Sample paper 2 (Maths- Standard) class -10th
Question paper -Mathematics
Time:-45 minutes Mm:- 26
Part-A(1 marks- each)
Section-I
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Direction-(Q no.s,1-16)Section I has 16 questions of 1 mark each.Internal choice is provided in 5 questions
1.The time in seconds taken by 150 athletes to run a 110m hurdle race are tabulated below.
| Class | 13.8-14 | 14-14.2 | 14.2-14.4 | 14.4-14.6 | 14.6-14.8 | 14.8-15 |
|---|---|---|---|---|---|---|
| Frequency | 2 | 4 | 5 | 71 | 48 | 20 |
Find the number of athlete who have completed the race in less than 14.6 second.
2.In the given figure AD is the bisector of angle A .if BD = 4 cm DC= 3 cm and AB= 6 cm then find AC.
Or
To divide a line segment AB in the ratio of 5:8,a ray AX is drawn first such that angle BAX is an acute angle and then points A1, A2,....are located equal distances on the ray AX .Find the point and in which B join.
3.If two tangents inclined at an angle of 60 degree are drawn to a circle of radius 5 centimetre, then find the length of each tangent.
Or
In the given figure if the angle between two radii of a circle is 130 degree then find the angle between the tangents at the ends of radii.
4.Find the number of maximum zeros in a cubic polynomial.
It5. Check whether the lines x + y =1 and 2 x + y = x + 2 are either parallel or perpendicular.
6.Find the area of shaded region.
7.In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm .if the tangents to the circle at point P and Q intersect at T then find the length of PT.
8.Evaluate
cos^2 30°+cos^2 45°+cos^2 60°+cos^2 90
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9. An acute angle ∅ when sin ∅ + cos ∅,0≤∅≤ 90 ° takes the greatest value.
Or
Given that sin alpha=1/2 and cos becta=1/2 what is the value of alpha + beta?
10.If a sector of a circle has area 100cm square then find the perimeter of this sector.
11.If point P lies inside the circle then find the number of tangent(s) drawn from point P.
12.The circumference of circle is equal to the sum of the circumference of two circles having diameter 34 cm and 8 cm. find the radius of the new circle.
13.Find the probability of getting a face card from a pack of card.
14.What can you say about the prime factorizations of the denominators of the rational number 34. (Bar)5678?
15.Find the number of zeroes lying between -2 to 2 of the polynomial f(x) whose graph is given in the figure .
Or
If alpha and beta are the zeros of polynomial p (x) =x^2- 5 x- 1 ,then find the value of alpha^2beta + alpha beta^2.
16.Which term of the AP 21, 18 ,15,.... is -81?
Or
Find the sum of the first 7 terms of AP sequence 27, 30, 33,......... .
Part -B (2 Marks each)
Direction (Q no.s 17- 22).These are very Short answer type of questions of 2 Marks each.
17. A trader was moving along a road selling the eggs. An idler killed who did not have much work to do, started to get the trader into a work duel .This grew into a fight, he pulled the basket with eggs and dashed it on the floor. The eggs broke, the trader requested the panchayat to ask the idler to pay for the broken eggs.The panchayat asked the trader,how many eggs were broken.
He gave the following response:
if counted in pairs one will remain ,if counted in 3's two will remain.
if counted in 4's ,three will remain.
if counted in 5's ,four will remain,
If counted in 6's five will remain , if counted in 7's nothing will remain and my basket cannot accommodate more than 150 eggs .How many eggs were there?
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18.The 6th term of an AP is zero. Prove that the 13th term of an ap is 3 times its 14th term.
19.If tan (A+B)= √3 and tan (A-B)=1/√3 ,0°<A+B≤90°,A>B,then find A and B.
Or
If cosecA °√2 ,then find the value of
2sin^2 A+3cot^2 A/4tan^2A-cos^2A.
20.A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is the thrice that of a red ball ,find the number of blue balls in the bag.
Or
A missing helicopter is reported to have crashed somewhere in the rectangular region show in figure. What is the probability that is crashed inside the lake shown (shaded region) in the figure?
21.Prove that the line segment joining the point of contact of two parallel tangents to a circle is a diameter of the circle.
22.In sports day activities of Meerut public School .the lines were drawn with chalk powder in the rectangular shape OBCD.Each lines is at 1/ 2 metre distance from each other. 60 flower pots have been placed at a distance of 1/2 metre from each other long OD .Yamini runs 1/4th of the distance on the 3rdline and makes a red flower. Kamala runs 1/5th ofthe distance OD on the 7th line and makes a yellow flower.
(See the fig)
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Thank you very much
By Anuranjan Gadekar
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