Question
In the given figure, $AB = AC$. Show that $AD > AB$.
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If $x=\frac{(\sqrt{3}+1)}{(\sqrt{3}-1)}$ and $y=\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}$, find the values of $x^3+y^3$
→The figure, given below, shows a trapezium $\text{ABCD} . M$ and $N$ are the mid-point of the non$-$parallel sides $A D$ and $B C$ respectively. Find :
$(i) MN$, if $AB =11 \ cm$ and $DC =8 \ cm.(ii) A B$, if $D C=20 \ cm$ and $M N=27 \ cm.(iii) DC$, if $MN =15 \ cm$ and $AB =23 \ cm$.
→$(i) MN$, if $AB =11 \ cm$ and $DC =8 \ cm.(ii) A B$, if $D C=20 \ cm$ and $M N=27 \ cm.(iii) DC$, if $MN =15 \ cm$ and $AB =23 \ cm$.
A sum of money, invested at compound interest, amounts to $Rs. 19,360$ in $2$ years and to $Rs. 23,425.60$ in $4$ years. Find the rate per cent and the original sum of money.
→Construct the frequency distribution table from the following cumulative frequency table:
$(i) $State the number of students in the age group $10 - 13.(ii)$ State the age$-$group which has the least number of students.
→| Ages | No. of students |
| Below $4$ | $0$ |
| Below $7$ | $85$ |
| Below $10$ | $140$ |
| Below $13$ | $243$ |
| Below $16$ | $300$ |
Solve:$\frac{a}{x}-\frac{b}{y}=0, \frac{a b^2}{x}+\frac{a^2 b}{y}=a^2+b^2$
→Find the value of $'a\ '$ and $' b\ '$ if:$(\sqrt{243})^{ a } \div 3^{ b +1}=1$ and $27^{ b }-81^{4-\frac{ a }{2}}=0$
→In a $\triangle ABC$, if $D$ is midpoint of $BC; AD$ is produced upto $E$ such as $DE = AD$, then prove that:$a. \text{DABD}$ and $\text{DECD}$ are congruent.$b. AB = EC,c. AB$ is parallel to $EC$
→In the give figure, if $\text{DPQR}$ is an isosceles triangle, prove that: $\angle QSR =$ exterior $\angle PRT.$
→A school organised a Health Check Up Camp for its students. The weights (in kg) of the students of a class were recorded as below:
41 40 36 52 50 48 47 45 40 41 42 49 50 51 38 41 40 45 40 39 49 51 48 46 44 50 57 38 41 51
Based on the above information, answer the following questions :
Q.1. The range of the data is:
(a) 20 kg (b) 21 kg (c) 22 kg (d) 23 kg
Q.2. Mean weight of the data is :
(a) 45 kg (b) 44.5 kg (c) 42.5 kg (d) 40.5 kg
Q.3. Median of the data is :
(a) 44 kg (b) 45 kg (c) 45.5 kg (d) 46 kg
Q.4. One student weighing 45 kg , was absent on that day. Next day, the teacher added his name in the list. The average weight of the new group is :
(a) 47 kg (b) 46.4 kg (c) 46 kg (d) 45 kg
Q.5. The median weight of the students after adding the absentee in the list is :
(a) 45 kg (b) 46 kg (c) 44.5 kg (d) 44.2 kg
41 40 36 52 50 48 47 45 40 41 42 49 50 51 38 41 40 45 40 39 49 51 48 46 44 50 57 38 41 51
Based on the above information, answer the following questions :
Q.1. The range of the data is:
(a) 20 kg (b) 21 kg (c) 22 kg (d) 23 kg
Q.2. Mean weight of the data is :
(a) 45 kg (b) 44.5 kg (c) 42.5 kg (d) 40.5 kg
Q.3. Median of the data is :
(a) 44 kg (b) 45 kg (c) 45.5 kg (d) 46 kg
Q.4. One student weighing 45 kg , was absent on that day. Next day, the teacher added his name in the list. The average weight of the new group is :
(a) 47 kg (b) 46.4 kg (c) 46 kg (d) 45 kg
Q.5. The median weight of the students after adding the absentee in the list is :
(a) 45 kg (b) 46 kg (c) 44.5 kg (d) 44.2 kg
From the following figure, find the values of:$(i) \sin B;(ii) \tan C;(iii)\sec^2 B - \tan^2B;(iv)\sin^2C + \cos^2C$
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