Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c26273b230584979a83.PNG' />
During the medical check-up of 35 students of a class, their weights were recorded as given above. Draw a less than type ogive for the given data and pick the correct option representing it.
Question 2 : <img style='object-fit:contain' src='61b19b06273b230584979948' />
The distribution given above gives the weights of 30 students of a class. Find the median weights of the students.
Question 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bff273b230584979a57.PNG' />
A survey conducted on 20 households in a locality by a group of students resulted in the above frequency table for the number of family members in a household. Find the mode of this data.
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c14273b230584979a70.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 mean number of letters in the surnames.
Question 5 : <img style='object-fit:contain' src='61b19a62273b230584979934' />
A class teacher has the above absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfb273b230584979a53.PNG' />
Find the mean of the above given data.
Question 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c10273b230584979a6b.PNG' />
The above distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mean of this data.
Question 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1a273b230584979a76.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 mode number of letters in the surnames.
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0f273b230584979a6a.PNG' />
The above distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Find the mode of the data.
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c09273b230584979a62.PNG' />
A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the above given data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
Question 11 : <img style='object-fit:contain' src='61b19a85273b230584979938' />
Consider the above distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using appropriate method.
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 : <img style='object-fit:contain' src='61b19afd273b230584979947' />
The length of 40 leaves of a plant are measured correct to the nearest milimetre and the data obtained is represented in the above table. Find the median length of leaves.
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c09273b230584979a63.PNG' />
The above distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency $f$.
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c12273b230584979a6d.PNG' />
The above table shows the ages of the patients admitted in a hospital during a year. Find the mode of the data given above.
Question 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfd273b230584979a55.PNG' />
The table above gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers.
Question 17 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfb273b230584979a52.PNG' />
The distribution above shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets.
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c02273b230584979a5a.PNG' />
A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the above data was obtained. Find the median height.
Question 20 :
Find the sum of the first 40 positive integers divisible by 6.
Question 21 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.
Question 22 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 23 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?
Question 24 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there in the AP?
Question 25 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.
Question 26 :
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 27 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 28 :
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum offirst n terms.
Question 29 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc6273b230584979a13.JPG' />
In the above fig. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in above figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
Question 31 :
11th term of the AP: – 3, -0.5, 2, . . ., is
Question 32 :
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
Question 33 : <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 35 :
Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$
Question 36 :
Check whether the following is quadratic equation : $(x+1)^2 = 2(x-3)$
Question 37 :
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the cost of each article?
Question 39 :
Check whether the following is a quadratic equation: $(x – 3)(2x +1) = x(x + 5)$
Question 40 :
Find the roots of the quadratic equation (by using the quadratic formula): $-3x^2+5x+12=0$
Question 41 :
Find the roots of the following quadratic equation (by the factorisation method): $2x^2+\frac{5}{3}x-2=0$
Question 42 :
Represent the following situation in the form of quadratic equations: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Question 43 :
Sum of the areas of two squares is $468 m^2$. If the difference of their perimeters is 24 m, find the sides of the two squares.
Question 44 :
The roots of the quadratic equation $ax^2 + bx + c = 0$ are given by $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$. TRUE or FALSE ?
Question 45 :
Represent the following situation in the form of a quadratic equation : Rohan’s mofher is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Question 46 :
State true or false:
A quadratic equation in the variable x is an equation of the form $ax^2 + bx + c = 0$, where a, b and c are real numbers and a≠ 0.
Question 47 :
Represent the following situation in the form of quadratic equations : The area of a rectangular plot is $528 m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Question 49 :
A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Question 52 :
Represent the following situation in the form of quadratic equations: The product of two consecutive positive integers is 306. We need to find the integers.
Question 53 :
Is the following situation possible? If so, determine their present ages.The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Question 54 :
Can we construct a triangle similar to a given triangle as per the given scale factor ?
Question 55 :
From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, what is the perimeter of the triangle PCD?
Question 56 :
Two circles with centres O and $O ^ { \prime }$ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and $O ^ { \prime }P$ are tangents to the two circles. What is the length of the common chord PQ?
