- Observe the given Venn diagram and answer the following questions.
- Write the common elements of sets \(A\) and \(B\).[1]
- Write a proper subset of set \(A\).[1]
- If \(t\) is removed from set \(B\), then write the relation of sets \(A\) and \(B\) in set notation.[1]
-
The common elements of sets \(A\) and \(B\) are those in the intersection region, whihch is
\( A \cap B = \{r, s\} \) -
From the Venn diagram, \(A = \{p, q, r, s\}\).
One proper subset of \(A\) is \(\{p, q\}\)Number of Elements Proper Subsets (examples) Count 0 \(\emptyset\) 1 1 \(\{p\}, \{q\}, \{r\}, \{s\}\) 4 2 \(\{p,q\}, \{p,r\}, \{p,s\}, \{q,r\}, \{q,s\}, \{r,s\}\) 6 3 \(\{p,q,r\}, \{p,q,s\}, \{p,r,s\}, \{q,r,s\}\) 4 Total Proper Subsets 15 -
If \(t\) is removed, then new set \(B = \{r, s\}\)
Then the relation of sets \(A\) and \(B\) in set notation is \( B \subset A \). - Ram obtained \(45\) marks in math subject of class \(8\) exam.
- Write it in scientific notation.[1]
- Convert it into binary number system.[2]
- Convert \(0.\overline{35}\) into a fraction.[1]
- A shopkeeper marked the price Rs 60000 for a computer and sold it with \(10\%\) discount.
- If marked price and discount percent are denoted by \(MP\) and \(D\%\) respectively, write the formula to find the discount amount.[1]
- What will be the discount amount if \(10\%\) discount is given?[1]
- Selling after \(10\%\) discount, it becomes a profit of Rs 4000. Find the cost price.[2]
- Formula to find the discount amount:
Discount Amount = \( \dfrac{D}{100} \times MP \) - Discount amount
Marked Price (MP) = Rs. 60,000
Discount = \(10\%\)
Thus
Discount Amount = \( \dfrac{10}{100} \times 60,000 = 6,000 \)
So, the discount amount is Rs. \(6,000\). - Cost price
Marked Price (MP) = Rs. 60,000
Discount = \(10\%\)
Thus
Selling Price (SP) = 90% of MP = \( \dfrac{90}{100} \times 60,000 = 54,000 \)
Profit = Rs. 4,000
We know
CP =SP-profit= \(54,000 - 4,000 = 50,000\)
So, the cost price was Rs. 50,000. - Roshani deposited Rs 40,000 in a bank to gain interest at the rate of 10% per annum for 18 months.
- Write the formula to find interest.[1]
- How much interest will she gain?[2]
- How much amount has to be returned to her by the bank?[1]
- If Roshani divides the interest she got to Manisha and Anushka in the ratio 2:3, how much money does each get?[2]
- Formula to find interest:
Interest (I) = \( \dfrac{P \times T \times R}{100} \) - Interest gained:
Principal (P) = Rs. 40,000
Rate (R) = 10%
Time (T) = 18 months = \( \dfrac{18}{12} \) years = 1.5 years
Thus,
Interest (I) = \( \dfrac{40,000 \times 1.5 \times 10}{100} = 6,000 \)
So, she will gain Rs. 6,000 as interest. - Total amount to be returned (Amount):
Principal (P) = Rs. 40,000
Interest (I) = Rs. 6,000
Thus,
Amount (A) = P + I = 40,000 + 6,000 = 46,000
So, the bank has to return Rs. 46,000 to her. - Money received by Manisha and Anushka:
Total Interest = Rs. 6,000
Ratio = 2:3
Sum of ratios = 2 + 3 = 5
Thus,
Manisha's share = \( \dfrac{2}{5} \times 6,000 = 2,400 \)
Anushka's share = \( \dfrac{3}{5} \times 6,000 = 3,600 \)
So, Manisha gets Rs. 2,400 and Anushka gets Rs. 3,600. - The given figure is a rectangular-shaped land belonging to Susma, and there is a swimming pool having 14 m diameter inside it. The length and breadth of the land are 100 m and 60 m respectively.
- Write the formula to find the area of a rectangle. [1]
- Find the area of the land. [1]
- Find the area of the land excluding the swimming pool. [2]
- Is a 90 m long wire enough to fence the swimming pool with 2 rounds of wire? Give a reason. [2]
- Area of rectangle formula
We know that,
Area (\( A \)) = Length (\( l \)) \(\times\) Breadth (\( b \)) - Area of the land
Given: Length (\( l \)) = 100 m, Breadth (\( b \)) = 60 m
Area of land (\( A_l \)) = \( 100 \times 60 = 6000 \) m² - Area excluding the swimming pool
The diameter (\( d \)) of pool = 14 m, so Radius (\( r \)) = 7 m.
Area of pool (\( A_p \)) = \( \pi r^2 = \frac{22}{7} \times 7^2 = 154 \) m²
Remaining Area = Area of land - Area of pool
\( = 6000 - 154 = 5846 \) m² - Wire adequacy check
Circumference of pool (\( C \)) = \( \pi d = \frac{22}{7} \times 14 = 44 \) m
Length of wire required for 2 rounds = \( 2 \times 44 = 88 \) m
Reason: Yes, a 90 m wire is enough because the required length (88 m) is less than the available length (90 m). - Evaluate: \((5a + x)^0\).[1]
- Simplify: \(\dfrac{x^2 + 2xy + y^2}{x^2 - y^2} \times \dfrac{x - y}{x + y}\).[2]
- Two algebraic expressions are given: \(3x^2 - 12\) and \(x^2 - 8x + 12\).
- Find the H.C.F. of the given expressions.[2]
- For what value of \(x\) does the expression \(3x^2 - 12\) become zero?[2]
- Two equations are given below: \(x + y = 6\) and \(x - y = 1\).
- Solve by using a graph.[2]
- What is this system of equations called?[1]
- In the adjoining figure, \(AB \parallel CD\).
- Write the name of a pair of corresponding angles.[1]
- Find the value of \(a\).[2]
- If the value of \(c\) is not \(50^\circ\), what is the relation of lines \(AB\) and \(CD\)? Write it.[1]
- \(\triangle ABC\) and \(\triangle PQR\) are two triangles.
- By which axiom are the given triangles congruent? Write it. Also write the name of a pair of corresponding angles.[2]
- Construct a rectangle \(PQRS\) with sides \(PQ = 8cm\) and \(QR = 5cm\).[3]
- What type of tessellation is given in the figure?[1]
- If \(A(-2,3)\), \(B(3,5)\), and \(C(6,1)\) are vertices of \(\triangle ABC\), write down the coordinates of the image of \(\triangle ABC\) after reflecting on the \(x\)-axis and sketch both figures on graph paper.[3]
- In the given figure, the bearing of point \(Q\) from point \(P\) is \(45^\circ\). Find the bearing of point \(P\) from \(Q\).[2]
- The marks secured by a student are given in the table below:
- Find the mode from the above data.[1]
- Present it in a pie chart.[2]
| Subject | Nepali | Math | Science | English |
|---|---|---|---|---|
| Marks | \(70\) | \(40\) | \(50\) | \(40\) |
No comments:
Post a Comment