Board Paper of Class 10 2007 Maths (SET 1)  Solutions
(i) All questions are compulsory.
(ii) The question paper consists of 25 questions divided into three sections A, B and C. Section A comprises of 7 questions of two marks each, Section B comprises of 12 questions of three marks each, and Section C comprises of 6 questions of five marks each.
(iii) Use of calculators is not permitted.
 Question 1
If x + k is the GCD of x^{2 }− 2x − 15 and x^{3} + 27, find the value of k.
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 Question 2
 Question 3
Find the sum of first 25 terms of an A.P. whose nth term is 1 − 4n.
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 Question 4
 Question 5
The mean of the following frequency distribution is 62.8. Find the missing frequency x.

Class
0 − 20
20 − 40
40 − 60
60 − 80
80 − 100
100 − 120
Frequency
5
8
x
12
7
8

 Question 6
Cards marked with numbers 3, 4, 5, ..., 50 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the drawn card is
(i) divisible by 7.
(ii) a number which is a perfect square.
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 Question 7
A washing machine is available for Rs. 13,500 cash or Rs. 6,500 as cash down payment followed by three monthly instalments of Rs. 2,500 each. Find the rate of interest charged under instalment plan.
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 Question 8
 Question 9
Simplify:
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 Question 10
Which term of the A.P. 3, 15, 27, 39,....... will be 132 more than its 54^{th} term?
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 Question 11
In the given figure, TA is a tangent to the circle from a point T and TBC is a secant to the circle. If AD is the bisector of ∠CAB, prove that ΔADT is isosceles.
OR
In ABC, AD⊥ BC and AD^{2} = BD.DC. Prove that ∠BAC is a right angle.
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 Question 12
Draw a ΔPQR with base QR = 6 cm, vertical angle P = 60° and median through P to the base is of length 4.5 cm.
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 Question 13
A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm.
The total height of the toy is 31 cm. Find the total surface area of the toy.
(Use)
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 Question 14
The enrolment of a secondary school in different classes is given below:

Class
VI
VII
VIII
IX
X
Enrolment
600
500
400
700
200
Draw a pie chart to represent the above data.
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 Question 15
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag.
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 Question 16
 Question 17
Show that the points (7, 10), (−2, 5) and (3, −4) are the vertices of an isosceles right triangle.
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 Question 18
In what ratio does the line x − y − 2 = 0 divide the line segment joining (3, −1) and (8, 9)?
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 Question 19
A man borrows money from a finance company and has to pay it back in two equal halfyearly instalments of Rs. 7,396 each. If the interest is charged by the finance company at the rate of 15% per annum, compounded semiannually, find the principal and the total interest paid.
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 Question 20
If a line is drawn parallel to one side of a triangle, to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.
Using the above, prove the following:
In the given figure, DE  BC and BD = CE. Prove that ABC is an isosceles triangle.
 Question 21
Prove that the sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
Using the above, find x and y in the given figure.
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 Question 22
The difference of two numbers is 5 and the difference of their reciprocals is . Find the numbers.
OR
By increasing the list price of a book by Rs. 10 a person can buy 10 less books for Rs. 1,200. Find the original list price of the book.
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 Question 23
A sphere, of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by cm. Find the diameter of the cylindrical vessel.
OR
A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.
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 Question 24
A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30°. A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45°. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl.
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 Question 25
Ms. Shahnaz earns Rs 35,000 per month (excluding HRA). She donates Rs 30,000 to Prime Minister Relief Fund (100% exemption) and Rs 40,000 to a Charitable Hospital (50% exemption). She contributes Rs 5,000 per month to Provident Fund and Rs 25,000 per annum towards LIC premium. She purchases NSC worth Rs 20,000. She pays Rs 2,300 per month towards income tax for 11 month. Find the amount of income tax she has to pay in 12^{th} month of the year.
Use the following to calculate income tax :

(a)
Saving :
100% exemption for permissible savings upto
Rs 1,00,000
(b)
Rates of income tax for ladies
Slab
Income tax
(i) Upto Rs 1,35,000
No tax
(ii) From Rs 1,35,001to Rs. 1,50,000
10% of taxable income exceeding Rs 1,35,000
(iii) From Rs 1,50,001 to Rs 2,50,000
Rs 1,500 + 20% of the amount exceeding Rs 1,50,000
(iv) From Rs 2,50,001 and above
Rs 21,500 + 30% of the amount exceeding Rs 2,50,000
(c)
Education Cess :
2% of Income tax payable


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