Question 3 :
Use Euclid's division algorithm to find the HCF of : 196 and 38220
Question 4 :
For any positive integer n, $n^3$– n is divisible by 6. Is it True or False?
Question 5 :
Using Euclid’s division algorithm, find if this pair of numbers is co-prime: 847, 2160.
Question 6 :
The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after _______.
Question 7 :
Solve the following pair of equations by substitution method: $s-7t+42=0 ; s-3t=6$
Question 8 :
What is/ are the algebraic method/ methods that can solve a pair of linear equations?
Question 9 :
Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: $5x – 8y + 1 =0 ; 3x - \frac{24}{5}y + \frac{3}{5} = 0$
Question 11 :
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per km?
Question 12 :
Solve the following pair of linear equations by the substitution method : $x + y = 14 ; x - y = 4$
Question 13 :
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where
Question 14 :
A pair of linear equations $a_1x + b_1y + c_1 = 0$; $a_2x + b_2y + c_2 = 0$ is said to be inconsistent, if
Question 15 :
The smallest value of k for which the equation $x^{2} + kx + 9 = 0$ has real roots, is
Question 16 :
The number of zeroes, the polynomial p (x) = $(x – 2)^2 + 4$ can have, is
Question 17 :
The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.
Question 18 :
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.
Question 19 :
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates ofthe vertices of the triangle formed by these lines and the y axis.
Question 20 :
Solve the following pair of linear equations by the elimination method and the substitution method : $3x + 4y = 10 ~and ~2x – 2y = 2$
Question 21 :
Solve the following pair of linear equations: $\frac{x}{a} - \frac{y}{b} = 0 ; ax + by = a^2 + b^2$
Question 22 :
Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Question 24 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a51273b23058497991f.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 25 :
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given: $-2\sqrt{3}$, -9
Question 26 :
The zeroes of $3x^4+6x^3–2x^2–10x–5$ are $\sqrt{\frac{5}{3}}$, $-\sqrt{\frac{5}{3}}$, -1 and -1. Is it true or false?
Question 27 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $\frac{21}{8}$, $\frac{5}{16}$