\(4^2\cdot4^3\) का सरल रूप क्या है?
What is the simplified form of \(4^2\cdot4^3\)?
#polynomials
#exponents
#product law
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A \(4^5\)
B \(4^6\)
C \(16^5\)
D \(4^1\)
Explanation opens after your attempt
Correct Answer
A. \(4^5\)
Step 1
Concept
When bases are the same in multiplication, exponents are added, so \(4^2\cdot4^3=4^5\). Add exponents when bases are the same.
Step 2
Why this answer is correct
The correct answer is A. \(4^5\). When bases are the same in multiplication, exponents are added, so \(4^2\cdot4^3=4^5\). Add exponents when bases are the same.
Step 3
Exam Tip
समान आधार में गुणा करने पर घातें जुड़ती हैं इसलिए \(4^2\cdot4^3=4^5\)। आधार समान हो तो घात जोड़ें।
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\(\frac{10^8}{10^5}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{10^8}{10^5}\)?
#polynomials
#exponents
#quotient law
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A \(10^{13}\)
B \(10^3\)
C \(10^{40}\)
D \(1^3\)
Explanation opens after your attempt
Correct Answer
B. \(10^3\)
Step 1
Concept
When bases are the same in division, exponents are subtracted, so \(\frac{10^8}{10^5}=10^3\). Subtract the lower exponent from the upper exponent.
Step 2
Why this answer is correct
The correct answer is B. \(10^3\). When bases are the same in division, exponents are subtracted, so \(\frac{10^8}{10^5}=10^3\). Subtract the lower exponent from the upper exponent.
Step 3
Exam Tip
समान आधार में भाग करने पर घातें घटती हैं इसलिए \(\frac{10^8}{10^5}=10^3\)। भाग में ऊपर की घात से नीचे की घात घटाएँ।
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(\(2^4\)2 ) का सरल रूप क्या है?
What is the simplified form of (\(2^4\)2 )?
#polynomials
#exponents
#power law
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A \(2^6\)
B \(2^8\)
C \(2^{16}\)
D \(4^4\)
Explanation opens after your attempt
Correct Answer
B. \(2^8\)
Step 1
Concept
In a power of a power, exponents are multiplied, so (\(2^4\)2 =28 ). Adding the exponents here is a mistake.
Step 2
Why this answer is correct
The correct answer is B. \(2^8\). In a power of a power, exponents are multiplied, so (\(2^4\)2 =28 ). Adding the exponents here is a mistake.
Step 3
Exam Tip
घात की घात में घातों का गुणा होता है इसलिए (\(2^4\)2 =28 )। यहाँ घातों को जोड़ना गलती है।
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यदि \(c\neq0\) है तो \(c^0\) का मान क्या है?
If \(c\neq0\), what is the value of \(c^0\)?
#polynomials
#zero exponent
#real numbers
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A (0)
B (1)
C (c)
D \(c^2\)
Explanation opens after your attempt
Step 1
Concept
The zero power of any non-zero base is (1). Therefore \(c^0=1\).
Step 2
Why this answer is correct
The correct answer is B. (1). The zero power of any non-zero base is (1). Therefore \(c^0=1\).
Step 3
Exam Tip
किसी भी अशून्य आधार की शून्य घात (1) होती है। इसलिए \(c^0=1\) है।
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\(3^{-2}\) किसके बराबर है?
What is \(3^{-2}\) equal to?
#polynomials
#negative exponent
#basics
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A \(\frac{1}{9}\)
B (9)
C (-9)
D \(\frac{1}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{9}\)
Step 1
Concept
A negative exponent moves the base to the denominator, so \(3^{-2}=\frac{1}{3^2}=\frac{1}{9}\). A negative exponent does not mean a negative answer.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{9}\). A negative exponent moves the base to the denominator, so \(3^{-2}=\frac{1}{3^2}=\frac{1}{9}\). A negative exponent does not mean a negative answer.
Step 3
Exam Tip
ऋणात्मक घात आधार को हर में ले जाती है इसलिए \(3^{-2}=\frac{1}{3^2}=\frac{1}{9}\)। ऋणात्मक घात का अर्थ ऋणात्मक उत्तर नहीं होता।
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(\(6\cdot7\)2 ) का सही रूप क्या है?
What is the correct form of (\(6\cdot7\)2 )?
#polynomials
#product power
#exponents
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A \(6^2\cdot7^2\)
B \(6^2\cdot7\)
C \(6\cdot7^2\)
D \(13^2\)
Explanation opens after your attempt
Correct Answer
A. \(6^2\cdot7^2\)
Step 1
Concept
The power of a product applies to every factor. Therefore (\(6\cdot7\)2 =62 \cdot72 ).
Step 2
Why this answer is correct
The correct answer is A. \(6^2\cdot7^2\). The power of a product applies to every factor. Therefore (\(6\cdot7\)2 =62 \cdot72 ).
Step 3
Exam Tip
गुणनफल की घात हर गुणक पर लगती है। इसलिए (\(6\cdot7\)2 =62 \cdot72 ) है।
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(\left\(\frac{7}{8}\right\)2 ) का मान क्या है?
What is the value of (\left\(\frac{7}{8}\right\)2 )?
#polynomials
#fraction power
#exponents
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A \(\frac{14}{16}\)
B \(\frac{49}{64}\)
C \(\frac{7}{64}\)
D \(\frac{49}{8}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{49}{64}\)
Step 1
Concept
The power of a fraction applies to both numerator and denominator. Hence (\left\(\frac{7}{8}\right\)2 =\frac{49}{64}).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{49}{64}\). The power of a fraction applies to both numerator and denominator. Hence (\left\(\frac{7}{8}\right\)2 =\frac{49}{64}).
Step 3
Exam Tip
भिन्न की घात अंश और हर दोनों पर लगती है। इसलिए (\left\(\frac{7}{8}\right\)2 =\frac{49}{64}) है।
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\(12^2\cdot12^3\) के बराबर कौन सा है?
Which is equal to \(12^2\cdot12^3\)?
#polynomials
#same base
#exponents
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A \(12^5\)
B \(12^6\)
C \(24^5\)
D \(12^1\)
Explanation opens after your attempt
Correct Answer
A. \(12^5\)
Step 1
Concept
For the same base (12), exponents (2) and (3) are added. So the correct answer is \(12^5\).
Step 2
Why this answer is correct
The correct answer is A. \(12^5\). For the same base (12), exponents (2) and (3) are added. So the correct answer is \(12^5\).
Step 3
Exam Tip
समान आधार (12) में घातें (2) और (3) जुड़ती हैं। इसलिए सही उत्तर \(12^5\) है।
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\(15^6\div15^2\) का सरल रूप क्या है?
What is the simplified form of \(15^6\div15^2\)?
#polynomials
#division law
#exponents
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A \(15^4\)
B \(15^8\)
C \(15^{12}\)
D \(1^4\)
Explanation opens after your attempt
Correct Answer
A. \(15^4\)
Step 1
Concept
For division with the same base, (6-2=4). Therefore \(15^6\div15^2=15^4\).
Step 2
Why this answer is correct
The correct answer is A. \(15^4\). For division with the same base, (6-2=4). Therefore \(15^6\div15^2=15^4\).
Step 3
Exam Tip
भाग में समान आधार होने पर (6-2=4) होता है। इसलिए \(15^6\div15^2=15^4\) है।
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\(21^1\) का मान क्या है?
What is the value of \(21^1\)?
#polynomials
#first power
#exponents
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A (0)
B (1)
C (21)
D (441)
Explanation opens after your attempt
Step 1
Concept
The first power of a number is the number itself. Therefore \(21^1=21\).
Step 2
Why this answer is correct
The correct answer is C. (21). The first power of a number is the number itself. Therefore \(21^1=21\).
Step 3
Exam Tip
किसी संख्या की (1) घात वही संख्या होती है। इसलिए \(21^1=21\) है।
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\(4^0+5^2\) का मान क्या है?
What is the value of \(4^0+5^2\)?
#polynomials
#zero exponent
#calculation
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A (25)
B (26)
C (29)
D (30)
Explanation opens after your attempt
Step 1
Concept
Here \(4^0=1\) and \(5^2=25\). Therefore (1+25=26).
Step 2
Why this answer is correct
The correct answer is B. (26). Here \(4^0=1\) and \(5^2=25\). Therefore (1+25=26).
Step 3
Exam Tip
यहाँ \(4^0=1\) और \(5^2=25\) है। इसलिए (1+25=26) है।
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\(6^2+3^3\) का मान क्या है?
What is the value of \(6^2+3^3\)?
#polynomials
#real number operations
#exponents
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A (63)
B (54)
C (45)
D (39)
Explanation opens after your attempt
Step 1
Concept
Find powers first: \(6^2=36\) and \(3^3=27\). Hence (36+27=63).
Step 2
Why this answer is correct
The correct answer is A. (63). Find powers first: \(6^2=36\) and \(3^3=27\). Hence (36+27=63).
Step 3
Exam Tip
पहले घात निकालें \(6^2=36\) और \(3^3=27\)। इसलिए (36+27=63) है।
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यदि \(w\neq0\) है तो \(\frac{w^a}{w^b}\) का सही रूप क्या है?
If \(w\neq0\), what is the correct form of \(\frac{w^a}{w^b}\)?
#polynomials
#quotient law
#exponents
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A \(w^{a+b}\)
B \(w^{a-b}\)
C \(w^{ab}\)
D \(w^{b-a}\)
Explanation opens after your attempt
Correct Answer
B. \(w^{a-b}\)
Step 1
Concept
In division with the same base, exponents are subtracted. Therefore \(\frac{w^a}{w^b}=w^{a-b}\).
Step 2
Why this answer is correct
The correct answer is B. \(w^{a-b}\). In division with the same base, exponents are subtracted. Therefore \(\frac{w^a}{w^b}=w^{a-b}\).
Step 3
Exam Tip
समान आधार के भाग में घातें घटती हैं। इसलिए \(\frac{w^a}{w^b}=w^{a-b}\) है।
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(\(s^5\)2 ) का सरल रूप क्या है?
What is the simplified form of (\(s^5\)2 )?
#polynomials
#algebraic exponents
#power law
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A \(s^7\)
B \(s^{10}\)
C \(s^{25}\)
D \(s^3\)
Explanation opens after your attempt
Correct Answer
B. \(s^{10}\)
Step 1
Concept
In a power of a power, \(5\cdot2=10\). Therefore (\(s^5\)2 =s^{10}).
Step 2
Why this answer is correct
The correct answer is B. \(s^{10}\). In a power of a power, \(5\cdot2=10\). Therefore (\(s^5\)2 =s^{10}).
Step 3
Exam Tip
घात की घात में \(5\cdot2=10\) होता है। इसलिए (\(s^5\)2 =s^{10}) है।
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((ab)5 ) का सही विस्तार क्या है?
What is the correct expansion of ((ab)5 )?
#polynomials
#product power
#algebra
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A \(a^5b^5\)
B \(ab^5\)
C \(a^5b\)
D \(a^5+b^5\)
Explanation opens after your attempt
Correct Answer
A. \(a^5b^5\)
Step 1
Concept
The power of a product applies to both factors. Hence ((ab)5 =a-5 b-5 ).
Step 2
Why this answer is correct
The correct answer is A. \(a^5b^5\). The power of a product applies to both factors. Hence ((ab)5 =a-5 b-5 ).
Step 3
Exam Tip
गुणनफल की घात दोनों गुणकों पर लगती है। इसलिए ((ab)5 =a-5 b-5 ) है।
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(\left\(\frac{m}{n}\right\)4 ) का सही रूप क्या है यदि \(n\neq0\)?
What is the correct form of (\left\(\frac{m}{n}\right\)4 ) if \(n\neq0\)?
#polynomials
#fraction law
#exponents
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A \(\frac{m^4}{n^4}\)
B \(\frac{m^4}{n}\)
C \(\frac{m}{n^4}\)
D \(\frac{m+n}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{m^4}{n^4}\)
Step 1
Concept
The exponent of a fraction applies to both numerator and denominator. Thus (\left\(\frac{m}{n}\right\)4 =\frac{m-4 }{n-4 }).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{m^4}{n^4}\). The exponent of a fraction applies to both numerator and denominator. Thus (\left\(\frac{m}{n}\right\)4 =\frac{m-4 }{n-4 }).
Step 3
Exam Tip
भिन्न की घात अंश और हर दोनों पर लगती है। इसलिए (\left\(\frac{m}{n}\right\)4 =\frac{m-4 }{n-4 }) है।
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कौन सा \(5^4\) के बराबर है?
Which is equal to \(5^4\)?
#polynomials
#meaning of exponent
#repeated multiplication
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A (5+5+5+5)
B \(5\cdot4\)
C \(5\cdot5\cdot5\cdot5\)
D \(4\cdot4\cdot4\cdot4\cdot4\)
Explanation opens after your attempt
Correct Answer
C. \(5\cdot5\cdot5\cdot5\)
Step 1
Concept
\(5^4\) means multiplying (5) by itself (4) times. An exponent shows repeated multiplication.
Step 2
Why this answer is correct
The correct answer is C. \(5\cdot5\cdot5\cdot5\). \(5^4\) means multiplying (5) by itself (4) times. An exponent shows repeated multiplication.
Step 3
Exam Tip
\(5^4\) का अर्थ (5) को (4) बार गुणा करना है। घात बार-बार गुणा को दिखाती है।
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((-6)2 ) का मान क्या है?
What is the value of ((-6)2 )?
#polynomials
#negative base
#real numbers
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A (36)
B (-36)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
The whole number ((-6)) is squared, so the answer is (36). Parentheses include the negative sign in the power.
Step 2
Why this answer is correct
The correct answer is A. (36). The whole number ((-6)) is squared, so the answer is (36). Parentheses include the negative sign in the power.
Step 3
Exam Tip
पूरी संख्या ((-6)) का वर्ग लिया गया है इसलिए उत्तर (36) है। कोष्ठक ऋण चिह्न को भी घात में शामिल करता है।
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\(-7^2\) का मान क्या है?
What is the value of \(-7^2\)?
#polynomials
#order of operations
#negative sign
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A (49)
B (-49)
C (14)
D (-14)
Explanation opens after your attempt
Step 1
Concept
Without parentheses, the exponent is applied first, so (-72 =-\(7^2\)=-49). Use parentheses for a negative base.
Step 2
Why this answer is correct
The correct answer is B. (-49). Without parentheses, the exponent is applied first, so (-72 =-\(7^2\)=-49). Use parentheses for a negative base.
Step 3
Exam Tip
कोष्ठक न होने पर घात पहले लगती है इसलिए (-72 =-\(7^2\)=-49)। ऋण आधार चाहिए तो कोष्ठक लगाएँ।
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\(6^2\cdot2^2\) का संक्षिप्त रूप क्या है?
What is the compact form of \(6^2\cdot2^2\)?
#polynomials
#same exponent
#product
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A \(8^2\)
B \(12^2\)
C \(12^4\)
D \(6^4\)
Explanation opens after your attempt
Correct Answer
B. \(12^2\)
Step 1
Concept
When exponents are equal, bases can be multiplied. Hence (62 \cdot22 =\(6\cdot2\)2 =122 ).
Step 2
Why this answer is correct
The correct answer is B. \(12^2\). When exponents are equal, bases can be multiplied. Hence (62 \cdot22 =\(6\cdot2\)2 =122 ).
Step 3
Exam Tip
समान घात होने पर आधारों का गुणा किया जा सकता है। इसलिए (62 \cdot22 =\(6\cdot2\)2 =122 ) है।
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\(\frac{18^2}{6^2}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{18^2}{6^2}\)?
#polynomials
#same exponent
#quotient
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A \(3^2\)
B \(12^2\)
C \(24^2\)
D \(108^2\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\)
Step 1
Concept
With equal exponents, (\frac{182 }{62 }=\left\(\frac{18}{6}\right\)2 =32 ). Simplify equal powers together.
Step 2
Why this answer is correct
The correct answer is A. \(3^2\). With equal exponents, (\frac{182 }{62 }=\left\(\frac{18}{6}\right\)2 =32 ). Simplify equal powers together.
Step 3
Exam Tip
समान घात होने पर (\frac{182 }{62 }=\left\(\frac{18}{6}\right\)2 =32 )। समान घात को साथ में सरल करें।
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\(v^4\cdot v^5\) का सरल रूप क्या है?
What is the simplified form of \(v^4\cdot v^5\)?
#polynomials
#algebraic terms
#exponents
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A \(v^9\)
B \(v^{20}\)
C \(2v^9\)
D (v)
Explanation opens after your attempt
Correct Answer
A. \(v^9\)
Step 1
Concept
For the same base (v), exponents add as (4+5=9). Therefore \(v^4\cdot v^5=v^9\).
Step 2
Why this answer is correct
The correct answer is A. \(v^9\). For the same base (v), exponents add as (4+5=9). Therefore \(v^4\cdot v^5=v^9\).
Step 3
Exam Tip
समान आधार (v) में घातें (4+5=9) जुड़ती हैं। इसलिए \(v^4\cdot v^5=v^9\) है।
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\(\frac{h^{12}}{h^7}\) का सरल रूप क्या है यदि \(h\neq0\)?
What is the simplified form of \(\frac{h^{12}}{h^7}\) if \(h\neq0\)?
#polynomials
#algebraic exponents
#division
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A \(h^{19}\)
B \(h^5\)
C \(h^{84}\)
D \(h^{-5}\)
Explanation opens after your attempt
Correct Answer
B. \(h^5\)
Step 1
Concept
For the same base (h), (12-7=5). Therefore \(\frac{h^{12}}{h^7}=h^5\).
Step 2
Why this answer is correct
The correct answer is B. \(h^5\). For the same base (h), (12-7=5). Therefore \(\frac{h^{12}}{h^7}=h^5\).
Step 3
Exam Tip
समान आधार (h) में (12-7=5) होता है। इसलिए \(\frac{h^{12}}{h^7}=h^5\) है।
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(\(r^3\)4 ) का सरल रूप क्या है?
What is the simplified form of (\(r^3\)4 )?
#polynomials
#power law
#algebra
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A \(r^7\)
B \(r^{12}\)
C \(r^{81}\)
D (r)
Explanation opens after your attempt
Correct Answer
B. \(r^{12}\)
Step 1
Concept
In a power of a power, \(3\cdot4=12\). Hence (\(r^3\)4 =r^{12}).
Step 2
Why this answer is correct
The correct answer is B. \(r^{12}\). In a power of a power, \(3\cdot4=12\). Hence (\(r^3\)4 =r^{12}).
Step 3
Exam Tip
घात की घात में \(3\cdot4=12\) होता है। इसलिए (\(r^3\)4 =r^{12}) है।
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यदि \(a\neq0\), \(b\neq0\) और \(c\neq0\) हैं तो \(a^0+b^0+c^0\) का मान क्या है?
If \(a\neq0\), \(b\neq0\), and \(c\neq0\), what is the value of \(a^0+b^0+c^0\)?
#polynomials
#zero exponent
#addition
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A (1)
B (2)
C (3)
D (a+b+c)
Explanation opens after your attempt
Step 1
Concept
The zero power of every non-zero base is (1). Hence \(a^0+b^0+c^0=3\).
Step 2
Why this answer is correct
The correct answer is C. (3). The zero power of every non-zero base is (1). Hence \(a^0+b^0+c^0=3\).
Step 3
Exam Tip
हर अशून्य आधार की शून्य घात (1) होती है। इसलिए \(a^0+b^0+c^0=3\) है।
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यदि \(y\neq0\) है तो \(y^{-5}\) का सही रूप क्या है?
If \(y\neq0\), what is the correct form of \(y^{-5}\)?
#polynomials
#negative exponent
#algebra
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A \(y^5\)
B \(\frac{1}{y^5}\)
C \(-y^5\)
D \(\frac{1}{5y}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{y^5}\)
Step 1
Concept
A negative exponent moves the base to the denominator. Therefore \(y^{-5}=\frac{1}{y^5}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{y^5}\). A negative exponent moves the base to the denominator. Therefore \(y^{-5}=\frac{1}{y^5}\).
Step 3
Exam Tip
ऋणात्मक घात आधार को हर में ले जाती है। इसलिए \(y^{-5}=\frac{1}{y^5}\) है।
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कौन सा ((a-b)2 ) के बराबर है?
Which is equal to ((a-b)2 )?
#polynomials
#identity
#common mistake
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A \(a^2-b^2\)
B \(a^2-2ab+b^2\)
C \(a^2+2ab+b^2\)
D \(a^2-b\)
Explanation opens after your attempt
Correct Answer
B. \(a^2-2ab+b^2\)
Step 1
Concept
The middle term in ((a-b)2 ) is (-2ab). The correct expansion is \(a^2-2ab+b^2\).
Step 2
Why this answer is correct
The correct answer is B. \(a^2-2ab+b^2\). The middle term in ((a-b)2 ) is (-2ab). The correct expansion is \(a^2-2ab+b^2\).
Step 3
Exam Tip
((a-b)2 ) में मध्य पद (-2ab) होता है। सही विस्तार \(a^2-2ab+b^2\) है।
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(7(x+2)) का विस्तार क्या है?
What is the expansion of (7(x+2))?
#polynomials
#distributive law
#expansion
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A (7x+2)
B (7x+14)
C (x+14)
D (9x)
Explanation opens after your attempt
Correct Answer
B. (7x+14)
Step 1
Concept
By the distributive law, (7(x+2)=7x+14). Multiply the outside factor by each term.
Step 2
Why this answer is correct
The correct answer is B. (7x+14). By the distributive law, (7(x+2)=7x+14). Multiply the outside factor by each term.
Step 3
Exam Tip
वितरण नियम से (7(x+2)=7x+14) होता है। बाहरी गुणक को हर पद से गुणा करें।
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(12a+9a) का सरल रूप क्या है?
What is the simplified form of (12a+9a)?
#polynomials
#like terms
#addition
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A (21a)
B (108a)
C \(21a^2\)
D (3a)
Explanation opens after your attempt
Step 1
Concept
Coefficients of like terms are added, so (12a+9a=21a). The variable (a) does not change.
Step 2
Why this answer is correct
The correct answer is A. (21a). Coefficients of like terms are added, so (12a+9a=21a). The variable (a) does not change.
Step 3
Exam Tip
समान पदों के गुणांक जोड़े जाते हैं इसलिए (12a+9a=21a)। चर (a) नहीं बदलता।
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(13x-5x) का सरल रूप क्या है?
What is the simplified form of (13x-5x)?
#polynomials
#like terms
#subtraction
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A (8x)
B (18x)
C \(8x^2\)
D (65x)
Explanation opens after your attempt
Step 1
Concept
For like terms, coefficients are subtracted, so (13x-5x=8x). The variable remains the same in like terms.
Step 2
Why this answer is correct
The correct answer is A. (8x). For like terms, coefficients are subtracted, so (13x-5x=8x). The variable remains the same in like terms.
Step 3
Exam Tip
समान पदों में गुणांक घटते हैं इसलिए (13x-5x=8x)। समान पदों में चर वही रहता है।
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\(6x\cdot5x^2\) का गुणनफल क्या है?
What is the product of \(6x\cdot5x^2\)?
#polynomials
#monomial multiplication
#exponents
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A \(11x^3\)
B \(30x^2\)
C \(30x^3\)
D \(30x^4\)
Explanation opens after your attempt
Correct Answer
C. \(30x^3\)
Step 1
Concept
The coefficients give \(6\cdot5=30\), and \(x\cdot x^2=x^3\). Therefore the answer is \(30x^3\).
Step 2
Why this answer is correct
The correct answer is C. \(30x^3\). The coefficients give \(6\cdot5=30\), and \(x\cdot x^2=x^3\). Therefore the answer is \(30x^3\).
Step 3
Exam Tip
गुणांक \(6\cdot5=30\) और \(x\cdot x^2=x^3\) है। इसलिए उत्तर \(30x^3\) है।
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\(\frac{35x^6}{7x^3}\) का सरल रूप क्या है यदि \(x\neq0\)?
What is the simplified form of \(\frac{35x^6}{7x^3}\) if \(x\neq0\)?
#polynomials
#monomial division
#exponents
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A \(5x^3\)
B \(28x^3\)
C \(5x^9\)
D \(245x^3\)
Explanation opens after your attempt
Correct Answer
A. \(5x^3\)
Step 1
Concept
The coefficient part is \(\frac{35}{7}=5\) and the variable part is \(\frac{x^6}{x^3}=x^3\). Thus the simplified form is \(5x^3\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^3\). The coefficient part is \(\frac{35}{7}=5\) and the variable part is \(\frac{x^6}{x^3}=x^3\). Thus the simplified form is \(5x^3\).
Step 3
Exam Tip
गुणांक \(\frac{35}{7}=5\) और चर भाग \(\frac{x^6}{x^3}=x^3\) है। इसलिए सरल रूप \(5x^3\) है।
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(6(2x+5)) का विस्तार क्या है?
What is the expansion of (6(2x+5))?
#polynomials
#expansion
#distributive property
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A (12x+5)
B (12x+30)
C (8x+30)
D (12x+10)
Explanation opens after your attempt
Correct Answer
B. (12x+30)
Step 1
Concept
By the distributive law, (6(2x+5)=12x+30). Multiply (6) by both terms inside the bracket.
Step 2
Why this answer is correct
The correct answer is B. (12x+30). By the distributive law, (6(2x+5)=12x+30). Multiply (6) by both terms inside the bracket.
Step 3
Exam Tip
वितरण नियम से (6(2x+5)=12x+30)। कोष्ठक के दोनों पदों से (6) को गुणा करें।
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\(4^2+4^3\) का मान क्या है?
What is the value of \(4^2+4^3\)?
#polynomials
#exponents
#common mistake
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A \(4^5\)
B (80)
C (64)
D (48)
Explanation opens after your attempt
Step 1
Concept
This is addition, so exponents are not added. \(4^2+4^3=16+64=80\).
Step 2
Why this answer is correct
The correct answer is B. (80). This is addition, so exponents are not added. \(4^2+4^3=16+64=80\).
Step 3
Exam Tip
यहाँ जोड़ है इसलिए घातें नहीं जुड़तीं। \(4^2+4^3=16+64=80\) है।
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किस नियम से (p(q+r)=pq+pr) मिलता है?
Which law gives (p(q+r)=pq+pr)?
#polynomials
#real number laws
#distributive law
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A वितरण नियम / Distributive law
B क्रमविनिमेय नियम / Commutative law
C साहचर्य नियम / Associative law
D शून्य घात नियम / Zero exponent law
Explanation opens after your attempt
Correct Answer
A. वितरण नियम / Distributive law
Step 1
Concept
(p) is multiplied by both (q) and (r). Therefore this is the distributive law.
Step 2
Why this answer is correct
The correct answer is A. वितरण नियम / Distributive law. (p) is multiplied by both (q) and (r). Therefore this is the distributive law.
Step 3
Exam Tip
(p) को (q) और (r) दोनों से गुणा किया गया है। इसलिए यह वितरण नियम है।
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कौन सा नियम (m+n=n+m) को दर्शाता है?
Which law is shown by (m+n=n+m)?
#polynomials
#commutative law
#real numbers
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A क्रमविनिमेय नियम / Commutative law
B वितरण नियम / Distributive law
C घात नियम / Exponent law
D प्रतिलोम नियम / Inverse law
Explanation opens after your attempt
Correct Answer
A. क्रमविनिमेय नियम / Commutative law
Step 1
Concept
Changing the order in addition does not change the sum. This is called the commutative law.
Step 2
Why this answer is correct
The correct answer is A. क्रमविनिमेय नियम / Commutative law. Changing the order in addition does not change the sum. This is called the commutative law.
Step 3
Exam Tip
जोड़ में क्रम बदलने से योग नहीं बदलता। इसे क्रमविनिमेय नियम कहते हैं।
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कौन सा नियम ((m+n)+p=m+(n+p)) को दिखाता है?
Which law is shown by ((m+n)+p=m+(n+p))?
#polynomials
#associative law
#real numbers
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A साहचर्य नियम / Associative law
B वितरण नियम / Distributive law
C भाग नियम / Division law
D शून्य नियम / Zero law
Explanation opens after your attempt
Correct Answer
A. साहचर्य नियम / Associative law
Step 1
Concept
Changing the grouping in addition does not change the sum. This is called the associative law.
Step 2
Why this answer is correct
The correct answer is A. साहचर्य नियम / Associative law. Changing the grouping in addition does not change the sum. This is called the associative law.
Step 3
Exam Tip
जोड़ में समूह बदलने से योग नहीं बदलता। इसे साहचर्य नियम कहते हैं।
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(0.65+0.25) का मान क्या है?
What is the value of (0.65+0.25)?
#polynomials
#decimal operations
#real numbers
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A (0.80)
B (0.90)
C (1.00)
D (1.10)
Explanation opens after your attempt
Step 1
Concept
Adding decimals gives (0.65+0.25=0.90). Align decimal points correctly.
Step 2
Why this answer is correct
The correct answer is B. (0.90). Adding decimals gives (0.65+0.25=0.90). Align decimal points correctly.
Step 3
Exam Tip
दशमलव जोड़ने पर (0.65+0.25=0.90) होता है। दशमलव बिंदु ठीक से मिलाएँ।
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\(\frac{5}{6}+\frac{1}{12}\) का मान क्या है?
What is the value of \(\frac{5}{6}+\frac{1}{12}\)?
#polynomials
#fraction addition
#real numbers
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A \(\frac{6}{18}\)
B \(\frac{11}{12}\)
C \(\frac{1}{2}\)
D \(\frac{7}{12}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{11}{12}\)
Step 1
Concept
Using common denominator (12), \(\frac{5}{6}=\frac{10}{12}\). Hence \(\frac{10}{12}+\frac{1}{12}=\frac{11}{12}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{11}{12}\). Using common denominator (12), \(\frac{5}{6}=\frac{10}{12}\). Hence \(\frac{10}{12}+\frac{1}{12}=\frac{11}{12}\).
Step 3
Exam Tip
समान हर (12) लेने पर \(\frac{5}{6}=\frac{10}{12}\) होता है। इसलिए \(\frac{10}{12}+\frac{1}{12}=\frac{11}{12}\) है।
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\(\frac{5}{8}\cdot\frac{16}{15}\) का मान क्या है?
What is the value of \(\frac{5}{8}\cdot\frac{16}{15}\)?
#polynomials
#fraction multiplication
#real numbers
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A \(\frac{2}{3}\)
B \(\frac{21}{23}\)
C \(\frac{80}{120}\)
D \(\frac{1}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{2}{3}\)
Step 1
Concept
Multiply and simplify: \(\frac{5}{8}\cdot\frac{16}{15}=\frac{80}{120}=\frac{2}{3}\). Cancelling first makes calculation easier.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{2}{3}\). Multiply and simplify: \(\frac{5}{8}\cdot\frac{16}{15}=\frac{80}{120}=\frac{2}{3}\). Cancelling first makes calculation easier.
Step 3
Exam Tip
गुणा करके सरल करें \(\frac{5}{8}\cdot\frac{16}{15}=\frac{80}{120}=\frac{2}{3}\)। पहले काटने से गणना आसान होती है।
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\(20-5\cdot3\) का मान क्या है?
What is the value of \(20-5\cdot3\)?
#polynomials
#order of operations
#real numbers
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A (45)
B (15)
C (5)
D (60)
Explanation opens after your attempt
Step 1
Concept
Multiply first: \(5\cdot3=15\), then (20-15=5). Follow the order of operations.
Step 2
Why this answer is correct
The correct answer is C. (5). Multiply first: \(5\cdot3=15\), then (20-15=5). Follow the order of operations.
Step 3
Exam Tip
पहले गुणा करें \(5\cdot3=15\), फिर (20-15=5)। क्रम नियम का पालन करें।
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\(7+3^2\cdot5\) का मान क्या है?
What is the value of \(7+3^2\cdot5\)?
#polynomials
#order of operations
#exponents
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A (52)
B (80)
C (100)
D (45)
Explanation opens after your attempt
Step 1
Concept
First \(3^2=9\), then \(9\cdot5=45\), and (7+45=52). Evaluate exponents before multiplication.
Step 2
Why this answer is correct
The correct answer is A. (52). First \(3^2=9\), then \(9\cdot5=45\), and (7+45=52). Evaluate exponents before multiplication.
Step 3
Exam Tip
पहले \(3^2=9\), फिर \(9\cdot5=45\), और (7+45=52)। घात का काम गुणा से पहले करें।
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\(6x^2+8x^2\) का सरल रूप क्या है?
What is the simplified form of \(6x^2+8x^2\)?
#polynomials
#like terms
#exponents
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A \(14x^2\)
B \(14x^4\)
C \(48x^2\)
D \(2x^2\)
Explanation opens after your attempt
Correct Answer
A. \(14x^2\)
Step 1
Concept
These are like terms, so the coefficients (6+8=14) are added. The exponent (2) does not change.
Step 2
Why this answer is correct
The correct answer is A. \(14x^2\). These are like terms, so the coefficients (6+8=14) are added. The exponent (2) does not change.
Step 3
Exam Tip
ये समान पद हैं इसलिए गुणांक (6+8=14) जुड़ते हैं। घात (2) नहीं बदलती।
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\(14x^5-9x^5\) का सरल रूप क्या है?
What is the simplified form of \(14x^5-9x^5\)?
#polynomials
#like terms
#subtraction
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A \(5x^5\)
B \(23x^5\)
C \(5x^0\)
D \(5x^{10}\)
Explanation opens after your attempt
Correct Answer
A. \(5x^5\)
Step 1
Concept
For like terms, coefficients are subtracted, so \(14x^5-9x^5=5x^5\). The variable and exponent stay the same.
Step 2
Why this answer is correct
The correct answer is A. \(5x^5\). For like terms, coefficients are subtracted, so \(14x^5-9x^5=5x^5\). The variable and exponent stay the same.
Step 3
Exam Tip
समान पदों में गुणांक घटते हैं इसलिए \(14x^5-9x^5=5x^5\)। चर और घात वही रहते हैं।
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(6x+7y+4) में पदों की संख्या कितनी है?
How many terms are there in (6x+7y+4)?
#polynomials
#terms
#basics
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The expression has three terms: (6x), (7y), and (4). Identify terms by plus or minus signs.
Step 2
Why this answer is correct
The correct answer is C. (3). The expression has three terms: (6x), (7y), and (4). Identify terms by plus or minus signs.
Step 3
Exam Tip
इस व्यंजक में (6x), (7y) और (4) तीन पद हैं। पदों को जोड़ या घटाव से अलग पहचानें।
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निम्न में से कौन \(z^4\) का समान पद है?
Which of the following is a like term of \(z^4\)?
#polynomials
#like terms
#identification
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A \(9z^4\)
B \(9z^3\)
C \(z^5\)
D \(9y^4\)
Explanation opens after your attempt
Correct Answer
A. \(9z^4\)
Step 1
Concept
Like terms have the same variable and exponent. In \(9z^4\), \(z^4\) is the same, so it is a like term.
Step 2
Why this answer is correct
The correct answer is A. \(9z^4\). Like terms have the same variable and exponent. In \(9z^4\), \(z^4\) is the same, so it is a like term.
Step 3
Exam Tip
समान पद में चर और घात समान होते हैं। \(9z^4\) में \(z^4\) वही है इसलिए यह समान पद है।
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\(5x^4\cdot2x^3\) का गुणनफल क्या है?
What is the product of \(5x^4\cdot2x^3\)?
#polynomials
#monomial multiplication
#exponents
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A \(7x^7\)
B \(10x^7\)
C \(10x^{12}\)
D (10x)
Explanation opens after your attempt
Correct Answer
B. \(10x^7\)
Step 1
Concept
The coefficients give \(5\cdot2=10\), and \(x^4\cdot x^3=x^7\). So the product is \(10x^7\).
Step 2
Why this answer is correct
The correct answer is B. \(10x^7\). The coefficients give \(5\cdot2=10\), and \(x^4\cdot x^3=x^7\). So the product is \(10x^7\).
Step 3
Exam Tip
गुणांक \(5\cdot2=10\) और \(x^4\cdot x^3=x^7\) है। इसलिए गुणनफल \(10x^7\) है।
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\(42a^7\div6a^4\) का सरल रूप क्या है यदि \(a\neq0\)?
What is the simplified form of \(42a^7\div6a^4\) if \(a\neq0\)?
#polynomials
#monomial division
#exponents
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A \(7a^3\)
B \(36a^3\)
C \(7a^{11}\)
D \(252a^3\)
Explanation opens after your attempt
Correct Answer
A. \(7a^3\)
Step 1
Concept
\(\frac{42}{6}=7\) and \(\frac{a^7}{a^4}=a^3\). Therefore the answer is \(7a^3\).
Step 2
Why this answer is correct
The correct answer is A. \(7a^3\). \(\frac{42}{6}=7\) and \(\frac{a^7}{a^4}=a^3\). Therefore the answer is \(7a^3\).
Step 3
Exam Tip
\(\frac{42}{6}=7\) और \(\frac{a^7}{a^4}=a^3\) है। इसलिए उत्तर \(7a^3\) है।
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\(7^2\cdot7^0\cdot7^4\) का सरल रूप क्या है?
What is the simplified form of \(7^2\cdot7^0\cdot7^4\)?
#polynomials
#mixed exponent law
#exponents
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A \(7^6\)
B \(7^8\)
C \(7^0\)
D \(7^1\)
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Correct Answer
A. \(7^6\)
Step 1
Concept
For the same base, the exponents add as (2+0+4=6). Hence the simplified form is \(7^6\).
Step 2
Why this answer is correct
The correct answer is A. \(7^6\). For the same base, the exponents add as (2+0+4=6). Hence the simplified form is \(7^6\).
Step 3
Exam Tip
समान आधार में घातें (2+0+4=6) जुड़ती हैं। इसलिए सरल रूप \(7^6\) है।
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\(\frac{2^3\cdot4^3}{8^2}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{2^3\cdot4^3}{8^2}\)?
#polynomials
#exponent laws
#simplification
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A \(2^3\)
B \(2^4\)
C \(2^5\)
D \(2^6\)
Explanation opens after your attempt
Correct Answer
C. \(2^5\)
Step 1
Concept
First write (43 =\(2^2\)3 =26 ) and (82 =\(2^3\)2 =26 ). Thus \(\frac{2^3\cdot2^6}{2^6}=2^{3+6-6}=2^3\), so the correct option is \(2^3\).
Step 2
Why this answer is correct
The correct answer is C. \(2^5\). First write (43 =\(2^2\)3 =26 ) and (82 =\(2^3\)2 =26 ). Thus \(\frac{2^3\cdot2^6}{2^6}=2^{3+6-6}=2^3\), so the correct option is \(2^3\).
Step 3
Exam Tip
पहले (43 =\(2^2\)3 =26 ) और (82 =\(2^3\)2 =26 ) लिखें। इसलिए \(\frac{2^3\cdot2^6}{2^6}=2^3\) नहीं बल्कि \(2^{3+6-6}=2^3\); सही विकल्प \(2^3\) है।
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