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question_answer1) In \[\Delta \,DEW,AB\parallel EW\]. If \[AD=4cm,\,\,DE\,=12cm\] and \[DW=24\text{ }cm\] , then find the of \[DB\].
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question_answer2) If \[\Delta \text{ }ABC\] is right angled at By what is the value of \[\sin \,(A+C)\].
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question_answer3) If \[\sqrt{3}\text{ }sin\text{ }\theta =cos\text{ }\theta \], find the value of \[\frac{3\,{{\cos }^{2}}\theta +2\,\cos \theta }{3\,\cos \theta +2}\].
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question_answer4)
| From the following frequency distribution, find the median class: |
| Cost of living index | 1400 ? 1550 | 1550 ? 1700 | 1700 ? 1850 | 1850 ? 2000 |
| Number of weeks | 8 | 15 | 21 | 8 |
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question_answer5) Show that \[3\sqrt{7}\] is an irrational number.
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question_answer6) Explain why \[(17\times 5\times 11\times 3\times 2+2\times 11)\] is a composite number?
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question_answer7)
| Find whether the following pair of linear equations is consistent or inconsistent: |
| \[3x+2y=8\] |
| \[6x-4y=9\] |
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question_answer8) X and Y are points on the sides AB and AC respectively of a triangle ABC such that \[\frac{AX}{AB},AY=2\,cm\] and \[YC=6\,cm\]. Find whether \[XY\parallel BC\] or not.
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question_answer9)
| Prove the following identity: |
| \[\frac{{{\sin }^{3}}\theta +{{\cos }^{2}}\theta }{\sin \theta +cos\theta }=1-\sin \theta .\cos \theta \]. |
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question_answer10)
| Show that the mode of the series obtained by combining the two series \[{{S}_{1}}\] and \[{{S}_{2}}\] given below is different from that of \[{{S}_{1}}\] and \[{{S}_{2}}\] taken separately: |
| \[{{S}_{1}}:3,\,\,5,\,\,8,\,\,8,\,\,9,\,\,12,\,\,13,\,\,9,\,\,9\] |
| \[{{S}_{2}}:7,\,\,4,\,\,7,\,\,8,\,\,7,\,\,8,\,\,13\] |
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question_answer11) The length, breadth and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.
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question_answer12)
| Solve by elimination: |
| \[3x-y=7\] |
| \[2x+5y+1=0\] |
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question_answer13) Find a quadratic polynomial, the sum and product of whose zeroes are 0 and \[-\frac{3}{5}\] respectively. Hence find the zeroes.
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question_answer14) The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.
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question_answer15)
| In given figure, \[EB\bot AC,\text{ }BG\bot AE\] and \[CF\bot AE\] Prove that: |
| (i)\[\Delta \,ABG\sim \Delta \,DCB\] |
| (ii) \[\frac{BC}{BD}=\frac{BE}{BA}\] |
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question_answer16) In triangle \[ABC\], if \[AP\bot BC\] and \[A{{C}^{2}}=B{{C}^{2}}-A{{B}^{2}}\], then prove that \[P{{A}^{2}}=PB\times CP\].
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question_answer17) If \[\sin \theta =\frac{12}{13},0{}^\circ <\theta <90{}^\circ ,\], find the value of: \[\frac{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }{2\sin \theta .\cos \theta }\times \frac{1}{{{\tan }^{2}}\theta }\]
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question_answer18) If \[sec\theta +tan\theta =p\], prove that \[\sin \theta =\frac{{{p}^{2}}-1}{{{p}^{2}}+1}\]
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question_answer19)
| Find the mean of the following distribution by Assumed Mean Method: |
| Class interval | Frequency |
| 10 ? 20 | 8 |
| 20 ? 30 | 7 |
| 30 ? 40 | 12 |
| 40 ? 50 | 23 |
| 50 ? 60 | 11 |
| 60 ? 70 | 13 |
| 70 ? 80 | 8 |
| 80 ? 90 | 6 |
| 90 ? 100 | 12 |
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question_answer20) The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of number of boys in the number of girls who appeared in the examination.
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question_answer21) Find HCF of numbers 134791, 6341 and 6339 by Euclid?s division algorithm.
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question_answer22)
| Draw the graph of the following pair of linear equations: |
| \[x+3y=6\] and \[2x-3y=2\] |
| Find the ratio of the areas of the two triangles formed by first line, \[x=0,\text{ }y=0\] and second line, \[x=0,\text{ }y=0\]. |
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question_answer23) If the polynomial \[({{x}^{4}}+2{{x}^{3}}+8{{x}^{2}}+12x+18)\]is divided by another polynomial \[({{x}^{2}}+5)\], the remainder comes out to be \[(px+q)\], find the values of p and q.
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question_answer24) What must be subtracted from \[p(x)=8{{x}^{4}}+14{{x}^{3}}-2{{x}^{2}}+8x-12\] so that \[4{{x}^{2}}+3x-2\] is factor of \[p(x)\]? This question was given to group of students for working together. Do you think teacher should promote group work?
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question_answer25) Prove ?If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio?.
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question_answer26)
| In the given figure, \[AD=3cm,\,\,AE=5cm,\,\,BD=4cm,\,\,CE=4cm,\,\,CF=2cm,\,\,BF=2.5cm\], then find the pair of parallel lines and hence their lengths. |
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question_answer27) If tan\[(A+B)=\sqrt{3}\] and tan\[(A-B)=\frac{1}{\sqrt{3}}\] , where\[0<A+B<90{}^\circ ,\text{ }A>B\], find A and B. Also calculate\[\tan \text{ }A.\text{ }\sin \text{ }(A+B)+\cos \text{ }A.\text{ }\tan \text{ }(A-B)\].
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question_answer28) Prove that: \[(1+cot\text{ }A+tan\text{ }A).\text{(}sin\text{ }A-cos\text{ }A)\]\[=\frac{{{\sec }^{3}}A-\cos e{{c}^{3}}A}{{{\sec }^{2}}A.\cos e{{c}^{2}}A}\]
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question_answer29) Prove the identity: \[\frac{\sin A+\cos A}{\sin A-\cos A}+\frac{\sin A-\cos A}{\sin A+\cos A}=\frac{2}{1-2{{\cos }^{2}}A}\]
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question_answer30)
| The following table gives the daily income of 50 workers of a factory. Draw both types (?less than type? and ?greater than type?) ogives. |
| Daily income in Rs. | No. of workers |
| 100 ? 120 | 12 |
| 120 ? 140 | 14 |
| 140 ? 160 | 8 |
| 160 ? 180 | 6 |
| 180 ? 200 | 10 |
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question_answer31)
| In a class test, marks obtained by 120 students are given in the following frequency distribution. If it is given that mean is 59, find the missing frequencies x and y. |
| Marks | No. of students |
| 0 ? 10 | 1 |
| 10 ? 20 | 3 |
| 20 ? 30 | 7 |
| 30 ? 40 | 10 |
| 40 ? 50 | 15 |
| 50 ? 60 | x |
| 60 ? 70 | 9 |
| 70 ? 80 | 27 |
| 80 ? 90 | 18 |
| 90 ? 100 | y |
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