Question 13 Marks
Draw frequency polygon of the following distribution
Weight of packet | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
Number of packets | 3 | 5 | 8 | 5 | 4 |
Question 23 Marks
In a school the weekly pocket money of 50 students is as follows. Find mode of pocket money.
Pocket money (in ₹) | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
No. of students | 2 | 8 | 12 | 14 | 8 | 6 |
Question 33 Marks
Draw the histogram.
Wages (in ₹) | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 |
No. of workers | 3 | 8 | 12 | 6 | 4 |
Question 43 Marks
The table below gives the ages of 120 drivers of cars involved in accidents during a certain year. Complete the table and draw a pie diagram.
Age of driver (in years) | Number of drivers | Central angle |
Under 20 | 25 | 75° |
20 – 40 | 50 | _____ |
40 – 60 | 35 | 105° |
Over 60 | 10 | 30° |
Question 53 Marks
Complete the following activity to find median marks of the students
Question 63 Marks
Complete the activity to find mean by direct method. Weekly wages (Rupees) | Class mark (𝑥𝑖) | No. of workers (𝑓𝑖) | 𝑥𝑖𝑓𝑖 |
1000 – 2000 | 1500 | 25 | 37500 |
2000 – 3000 | _____ | 45 | 112500 |
3000 – 4000 | 3500 | 50 | ______ |
4000 – 5000 | 4500 | 30 | ______ |
| | N = 150 | ∑ 𝑓𝑖 𝑥𝑖 =_____ |
Mean =$\frac{\Sigma f i x i}{\Sigma f i}$
$=\frac{\square}{150}=$_____
View full question & answer→Question 73 Marks
The following table shows the funds collected by 50 students for flood affected people. Find the mean of the funds
Question 83 Marks
A bag contains 8 red balls and some blue balls. If one ball is drawn randomly the probability of drawing a red ball to a blue ball are in the ratio 5 : 2, determine the probability of drawing a blue ball from the bag.
Question 93 Marks
Three horses A ,B and C are in a race. A is twice as likely to win as B and B is twice as likely to win as C What is their individual probability of winning?
Question 103 Marks
A missing helicopter is reported to have crashed somewhere in the rectangular region shown in the figure .What is the probability that it crashed inside the lake shown in the figure ?
Question 113 Marks
The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.
Question 123 Marks
A bag contains 5 white balls and some blue balls. If the probability of drawing a blue ball is double that of a white ball, determine the number of blue balls in the bag .
Question 133 Marks
A box contains $5$ strawberry chocolates, $6$ coffee chocolates and $2$ peppermint
chocolates. If one of the chocolates is picked from the box at randomly, Find the
probability of the following events by completing the activity.
(i) Event A : it is a coffee chocolate.
(ii) Event B : it is a peppermint chocolate.Activity : Let 'S' is the sample space.
$\therefore n(S) = 5+6+2 = 13$
(i) Event A : it is a coffee chocolate
$\therefore n(A) =$ …………
$\therefore P(A) = \frac{\square}{n(S)}$ ………… Formula
$\therefore P(A)=\frac{\square}{13}$
(ii) Event B : it is a peppermint chocolate.
$\therefore n(B) =$ …………
$\therefore P(B) =\frac{\square}{n(S)}$ ………… Formula
$\therefore P(B) =\frac{\square}{13}$
AnswerLet 'S' be the sample space.
$\therefore \mathrm{n}(\mathrm{S})=5+6+2=13$
Event B : it is a peppermint chocolate.
$\therefore n(B)=2$
$\therefore P(B)=\frac{n(B)}{n(S)} \quad \ldots ..$ Formula
$\therefore P(B)=\frac{2}{13}$
View full question & answer→Question 143 Marks
Prepare Business to consumer (B2C) tax invoice using given information. Write the name
of the supplier, address, state, date of invoice number, GSTIN etc. as per your choice.
Perform the following activities:
Supplier: M/s. ........................... Address: ......................................
State : ............... Date : ............. Invoice No.: .......................GSTIN: ...........................
Particulars : (i) Rate of mobile battery – Rs. 300, Rate of GST 12%, HSN 8507,
(ii) Rate of Headphone – Rs. 700, Rate of GST 18%, HSN 8518, 1.
Question 153 Marks
Pushpmala has invested Rs.24000 and purchased shares FV Rs.20 at a premium of Rs.4 Find the number of shares she purchased. Complete the given activity.
Answer FV = Rs.20, Premium = Rs.4
MV = FV + ___
= ___+ ___
= ___
Number of shares = $\frac{\text { Total investment }}{\text { M.V. }}$
$=\frac{24000}{\square \cdot}$
= ____ shares
View full question & answer→Question 163 Marks
Fill in the blanks given in the contract note of sale-purchase of shares. (B - buy S - sell)
No.of shares | M.V.of shares | Total Value | Brokerage 0.2% | 18% GST on Brokerage | Total Value of shares |
75 B | Rs.200 | | | | |
100S | Rs.45 | | | | |
Question 173 Marks
From the information, prepare the tax invoice for business to customer. (B2C)Write
any name, address, date, etc.
Supplier: M/s .............. Address.............Date .........
Invoice No. ............................... GSTIN………..............
Name of products:
(i) Pickle bottle Rs.75, 1 piece, Rate of GST 12%, HSN1509
(ii) Tea powder pouch Rs. 60, 1 piece, Rate of GST 5% , HSN4807
(iii) Perfume bottle Rs.225, 1 piece, Rate of GST 18%, HSN8519
Question 183 Marks
Decide whether 301 is term of given sequence 5,11,17,23,.......
Activity :- Here, d = ____ therefore this sequence is an A.P.
a= 5, d= ____
Let nth term of this A.P. be 301.
$t _{ n }$ = a + (n-1) ____
301 = 5 + (n-1)×6
301 = 6n-1
n =$\frac{302}{6}$ = ____
But n is not positive integer
Therefore, 301 is ____ the term of sequence 5,11,17,23.........
View full question & answer→Question 193 Marks
Find the sum of natural numbers between 1 to 140, which are divisible by 4.
Activity :- Natural numbers between 1 to 140 divisible by 4 are,
4,8,12,16,......136
Here d=4, therefore this sequence is an A.P.
a=4, d=4,$t _{ n }=136, \quad S _{ n }=?$
$t_n=a+(n-1) d$
_____= 4+(n-1)×4
_____= (n-1)×4
n =_____
Now,
$S _{ n }=\frac{ n }{2}+\left[ a + t _{ n }\right]$
$S_n=17 \times$____
$S _{ n }=$____
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is _____
View full question & answer→Question 203 Marks
Determine the sum of first $100$ terms of given A.P.$ 12,14,16,18,20........$
Activity :- here, a=12, ____ n=100, $S_{100}=?$
$ S _{ n }=\frac{ n }{2}[\square+( n -1) d ]$
$S _{100}=\frac{\square}{2}[24+(100-1) d ]$
$= 50 ( 24 +$ ____ )
= _____
View full question & answer→Question 213 Marks
Kalpana saves some amount every month. In first three months she saves $Rs.100,$
$Rs.150$ and $Rs.200$ respectively. In how many months will she save $Rs.1200?$
Activity :- Kalpana’s monthly saving is $Rs.100,Rs.150,Rs.200........Rs.1200$
Here $d=50.$Therefore this sequence is an A.P.
$a=10, d=50,$ $t _{ n }$___$ n=?$
$t _{ n }= a+(n-1)$____
_____$= 100+(n-1)\times 50$
$\frac{\square}{50}=n-1$
$n=\square$
therefore, she saves $Rs.1200$ in ____ months.
View full question & answer→Question 223 Marks
how many two-digit numbers are divisible by 5?
Activity :- Two-digit numbers divisible by 5 are, 10,15,20........95.
Here, d=5, therefore this sequence is an A.P.
Here a=10, d=5, Tn=95, n=?
$t _{ n }$= a+(n-1____)
____= 10+(n-1)×5
____= (n-1)×5
____= (n-1)
therefore n=____
there are ____two-digit numbers divisible by 5.
View full question & answer→Question 233 Marks
Form a quadratic equation such that one of its roots is 5. Form a quadratic equation for it and write. ( For the formation of word problem you can use quantities like age, rupees or natural numbers.) (sample solution for the above example is given below students can take another number to form another example)
Question 243 Marks
Complete the following activity to solve the given word problem. Sum of squares of two consecutive even natural numbers is 244 then find those numbers.
Activity: let the first even natural number be X,
Therefore its consecutive even natural number will be = (.....)
By the given condition,
$X^2+(x+2)^2=244$
$X^2+X^2+4 x+4-(\ldots .)=0$
$2 x^2+4 x-240=0$
$\quad X^2+2 x-120=0$
$X^2+(\ldots \ldots . .)-(\ldots \ldots)-120=0$
$X (x+12) – (…..) (x+12) = 0$
$(x + 12) (x – 10) = 0$
$X = (……) / X = 10$
But natural number cannot be negative $x = -12$ is not possible.
Therefore first even natural number is $x = 10.$
Second even consecutive natural number $= x+ 2= 10+ 2= 12.$
View full question & answer→Question 253 Marks
Complete the following activity to solve the given quadratic equation by formula method.$2 x^2+13 x+15=0$
$\text { Activity: } 2 x^2+13 x+15=0$
$a=(\ldots \ldots), b=13, c=15$
$b^2-4 a c=(13)^2-4 \times 2 \times(\ldots \ldots)$
$=169-120$
$b^2-4 a c=49$
$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$
$x=\frac{-(\ldots \ldots) \pm \sqrt{49}}{4}$
$x=\frac{-13 \pm(\ldots)}{4}$
$x=\frac{6}{4} \quad \text { or } \quad x=\frac{-20}{4}$
X = (….) or x = (….)
View full question & answer→Question 263 Marks
For the equation 3 ? − 2 ? = 17 find the value of x when y = −1 and find the value of y when x = 3.
Question 273 Marks
A person starts a job with some fixed salary and yearly increment. After 4 years his salary is Rs.15000 and after 10 years it becomes Rs.18000. Then find his monthly salary and increment.
Question 283 Marks
The solution of the equation ? ? + b y + 5 = 0 and ? ? − ? ? − 12 = 0 is (2, -3) Find the values of a and b.
Question 293 Marks
The graph of the equations 2 ? − ? − 4 = 0 and ? + ? + 1 = 0 intersect each other in point P (a, b) then find the coordinates of P?
Question 303 Marks
The length of the rectangle is 5 more than twice its breadth. The perimeter of a rectangle is 52 cm then find the length of the rectangle.
Question 313 Marks
Solve: 99x + 101y = 499; 101x + 99y = 501
Question 323 Marks
Solve: 4m – 2n = - 4; 4m + 3n =16
Question 333 Marks
Difference between two numbers is 3, the sum of three times the bigger number and two times the smaller number is 19. Then find the numbers.
Question 343 Marks
Solve by Cramer’s rule, 3x – 4y = 10; 4x + 3y = 5
Question 353 Marks
Ajay is younger than Vijay by 3 years. The sum of their ages is 25 years, what is the age of Ajay.
Question 363 Marks
Solve the given simultaneous equations graphically ? + ? = 5 and ? = 5,
Question 373 Marks
The angles of a triangle ABC are in the ratio 1:2:3, show this information in pie diagram.
Question 383 Marks
Observe the frequency polygon given alongside
Prepare frequency table and find mean of the net asset value.
Question 393 Marks
120 students of standard 10 were asked which game they
like and from this information pie chart is prepared, observe
the pie diagram and answer the questions.
a) How many students like to play Tennis?
b) What will be central angle for Kho-Kho?
c) How many students like Kabaddi?
Question 403 Marks
If two dice are rolled simultaneously, find the probability of the following events.
i) Event A : The sum of the digits on the upper faces is at least 10.
ii) Event B : The sum of the digits on the upper faces is 33.
Question 413 Marks
If Three coins are tossed simultaneously, find the probability of the
following events.
i) Event A : To get no heads.
ii) Event B : To get at least two heads.
Question 423 Marks
If One coin and one die are thrown simultaneously, find the probability of the following events.
i) Event A : To get a tail and an even number.
ii) Event B: To get head and an odd number.
Question 433 Marks
A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,
(i) a red balloon
(ii) a blue balloon.
Question 443 Marks
Mr. Trivedi invested Rs.45,000 in shares of face value Rs.100 at market value Rs.125. If the company declared 30% dividend at the end of the year, what was the income from dividend?
Question 453 Marks
Mr. Hariram investment in shares is given below. Find his total investment in shares.
Company A: 200 shares, face value = Rs.100 Premium = Rs. 25
Company B: 500 shares, face value = Rs.100 Market Value = Rs. 200
Company C: 50 shares, face value =Rs 100 Discount =Rs.20
Question 463 Marks
If 50 shares of FV Rs.20 were purchased for MV of Rs.30. Company declared 30% dividend on the shares then find (i) Sum invested (ii) Dividend received (ii) Rate of return
Question 473 Marks
Hamid purchased some educational stationary and paid GST of Rs.1800. He sold all educational stationary Nishaben and collected GST of Rs.2100. Find the GST CGST and SGST to be paid
Question 483 Marks
A share of the value Rs. 100 was purchased for Rs.150. The company declared a dividend of 60%. What is the rate of return on investment?
Question 493 Marks
What is the sum of an odd numbers between 1 to 50
Question 503 Marks
The $n^{\text {th }}$ term of an A.P $5,8,11,14 \ldots \ldots$ is 68. Find $n=?$
View full question & answer→Question 513 Marks
Merry got a job with salary Rs.15000 per month. If her salary increases by Rs.100 per month, how much would be her salary after 20 months?
Question 523 Marks
If $t_n=2 n-5$ is the nth term of an A.P., then find its first five terms.
View full question & answer→Question 533 Marks
For an A.P., $t_4=12$ and its common difference $d=-10$, then find $t_n$.
View full question & answer→Question 543 Marks
Find the sum of three-digit natural numbers, which are divisible by 4.
Question 553 Marks
Find the first terms and common difference of an A.P. whose $t_8=3$ and $t_{12}=52$.
View full question & answer→Question 563 Marks
Find $S_{10}$ if $a=6$ and $d=3$
View full question & answer→Question 573 Marks
Find 27th and nth term of given A.P. 5,2,-1,-4.............
Question 583 Marks
12,16,20,24………Find 25th term of this A.P.
Question 593 Marks
Solve the following quadratic equations by formula method.
a) $5 m^2-4 m-2=0$
b) $Y^2+\frac{1}{3} y=2$
View full question & answer→Question 603 Marks
Solve the following quadratic equation.
$\sqrt{3} x^2+\sqrt{2} x-2 \sqrt{3}=0$
View full question & answer→Question 613 Marks
Mukund has Rs. 50 more than Sagar. If the product of the amount they have is 15,000 then find the amount each has.
Question 623 Marks
If the roots of the given quadratic equations are real and equal then find the value of ‘k’.
kx (x-2) + 6 = 0
Question 633 Marks
Form a quadratic equation if the roots of the quadratic equation are $2+\sqrt{7}$ and $2-\sqrt{7}$
View full question & answer→Question 643 Marks
Write any two linear equations in two variables in which the value of one variable is 12 and the other 10
Question 653 Marks
I held a number 75 in my mind.
Write any condition showing the relation between their digits.
Write the condition showing relation between the number and the number obtained by interchanging the digits.
Question 663 Marks
From the railway station I took a rickshaw to go home. It is decided that I have to pay Rs. X for the first kilometre and for each kilometre Rs. Y for the next. For 10 kilometres the fare is Rs. 40 and for 16 kilometres fare is Rs. 58. Find the fare for the first kilometre.
Question 673 Marks
Form the simultaneous linear equation using the determinants.
$D=\left|\begin{array}{cc}4 & -3 \\ 2 & 5\end{array}\right| \quad D x=\left|\begin{array}{cc}5 & -3 \\ 9 & 5\end{array}\right| \quad D y=\left|\begin{array}{ll}4 & 5 \\ 2 & 9\end{array}\right|$
View full question & answer→
