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$x^2+7 x+5=0$
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| Draw a circle with center O and radius 3 cm |
| ↓ |
| Take any point P on the circle |
| ↓ |
| Draw ray OP |
| ↓ |
| Draw perpendicular to ray OP from point P |
The first term of an A.P. is 5 and the common difference is 4 . Complete the following activity to find the sum of first 12 terms of this A.P.
A die is rolled. Complete the following activity to find the probability of getting a prime number on the upper face of the die :
A die is rolled. S is the sample space.
A die is rolled. S is the sample space.
In figure 1.66, seg PQ || seg DE, A(Δ PQF) = 20 units, PF = 2 DP, then find A(DPQE) by completing the following activity.
A(Δ PQF) = 20 units, PF = 2 DP, Let us assume DP = x. ∴ PF = 2x
$DF = DP +\square=\square+\square=3 x$
In Δ FDE and Δ FPQ,
∠FDE ≅ ∠ .......... corresponding angles
∠FED ≅ ∠ ......... corresponding angles
∴ Δ FDE ~ Δ FPQ .......... AA test
$\therefore \frac{ A (\Delta FDE )}{ A (\Delta FPQ )}=\frac{\square}{\square}=\frac{(3 x )^2}{(2 x )^2}=\frac{9}{4}$
$A (\Delta FDE )=\frac{9}{4} A(\Delta FPQ )=\frac{9}{4} \times \square=\square$
$A (\square DPQE )= A (\Delta FDE )- A (\Delta FPQ )$
$\quad=\square-\square$
$\quad=\square$
→A(Δ PQF) = 20 units, PF = 2 DP, Let us assume DP = x. ∴ PF = 2x
$DF = DP +\square=\square+\square=3 x$
In Δ FDE and Δ FPQ,
∠FDE ≅ ∠ .......... corresponding angles
∠FED ≅ ∠ ......... corresponding angles
∴ Δ FDE ~ Δ FPQ .......... AA test
$\therefore \frac{ A (\Delta FDE )}{ A (\Delta FPQ )}=\frac{\square}{\square}=\frac{(3 x )^2}{(2 x )^2}=\frac{9}{4}$
$A (\Delta FDE )=\frac{9}{4} A(\Delta FPQ )=\frac{9}{4} \times \square=\square$
$A (\square DPQE )= A (\Delta FDE )- A (\Delta FPQ )$
$\quad=\square-\square$
$\quad=\square$
Write the values of the following trigonometric ratios.
$\sin 60^{\circ}=\frac{⬜}{⬜}$
→$\sin 60^{\circ}=\frac{⬜}{⬜}$
Complete the following table using given information.
Complete the following table to draw the graph of $2x – 6y = 3$
→Complete the following activity to find the length of hypotenuse of right angled triangle, if sides of right angle are $9 cm$ and $12 cm$.
Activity: In $\triangle P Q R, m \angle P Q R=90^{\circ}$
By Pythagoras Theorem,
$P Q^2+\square=P R^2$
$\therefore P R^2=9^2+12^2$
$\therefore P R^2=\square+144$
$\therefore P R^2=\square$
$\therefore P R=15$
$\therefore$ Length of hypotenuse of triangle PQR is $\square cm$.
→Activity: In $\triangle P Q R, m \angle P Q R=90^{\circ}$
By Pythagoras Theorem,
$P Q^2+\square=P R^2$
$\therefore P R^2=9^2+12^2$
$\therefore P R^2=\square+144$
$\therefore P R^2=\square$
$\therefore P R=15$
$\therefore$ Length of hypotenuse of triangle PQR is $\square cm$.
To draw the graph of $4 x+5 y=19$, complete the following activity to find $y$, when $x=1$.
→A card is drawn from a well-shuffled pack of 52 playing cards. Complete the following activity to find the probability of the event that the card drawn is a red card:
Suppose S is the sample space. .. n(S) = 52.
Event A Card drawn is a red card.
Suppose S is the sample space. .. n(S) = 52.
Event A Card drawn is a red card.