Mark
Evaluate: (104)3 using a suitable identity.
Answer
(104)3 = (100 + 4)3
Using identity (x + y)3 = x3 + 3xy(x + y) + y3
We get,
(100 + 4)3 = (100)3 + 3 $\times$ 100 $\times$ 4 (100 + 4) + 43
= 10,00 000 + 1,200 $\times$ 104 + 64
= 10,00,000 + 1,24,800 + 64
= 11,24,864
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Question 671 Mark
Expand (4a – 2b – 3c)2
Answer
Using Identity (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx, we have
(4a – 2b – 3c)2 = [4a + (–2b) + (–3c)]2
= (4a)2 + (–2b)2 + (–3c)2 + 2(4a)(–2b) + 2(–2b)(–3c) + 2(–3c)(4a)
= 16a2 + 4b2 + 9c2 – 16ab + 12bc – 24ac
This is the required expansion.
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Question 681 Mark
Write (3a + 4b + 5c)2 in expanded form.
Answer
Comparing the given expression with (x + y + z)2, we find that x = 3a, y = 4b and z = 5c.
Therefore, using Identity (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx,
we have (3a + 4b + 5c)2 = (3a)2 + (4b)2 + (5c)2 + 2(3a)(4b) + 2(4b)(5c) + 2(5c)(3a)
= 9a2 + 16b2 + 25c2 + 24ab + 40bc + 30ac
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Question 691 Mark
Factorise: $\frac{25}{4} x^{2}-\frac{y^{2}}{9}.$
Answer
a2-b2 = (a+b)(a-b)

$\frac{25 x^{2}}{4}-\frac{y^{2}}{9}=\left(\frac{5}{2} x\right)^{2}-\left(\frac{y}{3}\right)^{2}$

$=\left(\frac{5}{2} x+\frac{y}{3}\right)\left(\frac{5}{2} x-\frac{y}{3}\right)$

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Question 701 Mark
Find the degree of the polynomial:  2
Answer
The only term here is 2 which can be written as 2x0 . So the exponent of x is 0. Hence, the degree of the polynomial is 0.
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Question 711 Mark
Find the degree of the polynomial : 2 – y2 – y3 + 2y8
Answer
The highest power of the variable is 8. Therefore, the degree of the polynomial is 8.
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Question 721 Mark
Find the products using appropriate identities:
(x - 3) (x + 5)
Answer
We know the Identity i.e., (x + a) (x + b) = x2 + (a + b)x + ab,
We have (x – 3) (x + 5) = x2 + (–3 + 5)x + (–3)(5) = x2 + 2x – 15
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Question 731 Mark
Find the products using appropriate identities:
(x + 3) (x + 3)
Answer
We have the Identity: (x + y)2 = x2 + 2xy + y2.
Put y = 3 in it,
we get (x + 3) (x + 3) = (x + 3)2 = x2 + 2(x)(3) + (3)2 = x2 + 6x + 9
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Question 741 Mark
Find the degree of the polynomial : x5 – x4 + 3
Answer
The highest power of the variable is 5. Therefore, the degree of the polynomial is 5.
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