Mathematics

Q.

The equation (x^{​​​​​​x}) raised to x = 2 is satisfied when x is equal to

Q.

Prove that $3+2\sqrt{5}$ is irrational

Q.

Locate $\sqrt{3}$ on the number line.

Q. Represent $\sqrt{2}$ on the number line.

Q. 40. Find the zeros of the quadratic polynomial 4u2+8u and verify the relationship between the zeros and the coefficient

Q. Prove that root 3 is an irrational number

Q. Find the volume of a pyramid whose square base is 10 cm. and height 8 cm

Q.

Prove that $\surd 3+\surd 5$ is irrational.

Q.

How we can express $0.\overline{001}$ in the form of $\frac{p}{q}$ , where $q\ne 0$

Q.

Question 6
Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers.

Q.

Give Some Examples Where Factors Other Than Income Are Important Aspects Of Our Life?

Q. Without actual division, find which of the following rational numbers are terminating decimals. (i) $\frac{13}{80}$ (ii) $\frac{7}{24}$ (iii) $\frac{5}{12}$ (iv)$\frac{31}{375}$ (v) $\frac{16}{125}$

Q.

What is the value of $5$ million dollars in Indian rupees? (Given one dollar = $75$ rupee​)

Q.

Why any number power 0 =1?

Q.

Using appropriate properties find:$\frac{2}{5}\times \left(\frac{-3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

Q.

Find two rational number between $\sqrt{2}$ and $\sqrt{3}$.

Q.

If one zero of polynomial (a^{​​​​​​2}​​​​​+9)x^{​​​​​​2}+13x+6a is reciprocal of other find value of a.

Q.

Find three different irrational numbers between $\frac{5}{7}$ and $\frac{9}{11}$.

Q.

There Are Two Bags $A$ and $B$. $A$Contains $6RedFlowers$ and $3PinkFlowers$. Where As Bag $B$ Contains$2RedFlowers$ and $7PinkFlowers$. One Flower Is Chosen From a Bag Randomly. What Is the Probability That the Flower Chosen Is $Pink$?

Q. If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is 4.

1. True
2. False

Q.

Represent √7 on number line.

Q.

The sum of two numbers is 8 and the sum of their reciprocals is $\frac{8}{15}$. Find the numbers.

Q.

Express 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Q.

If $x=2+\sqrt{3}$, find the value of $x^3+\frac{1}{x^3}$.

Q. The maximum number of digits in the repeating block of digits of 1/17 is q-1=17-1=16. Does q-1 hold true for all rational numbers?

Q.

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?

1. $\frac{2}{5}$

2. $\frac{3}{5}$

3. $\frac{1}{4}$

4. None of the above

Q. Question 1
Express $0.6+0.\overline{7}+0.4\overline{7}$ In the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Q.

Factorize:$x^3+13x^2+32x+20$.

Q.

If $x=3+2\sqrt{2}$, then find the value of $\sqrt{x}-\frac{1}{\sqrt{x}}$.

Q.

Give an example of each, of two irrational numbers whose:

(i) difference is a rational number.

(ii) difference is an irrational number.

(iii) sum is a rational number.

(iv) sum is an irrational number.

(v) product is a rational number.

(vi) product is an irrational number.

(vii) quotient is a rational number.

(viii) quotient is an irrational number.