Question
Complete the following cumulative frequency table:
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In □ABCD, side BC || side AD, side AB ≅ side DC. If ∠A = 72°, then find the measures of ∠B and ∠D.
Construction: Draw seg BP ⊥ side AD, A – P – D, seg CQ ⊥ side AD, A – Q – D.
Construction: Draw seg BP ⊥ side AD, A – P – D, seg CQ ⊥ side AD, A – Q – D.
In the adjoining figure, two circles with centres at A and B, and of radii $5\ cm$ and $3\ cm$ touch each other internally.
If the perpendicular bisector of AB meets the bigger circle in P and Q,
find the length of PQ.
→If the perpendicular bisector of AB meets the bigger circle in P and Q,
find the length of PQ.
Given below is the bar graph indicating the marks obtained out of 50 in mathematics paper by 100 students. Read the bar graph and answer the following questions:
- It is decided to distribute workbooks on mathematics to the students obtaining less than 20 marks, giving one workbook to each of such students. If a workbook costs Rs. 5, what sum is required to buy the workbooks?
- Every student belonging to the highest mark group is entitled to get a prize of Rs. 10. How much amount of money is required for distributing the prize money?
- Every student belonging to the lowest mark-group has to solve 5 problems per day. How many problems, in all, will be solved by the students of this group per day?
- State whether true or false:
- 17% students have obtained marks ranging from 40 to 49.
- 59 students have obtained marks ranging from 10 to 29.
- What is the number of students getting less than 20 marks?
- What is the number of students getting more than 29 marks?
- What is the number of students getting marks between 9 and 40?
- What is the number of students belonging to the highest mark group?
- What is the number of students obtaining more than 19 marks?
In the given figure, POQ is a diameter and PQRS is a cyclic quadrilateral. If $\angle\text{PSR}=150^\circ,$ find $\angle\text{RPQ}.$
→Construct ∆XYZ, such that XY + XZ = 10.3 cm, YZ = 4.9 cm, ∠XYZ = 45°.
If $p(x) = 5 - 4x + 2x^2$, find:
→- $p(0)$
- $p(3)$
- $p(-2)$
The polynomial $p(x)=x^4-2 x^3+3 x^2-a x+b$ when divided by $(x-1)$ and $(x+1)$ leaves the remainders 5 and 19 respectively.
Find the values of $a$ and $b$. Hence, find the remainder when $p(x)$ is divided by $(x-2)$.
→Find the values of $a$ and $b$. Hence, find the remainder when $p(x)$ is divided by $(x-2)$.
In figure, $\angle\text{AOB}=90^\circ,$ $AC = BC, OA = 12cm$ and $OC = 6.5cm$.
Find the area of $\triangle\text{AOB}.$
→Find the area of $\triangle\text{AOB}.$
An equilateral triangle of side 9cm is inscribed in a circle. Find the radius of the circle.
In figure, ABCD is a trapezium in which $AB = 7cm, AD = BC = 5cm, DC = x cm$, and distance between AB and DC is $4cm$. Find the value of x and area of trapezium ABCD.
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