CLASS: X SAMPLE TEST PAPER-7
TIME: 3 HRS
SUBJECT: MATHEMATICS MM: 80
GENERAL INSTRUCTIONS:
(i) All questions are compulsory.
(ii) The question paper consists of 30 questions divided into 4 sections A,B,C and D.
(iii) Section A contains 6 questions of 1 mark each, Section B contains 6 questions of
2 marks each, Section C contains 10 questions of 3 marks each and Section D
contains 8 questions of 4 marks each.
(iv) Use of calculator is not allowed.
Section-A
1. Write the Fundamental Theorem of Arithmetic.
2. The graph of y= P(x)is given in the figure for some polynomial P(x) .Find the number
of zeroes of P(x) y
y=p(x)
,
x’ x
y’
3. ∆ ABC is a right angled triangle right angled at C, and D is the mid-point of BC.
tan 𝜃 1
∠ADC = Φ,∠ABC = θ. Show that tan 𝛷 = 2
4. Find the modal class for the following distribution
Class 0-5 5-10 10-15 15-20 20-25
Interval
Frequency 10 13 12 20 9
5. Three coins are tossed simultaneously. Find the probability of getting three heads.
6. Find the points on the x-axis which are at a distance of 2√ 5 from the point (7, 4).
Section-B
7. Find the quadratic polynomial whose zeroes are -3 and 2.
8. Check whether 6𝑛 can end with the digit 0 for natural number n.
9. Find the ratio in which the Y-axis divide the line segment joining the points (5,-6) and
(-1,-4)
10. E and F are points on the sides PQ and PR respectively of a ∆ PQR. PE = 3.9 cm, EQ =
2.6 cm, PF = 3.6 cm and FR =2.4 cm. Find whether EF is parallel to QR .Give reason
for your answer.
11. In a frequency distribution, the mode and mean are 26.6 and 28.1 respectively. Find out
the median.
, Section- C
12. Find the sum of all three digit numbers which leave the same remainder 2 when divided
by 5.
13. The product of the digits of a two digit positive number is 24. If 18 is added to the number
then the digits of the number are interchanged. Find the number.
14. Solve for x and y:
5 1 6 3
+ =2 ; - =1
𝑥−1 𝑦−2 𝑥−1 𝑦−2
19. OACBO represents a quadrant of a circle of radius 7 cm with centre at O. If OD=5 cm,
find the area of the shaded region.
20. The rain water from a roof 22 m by 20 m drains into a conical vessel having the
diameter of base as 2 m and height 3.5 m. If the vessel is just full, find the rainfall in
mm.
21. Cards marked with numbers 13, 14, 15, ......... 60 are placed in a box and mixed
thoroughly. One card is drawn at random from the box. Find the probability that the
number on the card is.
i) divisible by 5
ii) a number which is a perfect square.
SECTION D
22. Draw the graph of the following pair of linear equation
x+ 3y =6; 2x-3y=12
` Find the area of triangle bounded by the lines and the x axis.
23. The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return
downstream to the original point in 2hrs 45 min. Find the speed of the stream.
24. State and Prove Basic Proportionality Theorem.
25. In fig 8. , AB=12 cm, BC=8 cm and AC= 10 cm. Find AD, BE and CF.
TIME: 3 HRS
SUBJECT: MATHEMATICS MM: 80
GENERAL INSTRUCTIONS:
(i) All questions are compulsory.
(ii) The question paper consists of 30 questions divided into 4 sections A,B,C and D.
(iii) Section A contains 6 questions of 1 mark each, Section B contains 6 questions of
2 marks each, Section C contains 10 questions of 3 marks each and Section D
contains 8 questions of 4 marks each.
(iv) Use of calculator is not allowed.
Section-A
1. Write the Fundamental Theorem of Arithmetic.
2. The graph of y= P(x)is given in the figure for some polynomial P(x) .Find the number
of zeroes of P(x) y
y=p(x)
,
x’ x
y’
3. ∆ ABC is a right angled triangle right angled at C, and D is the mid-point of BC.
tan 𝜃 1
∠ADC = Φ,∠ABC = θ. Show that tan 𝛷 = 2
4. Find the modal class for the following distribution
Class 0-5 5-10 10-15 15-20 20-25
Interval
Frequency 10 13 12 20 9
5. Three coins are tossed simultaneously. Find the probability of getting three heads.
6. Find the points on the x-axis which are at a distance of 2√ 5 from the point (7, 4).
Section-B
7. Find the quadratic polynomial whose zeroes are -3 and 2.
8. Check whether 6𝑛 can end with the digit 0 for natural number n.
9. Find the ratio in which the Y-axis divide the line segment joining the points (5,-6) and
(-1,-4)
10. E and F are points on the sides PQ and PR respectively of a ∆ PQR. PE = 3.9 cm, EQ =
2.6 cm, PF = 3.6 cm and FR =2.4 cm. Find whether EF is parallel to QR .Give reason
for your answer.
11. In a frequency distribution, the mode and mean are 26.6 and 28.1 respectively. Find out
the median.
, Section- C
12. Find the sum of all three digit numbers which leave the same remainder 2 when divided
by 5.
13. The product of the digits of a two digit positive number is 24. If 18 is added to the number
then the digits of the number are interchanged. Find the number.
14. Solve for x and y:
5 1 6 3
+ =2 ; - =1
𝑥−1 𝑦−2 𝑥−1 𝑦−2
19. OACBO represents a quadrant of a circle of radius 7 cm with centre at O. If OD=5 cm,
find the area of the shaded region.
20. The rain water from a roof 22 m by 20 m drains into a conical vessel having the
diameter of base as 2 m and height 3.5 m. If the vessel is just full, find the rainfall in
mm.
21. Cards marked with numbers 13, 14, 15, ......... 60 are placed in a box and mixed
thoroughly. One card is drawn at random from the box. Find the probability that the
number on the card is.
i) divisible by 5
ii) a number which is a perfect square.
SECTION D
22. Draw the graph of the following pair of linear equation
x+ 3y =6; 2x-3y=12
` Find the area of triangle bounded by the lines and the x axis.
23. The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return
downstream to the original point in 2hrs 45 min. Find the speed of the stream.
24. State and Prove Basic Proportionality Theorem.
25. In fig 8. , AB=12 cm, BC=8 cm and AC= 10 cm. Find AD, BE and CF.
