# Solved papers for 10th Class Mathematics Solved Paper - Mathematics-2014 Term-I

### done Solved Paper - Mathematics-2014 Term-I

• question_answer1) In the given figure if $DE\parallel BC,AE=8\,cm,\,\,EC=2cm$ and $BC=6\,cm$, then find DE.

• question_answer2) Evaluate: $10.\frac{1-{{\cot }^{2}}45{}^\circ }{1+{{\sin }^{2}}90{}^\circ }$

• question_answer3) If cosec$\theta =\frac{5}{4}$, find the value of $cot\text{ }\theta$.

 Following table shows sale of shoes in a store during one month: Size of shoe 3 4 5 6 7 8 Number if pairs sold 4 18 25 12 5 1 Find the model size of the shoes sold.

• question_answer5) Find the prime factorisation of the denominator of rational number expressed as $6.\overline{12}$ in simplest form.

• question_answer6) Find a quadratic polynomial, the sum and product of whose zeroes are $\sqrt{3}$ and $\frac{1}{\sqrt{3}}$ respectively.

 Complete the following factor tree and find the composite number x. • question_answer8) In a rectangle ABCD, E is middle point of AD. If $AD=40\text{ }m$ and $AB=48\text{ }m$, then find EB.

• question_answer9) If $x=p\text{ }sec\theta +q\text{ }tan\theta$ and $y=p\text{ }tan\theta +q\text{ }sec\theta$ then prove that ${{x}^{2}}-{{y}^{2}}={{p}^{2}}-{{q}^{2}}$.

 Given below is the distribution of weekly pocket money received by students of a class. Calculate the pocket money that is received by most of the students. Pocket Money (in Rs.) 0 ? 20 20 ? 40 40 ? 60 60 ? 80 80 ? 100 100 ? 120 120 ? 140 No. of Students 2 2 3 12 18 5 2

• question_answer11) Prove that $3+2\sqrt{3}$ is an irrational number.

 Solve by elimination: $3x=y+5$ $5x-y=11$

• question_answer13) A man earns Rs. 600 per month more than his wife, One-tenth of the man?s salary and one-sixth of the wife?s salary amount to Rs. 1,500, which is saved every month. Find their incomes.

• question_answer14) Check whether polynomial $x-1$ is a factor of the polynomial ${{x}^{3}}-8{{x}^{2}}+19x-12$. Verify by division algorithm.

• question_answer15) If the perimeters of two similar triangles ABC and DEF are 50 cm and 70 cm respectively and one side of$\Delta \,ABC=20\text{ }cm$, then find the corresponding side of $\Delta \,DEF$.

 In the figure if $DE\parallel OB$ and $EF\parallel BC$, then prove that $DF\parallel OC$ • question_answer17) Prove the identify: $(sec\text{ }A-cos\text{ }A)\,.\,(cot\text{ }A+tan\text{ }A)=tan\text{ }A\,.\,\,sec\text{ }A$.

• question_answer18) Given $2\,\,cos\,\,3\theta =\sqrt{3}$, find the value of $\theta$.

 For helping poor girls of their class, students saved pocket money as shown in the following table: Money saved (in Rs.) 5 ? 7 7 ? 9 9 ? 11 11 ? 13 13 ? 15 Number of students 6 3 9 5 7 Find mean and median for this data.

 Monthly pocket money of students of a class is given in the following frequency distribution: Pocket money (in Rs.) 100 ? 125 125 ? 150 150 ? 175 175 ? 200 200 ? 225 Number of students 14 8 12 5 11 Find mean pocket money using step deviation method.

• question_answer21) If two positive integers x and y are expressible in terms of primes as $x={{p}^{2}}{{q}^{3}}$ and $y={{p}^{3}}q$, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain.

• question_answer22) Sita Devi wants to make a rectangular pond on the road side for the purpose of providing drinking water for street animals. The area of the pond will be decreased by 3 square feet if its length is decreased by 2 ft. and breadth is increased by 1 ft. Its area will be increased by 4 square feet if the length is increased by 1 ft. and breadth remains same. Find the dimensions of the pond. What motivated Sita Devi to provide water point for street animals?

• question_answer23) If a polynomial ${{x}^{4}}+5{{x}^{3}}+4{{x}^{2}}-10x-12$ has two zeroes as $-2$ and $-3$, then find the other zeroes.

• question_answer24) Find all the zeroes of the polynomial $8{{x}^{4}}+8{{x}^{3}}-18{{x}^{2}}-20x-5,$ if it is given that two of its zeroes are $\sqrt{\frac{5}{2}}$ and $-\sqrt{\frac{5}{2}}$.

 In the figure, there are two points D and E on side AB of $\Delta \,ABC$ such that $AD=BE$. If $DP\parallel BC$and $EQ\parallel AC$, then prove that $PQ\parallel AB$. In $\Delta \,ABC$, altitudes AD and CE intersect each other at the point P. Prove that (i) $\Delta \,APE\sim \Delta \,CPD$ (ii) $AP\times PD=CP\times PE$ (iii) $\Delta \,ADB\tilde{\ }\Delta \,CEB$ (iv) $AB\times CE=BC\times AD$

• question_answer27) Prove that: ${{(cot\text{ }A+sec\text{ }B)}^{2}}-{{(tan\text{ }B-cosec\text{ }A)}^{2}}=2(cot\text{ }A.sec\text{ }B+tan\text{ }B.cosec\text{ }A).$

• question_answer28) Prove that: $(sin\,\theta +cos\,\theta +1).(sin\,\theta -1+cos\,\theta ).sec\,\theta \text{ }.\text{ }cosec\text{ }\theta =2$.

 If $tan\,(20{}^\circ -3\alpha )=cot\,\text{(}5\alpha -20{}^\circ )$, then find the value of $\alpha$ and hence evaluate: $sin\text{ }\alpha \,.\text{ }sec\text{ }\alpha \,.\text{ }tan\text{ }\alpha -cosec\text{ }\alpha \text{ }.\text{ }cos\text{ }\alpha \text{ }.\text{ }cot\text{ }\alpha$.

 The frequency distribution of weekly pocket money received by a group of students is given below: Pocket money in (Rs.) More than or equal to 20 More than or equal to 40 More than or equal to 60 More than or equal to 80 More than or equal to 100 More than or equal to 120 More than or equal to 140 More than or equal to 160 More than or equal to 180 More than or equal to 200 Number of Students 90 76 60 55 51 49 33 12 8 4 Draw a ?more than type? ogive and from it, find median. Verify median by actual calculations.

 Cost of living Index for some period is given in the following frequency distribution: Index 1500 ? 1600 1600 ? 1700 1700 ? 1800 1800 ? 1900 1900 ? 2000 2000 ? 2100 2100 ? 2200 No. of weeks 3 11 12 7 9 8 2 Find the mode and median for above data.

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