Class X CBSE Important Question Mathematics

6/17/2012 CBSE

1.Find the value of ‘k’ so that the equation 9x2-Kx-81 = 0 has
equal roots.


2.Find the value of k for which the system of equations

8x + 5y = 9



Kx + 10y = 15


3. Find the value of x if p+1=0 and x2+px-6=0

OR

The GCD and LCM of two polynomials p(x) and Q(x) are x (x+a) and

12x2( x + a)(x2 - a2) espectively.If P(x) =
4x(x + a)2, find Q(x).


 


4. Sheetal buys goods worth of Rs 6800.She gets a rebate of 8%on it After
getting the rebate if sales tax is charged at 6% ,find the amount she has to pay
for the goods.

OR

Without using trigonometric tables, evaluate:

cos 70°/ sin 20°+ cos 59°/sin
31°
- 8 sin2
30°.

     


The mean of the numbers 1, 7, 5, 3, 4, 4 is m. The numbers 3, 2, 4, 2, 3, 3,
p have mean m -1 and median q. Find

(i) p (ii) q (iii) the mean of p and q.



6. The diagonal of a rhombus are 24cm and 10 cm. Find its perimeter.



7. If the product of two positive consecutive odd integers is 195, find the
integers.



8 .A spherical ball of aluminimum is melted and cast into smaller spheres each
with radius equal to quarter the radius of the bigger one. How many smaller
spheres can be made ?



9. The area of a field in the form of a trapezium is 1600 sq.m. If the altitude
of the field is 50m, find its parallel sides if each is multiple of 16. How many
solutions are possible to the problem ?



10. The radius of the base of a cone and a sphere are both equal to 8 cm. Given
that the volumes of these solids are also the same, calculate the slant height
of the cone correct to one place of decimals.



11. Draw a circle with radius 3 cm and centre O. Take a chord PQ = 4 cm. Draw a
tangent to the circle at P. Measure the acute angle between the tangent and
chord PQ.


 


12.


From the top of a cliff 150 m high, the angles of depression of two boats are
60° and 30°. Find the distance between the boats, if the boats are

(i) on the same side of cliff.

(ii) on the opposite sides of the cliff.


13. Mrs. Ram is a teacher in a public school. Her annual salaried income is
Rs 1,16,760. She donates Rs 1,001 to the Prime Minister's Relief Fund, which has
100% tax exemption. She contributes Rs 2,562 per month to her P.F. account, pays
an annual premium of Rs 7,376 towards her Life Insurance Policy. Calculate the
income tax paid by Mrs. Ram if her earlier deductions for the first eleven
months of income tax were at the rate of Rs 145 per month



In parallelogram ABCD, M is the mid point of side CD. A line BM is drawn

intersecting AC in L and AD produced in E. Prove that EL @ 2 BL


14. A vessel is in the form of an invalid cone with height 8 cm and radius 5
cm. It is completely filled with water. Spherical lead shots of radius of 0.5 cm
are dropped into the vessel and hence one fourth of the water overflows. Find
the number of lead - to dropped into the vessel


 OR





A) If a pair of opposite angles of a quadrilateral is supplementary, the
quadrilateral is a cyclic quadrilateral ,prove it


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