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 coordinates 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)
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