# CBSE Set Q Maths Class X 1998 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 trigonometric tables is permitted. Use of calculator
is not permitted.

**Section - A**

**Q1) **Determine the value of c
for which the following system of linear equation has no solution:

cx + 3y = 3; 12x + cy = 6 **(Marks 2)**

**Q2) **The GCD and LCM of two
polynomials P(x) and Q(x) are x(x + a) and 12x^{2}(x + a)(x^{2}
+ a^{2}) respectively. If P(x) = 4(x + a)^{2}, find Q(x) **(Marks
2)**

**Q3) **If q is the mean
proportional between p and r, show that pqr(p + q + r)^{3} = (pq + qr +
pr)^{3 } **(Marks 2)**

**Q4) **Find the value of
such that the quadratic equation (
- 12)x^{2} + 2(
- 12)x + 2 = 0 has equal roots. **(Marks 2)
**

**Q5) **In Fig 1, OPQR is a
rhombus, three of whose vertices lie on a circle with centre O. If the area of
the rhombus is 323 cm^{2},
find the radius of the circle. **(Marks 2)
**

**Q6) **The sales price of a
television, inclusive of sales tax, is Rs. 13,500. If sales tax is charged at
the rate of 8% of the list price, find the list price of the television. **(Marks
2)**

**Q7) **Without using
trigonometric tables evaluate : 2(cos 67^{o}/sin 23^{o}) - (tan
40^{o}/cot 50^{o}) - sin90^{o} **(Marks 2)
**

**Q8) **If cos /cos
= m and cos /sin
= n, show that

(m^{2} + n^{2})cos^{2}
= n^{2} **(Marks 2)**

**Q9) **In Fig 2, ABCD is a
parallelogram in which DC = 10 cm and BC = 43
cm. AP is perpendicular to DC. If
ADC = 60^{o}, find the length of AP. **(Marks 2)
**

**Q10) **ABC
is right angled at B. On the side AC, a point D is taken such that AD = DC and
AB = BD. Find the measure of
CAB. **(Marks 2)
**

**Q11) **In Fig. 3, ABCD is a
quadrilateral in which AD = BC and
ADC = BCD. Show that the
points A, B, C and D lie on a circle. **(Marks 2)
**

**Q12) **D is a point on the side
BC of ABC such that
ADC and BAC are equal.
Prove that CA^{2} = DC x CB. **(Marks 2)
**

**Q13) **If the mean of n
observations

x_{1}, x_{2}, x_{3}, ..., x_{n} is ,
prove that

(x_{1} - ) + (x_{2}
- ) + (x_{3} - )
+ ... + (x_{n} - ) = 0
**(Marks 2)
**

**Q14) **Flow Chart - Omitted
being out of Syllabus. **(Marks 2)**

**Q15) **The median of the
following observations arranged in ascending order is 24. Find x.

11, 12, 14, 18, x + 2, x + 4, 30, 32, 35, 41 **(Marks 2)
**

**Section - B**

**Q16) **Solve graphically the
following system of linear equations : 2x - y = 2; 4x - y = 8.

Also, find the co-ordinates of the points where the lines meet the axis of x.
**(Marks 4)**

**Q17) **Factorise. Omitted,
being out of Syllabus. **(Marks 4)**

**Q18) **Students of a class are
made to stand in rows. If 4 students are extra in a row, there would be 2 rows
less. If 4 students are less in a row, there would be 4 more rows. Find the
number of students in the class. **(Marks 4)**

**Q19) **In a flight of 2800 km,
an aircraft was slowed down due to bad weather. Its average speed for the trip
was reduced by 100 km/hour and time increased by 30 minutes. Find the original
duration of flight. **(Marks 4)**

**Q20) **A solid is in the form
of a cylinder with hemispherical ends. The total height of the solid is 19 cm
and the diameter of the cylinder is 7cm. Find the volume and surface area of the
solid. **(Marks 4)**