# CBSE Set Q Maths Class X 1999 Sample Test Papers For Class 10th for students online

**Maths Class X (CBSE)
You are on Set no 1 Qno. 1 to 20
**

Time allowed : 3 hours
Maximum Marks : 100

General Instructions :

(i) Question number 1 to 15 carry 2 marks each.

(ii) Question number 16 to 25 carry 4 marks each.

(iii) Question number 26 to 30 carry 6 marks each.

(iv) Write the serial number of the question before attempting it.

(v) Use of logarithmic and trignometric tables is permitted. Use of calculator
is not permitted.

**Section - A**

**Q1) **Evaluate without using
trignometric table:

cos 75^{o}/sin 15^{o} + sin 12^{o}/cos 78^{o} -
cos 18^{o}/sin 72^{o} **(Marks 2)**

**Q2) **Evaluate (sec^{2}
- 1)(1 - cosec^{2}
) **(Marks 2)**

**Q3) **If tan A = b/a where a
and b are real numbers, find the value of sin^{2} A **(Marks 2)**

**Q4) **A cricketer has mean
score of 58 runs in nine innings. Find out how many runs are to be scored in the
tenth innings to raise the mean score to 61. **(Marks 2)
**

**Q5) **Find the mean of the
following data:

46, 64, 87, 41, 58, 77, 35, 90, 55, 33, 92

If in the data, the observation 92 is replaced by 19, determine the new median.
**(Marks 2)**

**Q6) **Harshad purchased a
motorcycle for Rs. 42,952 which includes the amount of sales tax. If the tax
charged is 12% of the list price, find the list price of the motorcycle. **(Marks
2)**

**Q7) **The circumference of the
edge of a hemispherical bowl is 132 cm. Find the capacity of the bowl (
= 22/7) **(Marks 2)
**

**Q8) **Find the value of c for
which the quadratic equation 4x^{2} - 2(c + 1)x + (c + 4) = 0 has equal
roots.

**(Marks 2)**

**Q9) **The ages of two girls are
in the ratio 5 : 7. Eight years ago their ages were in the ratio 7 : 13. Find
their present ages. **(Marks 2)
**

**Q10) **Find the value of k for
which the system of equation 8x + 5y = 9, kx + 10y = 15 has no solution.

**(Marks 2)
**

**Q11) **Find the G.C.D. of 24(4x^{2}
- 9) and 18(2x^{2} + 5x - 12) **(Marks 2)
**

**Q12) **Flow chart. Deleted from
the syllabus. **(Marks 2)**

**Q13) **In figure ABCD is a
cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ABC
= 92^{o}, FAE =
20^{o}, find BCD. **(Marks 2)
**

**Q14) **Determine the length of
an altitude of an equilateral triangle of side 2a cm. **(Marks 2)
**

**Q15) **In the figure, a circle
touches all the four sides of a quadrilateral ABCD where sides AB = 6 cm, BC = 7
cm and CD = 4 cm. Find AD. **(Marks 2)
**

**Section - B**

**Q16) **Solve graphically:

2x - y = 1, x + 2y = 8. Also, find the co-ordinates of the points where the line
meet the axis of y. **(Marks 4)**

**Q17) **Simplify :- (2x^{2}
+ x - 3)/(x - 1)^{2}
(2x^{2} + 5x - 3)/(x^{2} - 1) **(Marks 4)
**

**Q18) **Cyclic factorization.
Deleted from the syllabus. **(Marks 4)**

**Q19) **The sum of radius of
base and the height of a solid cylinder is 37 cm. If the total surface area of
the solid cylinder is 1628 cm^{2}, find the volume of the cylinder (
= 22/7). **(Marks 4)**

**Q20) **A plane left 30 minutes
late than the scheduled time and in order to reach the destination 1500 km away
in time, it has to increase the speed by 250 km/hr from the usual speed. Find
the usual time. **(Marks 4)**