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SA1-page2 is the continuation of KVS Hyd SA 1

12) In quadrilateral ABCD,  \( \angle  B = 90°\) if AD² = AB² + BC ² + CD² prove that \(\angle ACD = 90°\).


In the adjoining figure and \( \angle PQR = 90°, \angle SPQ = 90°\). If QR= 5cm,   PR = 13cm and PS = 14 cm then find the value of Tan S.

13) If sinΘ = \(\frac{3}{5}\) then find cosΘ.

14) The median class of a frequency distribution is 125 - 145. The frequency and cumulative frequency of the class preceding the median class are 20 and 22 respectively. Find the sum of frequency (n), if the median is 137.


15) Show that 5 + 3√2 is an irrational number.

16) What real number should be subtracted from the polynomial
3x³ + 10x² - 14x + 9 so that the polynomial 3x - 2 divides exactly?

17) Solve for 'x' and 'y'         
      5x + \(\frac{4}{y}\) = 9;   7x - \(\frac{2}{y}\)=5; y\(\neq\)0.

18) The sum of numerator and denominator of a fraction is 8 . If 3 is added to both the numerator and denominator , the fraction becomes 3/4 . Find the fraction.

19) If the areas of two similar triangles are equal then prove that they are congruent.


    In the figure given below, AB\(\perp \)BC, DE\(\perp\)AC, GF\(\perp\)BC. Prove that \(\Delta ADE\) ~ \(\Delta GCF \).



20) In a Rhombus, prove that the sum of the squares all sides is equal to the sum of the squares of its diagonals.

21) Prove that  \( \frac{cos(90^{\circ}-A)*Sin(90^{\circ}-A)}{Tan(90^{\circ}-A)}=Sin^{2}A\)

22) If Cos\(\theta =\frac{3}{5}\) Then find the value of \(Cos\theta + Cosec \theta \)


Evaluate \(Cos^{2}20^{\circ}+Cos^{2}70^{\circ}+ Sin 48^{\circ}*sec 42^{\circ} +Cos 40^{\circ}*Cosec 50^{\circ}\)

23) Find the mode of the given distribution:

24)Find the mean of the following distribution is 62.8. Find the missing frequency 'x' .

25) Prove that the cube of any positive integer can be expressed in the form 9m, 9m+1, 9m+8 .


 Prove that √5 is an irrational number .

26)Solve graphically x-y =1 and 2x+y=8 . Shade the region bounded by the lines and y-axis , also find the area.

27) Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.


 Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

28) Find all zeroes of the polynomial \(x^{4}+3x^{3}-6x-4\) if two of its zeroes are -√2 and √2.

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