Solved papers for 10th Class Mathematics Solved Paper - Mathematics-2016

done Solved Paper - Mathematics-2016

  • question_answer1) In \[\Delta \,ABC,D\]and \[E\] are points \[AC\] and \[BC\] respectively such that \[DE\parallel AB\]. If \[AD=2x,\text{ }BE=2x-1,CD=x+1\] and\[CE=x-1\], then find the value of \[x\].

    View Answer play_arrow
  • question_answer2) In A, B and C are interior angles of \[\Delta \text{ }ABC\], then prove that: \[\sin \frac{(A+C)}{2}=\cos \frac{B}{2}\].

    View Answer play_arrow
  • question_answer3) If \[x=3\text{ }sin\text{ }\theta \] and \[y=4\text{ }cos\,\theta \], find the value of \[\sqrt{16{{x}^{2}}+9{{y}^{2}}}\].

    View Answer play_arrow
  • question_answer4) If empirical relationship between mean, median and mode is expressed as mean \[=k\](3 median\[\]mode), then find the value of\[k\].

    View Answer play_arrow
  • question_answer5) Express 23150 as product of its prime factors. Is it unique?

    View Answer play_arrow
  • question_answer6) State whether the real number 52.0521 is rational or not. If it is rational express it in the form \[\frac{p}{q}\], where \[p,q\] are co-prime, integers and \[q\ne 0\]. What can you say about prime factorisation of \[q\]?

    View Answer play_arrow
  • question_answer7)

    Given the linear equation \[x-2y-6=0\], write another linear equation in these two variables, such that the geometrical representation of the pair so formed is:
    (i) coincident lines
    (ii) intersection lines

    View Answer play_arrow
  • question_answer8) In an isosceles \[\Delta \text{ }ABC\] right angled at B, prove that \[A{{C}^{2}}=2A{{B}^{2}}\].

    View Answer play_arrow
  • question_answer9)

    Prove the following identity:
    \[{{\left[ \frac{1-\tan \,A}{1-\cot \,A} \right]}^{2}}={{\tan }^{2}}A:\angle A\] is acute

    View Answer play_arrow
  • question_answer10)

    Given below is a cumulative frequency distribution table. Corresponding to it, make an ordinary frequency distribution table.
    \[x\] \[cf\]
    More than or equal to 0 45
    More than or equal to 10 38
    More than or equal to 20 29
    More than or equal to 30 17
    More than or equal to 40 11
    More than or equal to 50 6

    View Answer play_arrow
  • question_answer11) Find LCM and HCF of 3930 and 1800 by prime factorisation method.

    View Answer play_arrow
  • question_answer12) Using division algorithm, find the quotient and remainder on dividing \[f(x)\] by \[g(x)\] where \[f(x)=6{{x}^{3}}+13{{x}^{2}}+x-2\] and\[g(x)=2x+1\].

    View Answer play_arrow
  • question_answer13) If three zeroes of a polynomial \[{{x}^{4}}-{{x}^{3}}-3{{x}^{2}}+3x\] are \[0,\sqrt{3}\] and \[-\sqrt{3}\], then find the fourth zero.

    View Answer play_arrow
  • question_answer14)

    Solve the following pair of equations by reducing them to a pair of linear equations:

    View Answer play_arrow
  • question_answer15) \[\Delta \text{ }ABC\] is a right angled triangle in which \[\angle B=90{}^\circ \]. D and E are any point on AB and BC respectively. Prove that\[A{{E}^{2}}+C{{D}^{2}}=A{{C}^{2}}+D{{E}^{2}}\].

    View Answer play_arrow
  • question_answer16)

    In the given figure, RQ and TP are perpendicular to PQ, also \[TS\bot PR\] prove that \[\text{ST}\text{.RQ=PS}\text{.PQ}\].

    View Answer play_arrow
  • question_answer17) If sec\[A=\frac{2}{\sqrt{3}}\], find the value of \[\frac{\tan \,\,A}{\cos \,\,A}+\frac{1+\sin \,\,A}{\tan \,\,A}\]

    View Answer play_arrow
  • question_answer18) Prove that: \[{{\sec }^{2}}\theta -{{\cot }^{2}}(90{}^\circ -\theta )=co{{s}^{2}}(90{}^\circ -\theta )+co{{s}^{2}}\theta .\]

    View Answer play_arrow
  • question_answer19)

    For the month of February, a class teacher of Class IX has the following absentee record for 45 students- Find the mean number of days, a student was absent.
    Number of days of absent 0 ? 4 4 ? 8 8 ? 12 12 ? 16 16 ? 20 20 ? 24
    Number of students 18 3 6 2 0 1

    View Answer play_arrow
  • question_answer20)

    Find the missing frequency (x) of the following distribution, if mode is 34.5:
    Marks obtained 0 ? 10 10 ? 20 20 ? 30 30 ? 40 40 ? 50
    Number of students 4 8 10 x 8

    View Answer play_arrow
  • question_answer21) Prove that \[\sqrt{5}\] is an irrational number. Hence show that \[3+2\sqrt{5}\] is also an irrational number.

    View Answer play_arrow
  • question_answer22) Obtain all other zeroes or the polynomial\[{{x}^{4}}+6{{x}^{3}}+{{x}^{2}}-24x-20\], if two of its zeroes are \[+2\] and \[-5\].

    View Answer play_arrow
  • question_answer23)

    Draw graph of following pair of linear equations:
    Also write the coordinate of the points where these lines meets x-axis and y-axis.

    View Answer play_arrow
  • question_answer24) A boat goes \[30\text{ }km\] upstream and \[44\text{ }km\] downstream in 10 hours. The same boat goes \[40\text{ }km\] upstream information some student guessed the speed of the boat in still water as \[8.5\text{ }km/h\] and speed of the stream as \[3.8\text{ }km/h\]. Do you agree with their guess? Explain what do we learn from the incident?

    View Answer play_arrow
  • question_answer25) In an equilateral \[\Delta \text{ }ABC,\text{ }E\] is any point on \[BC\] such that \[BE=\frac{1}{4}BC\]. Prove that \[16\text{ }A{{E}^{2}}=13\text{ }A{{B}^{2}}\].

    View Answer play_arrow
  • question_answer26)

    In the figure if \[\angle ABD=\angle XYD=\angle CDB=90{}^\circ .\text{ }AB=a,XY=c\] and \[CD=b\], then prove that\[c\text{ (}a+b)=ab\].

    View Answer play_arrow
  • question_answer27)

    In the \[\Delta \,ABC\](see figure), \[\angle A=\] right angle, \[AB=\sqrt{x}\] and \[BC=\sqrt{x+5}\]. Evaluate
    \[sin\text{ }C.\text{ }cos\text{ }C.\text{ }tan\text{ }C+co{{s}^{2}}C.\text{ }sin\text{ }A\]

    View Answer play_arrow
  • question_answer28) If \[\frac{\cos \,B}{\sin \,A}=n\] and \[\frac{\cos \,B}{\cos \,A}=m\] then show that \[({{m}^{2}}+{{n}^{2}})co{{s}^{2}}A={{n}^{2}}\].

    View Answer play_arrow
  • question_answer29) Prove that: \[\frac{\sec \,A-1}{\sec \,A+1}={{\left( \frac{\sin \,A}{1+\cos \,A} \right)}^{2}}={{(cot\,A-cosec\,A)}^{2}}\]

    View Answer play_arrow
  • question_answer30)

    Following table shows marks (out of 100) of students in a class test:
    Marks No. of students
    More than or equal to 0 80
    More than or equal to 10 77
    More than or equal to 20 72
    More than or equal to 30 65
    More than or equal to 40 55
    More than or equal to 50 43
    More than or equal to 60 28
    More than or equal to 70 16
    More than or equal to 80 10
    More than or equal to 90 8
    More than or equal to 100 0
    Draw a ?more than type? ogive. From the curve, find the median. Also, check the value of the median by actual calculation.

    View Answer play_arrow
  • question_answer31)

    From the following data find the median age of 100 residents of a colony who took part in swachch bharat abhiyan:
    Age (in yrs.) More than or equal to No. of residents
    0 50
    10 46
    20 40
    30 20
    40 10
    50 3

    View Answer play_arrow

Study Package

Solved Paper - Mathematics Term-I - 2016
  15 10



You need to login to perform this action.
You will be redirected in 3 sec spinner