Question 1 :
Can $x^2-1$ be quotient on division of $x^6+2x^3+x-1$ by a polynomial in x of degree 5?
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be2273b230584979a37.png' />
Look at the graph given 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 3 :
Find the roots of the following quadratic equation by factorisation: $\sqrt{2}x^2+7x+5\sqrt{2}=0$
Question 5 :
Values of $k$ for which the quadratic equation $2x^2–kx+k=0$ has equal roots is
Question 6 :
Choose the correct answer from the given four options in the question: If two positive integers p and q can be expressed as $p = ab^2$ and $ q = a^3$ b; a, b being prime numbers, then LCM (p, q) is _____ .
Question 7 :
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Question 8 :
The wickets taken by a bowler in 10 cricket matches are as follows: 2, 6 ,4 ,5, 0, 2, 1, 3, 2, 3. Find the mode of the data.
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0b273b230584979a65.PNG' />
A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c17273b230584979a73.PNG' />
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as given above. Determine the median number of letters in the surnames.
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ab8273b23058497993e.PNG' />
The above given distribution shows the number of runs scored by some top batsmen of the world in one-day inetrnational cricket matches. Find the mode.
Question 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c15273b230584979a71.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median.
Question 13 :
In the following AP, find the missing term: 2, __ ,26
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc3273b230584979a0e.JPG' />
In the above fig, find the missing value corresponding to (iii)
Question 15 :
The sum of the third and the seventh termsof an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Question 16 :
30th term of the AP: 10, 7, 4, . . . , is
Question 17 :
A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red ?
Question 18 :
Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. If the queen is drawn and put aside, what is the probability that the second card picked up is a queen?
Question 19 :
The points (4, 5), (7, 6) and (6, 3) are collinear. State true or false.
Question 20 :
Find a relation between x and y if the points $\left(x, y\right)$, $\left(1, 2\right)$ and $\left(7, 0\right)$ are collinear.
Question 22 :
Find the coordinates of the points of trisection of the line segment joining $\left(4, -1\right)$ and $\left(-2, -3\right)$.
Question 23 :
The points (0, 5), (0, –9) and (3, 6) are collinear. State true or false.
Question 24 :
A pair of linear equations which has no solution, is called an __________________ pair of linear equations.
Question 25 :
Other than algebraical methods, how can the pair of linear equations be solved?
Question 26 :
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Question 27 :
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?
Question 28 :
Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis.
Question 29 :
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?
Question 30 :
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60$^{\circ}$, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be?(in degrees)
