Name of the Board : CBSE Academic
Class : X STD
Subject : Mathematics (Set – II)
Year : 2015-16
Website : http://cbseacademic.in/SQP_CLASSX_2015_16.html
Download Sample Question Paper : https://www.pdfquestion.in/uploads/8099Maths.pdf
Mathematics Sample Question Paper :
Time: 3 hours
M. M. : 90
Related : CBSE Academic Class X Information & Communication Technology Sample Question Paper 2015-16 : www.pdfquestion.in/8097.html
General Instructions:
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D.
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 11 questions of 4 marks each.
4. Use of calculators is not permitted.
Section A : (Question numbers 1 to 4 carry 1 mark each)
1. Find the value of k, for which one root of the quadratic equation kx2-14x+8=0 is six times the other.
2. Find the tenth term of the sequence 2, 8, 18, ………
3. Out of 200 bulbs in a box, 12 bulbs are defective. One bulb is taken out at random from the box. What is the probability that the drawn bulb is not defective?
4. Find the value of a, for which point P ( 1, 2) is the midpoint of the line segment joining the points Q (-5, 4) and R(-1, 0).
Section B : (Question numbers 5 to 10 carry 2 marks each)
5. If 2 is a root of the equation x2+kx+12=0 and the equation x2+kx+q=0 has equal roots, find the value of q.
6. How many two digit numbers are divisible by 7?
7. Find a relation between x & y such that the point P(x,y) is equidistant from the points A(-5,3) and B(7,2).
8. Find the perimeter of the shaded region if ABCD is a square of side 21 cm and APB & CPD are semicircles. (Use p=22/7).
9. A sphere of diameter 6cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?
10. Find the number of coins of 1.5 cm diameter and 0.2 cm thickness to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Section C : (Question numbers 11 to 20 carry 3 marks each)
11. The ninth term of an AP is equal to seven times the second term and twelfth term exceeds five times the third term by 2. Find the first term and the common difference.
Section D : (Question numbers 21 to 31 carry 4 marks each)
21. Three eighth of the students of a class opted for visiting an old age home. Sixteen students opted for having a nature walk. Square root of total number of students in the class opted for tree plantation in the school. The number of students who visited an old age home is same as the number of students who went for a nature walk and did tree plantation. Find the total number of student. What values are inculcated in students through such activities?
22. The minimum age of children to be eligible to participate in a painting competition is 8 years. It is observed that the age of youngest boy was 8 years and the ages of rest of participants are having a common difference of 4 months.If the sum of ages of all the participants is 168 years, find the age of eldest participant in the painting competition.
23. Prove that the lengths of the tangents drawn from an external point to a circle are equal. Using the above theorem, prove that AB+CD = AD+BC, if a quadrilateral ABCD is drawn to circumscribe a circle.
24. Draw a pair of tangents inclined to each other at an angle of 60o to a circle of radius 3 cm.
25. From the top of tower, 100 m high, a man observes two cars on the opposite sides of the tower with the angles of depression 30o& 45 o respectively. Find the distance between the cars. (Use ?3=1.73).
26. From a point on the ground, the angles of elevation of the bottom and top of a tower fixed at the top of a 20 m high building are 45 o& 60 o respectively. Find the height of the tower.
27. Cards marked with numbers 3, 4, 5, ………..…., 50 are placed in a bag and mixed thoroughly. One card is drawn at random from the bag. Find the probability that number on the card drawn is:
a. Divisible by 7.
b. A perfect square.