X guess question for CBSE 2012 Mathematics

By JSUNIL TUTORIAL CBSE MATHS & SCIENCE     Class-X Quadratic Equations

Q1. Solve 36x²-12ax+(a²-b²)=0

Q2. Solve 1/a+b+x=⅟a+⅟b+⅟x

[x≠0,x≠-(a+b)]

Q3. Solve 5^(x+I) +5^(2-x)=5³+1

Q4. If -4 is a root of the equation x²+px-4=0 and the equation x²+px+q=0 has equal roots.

Find the values of p&q. [Ans. P=3,q=9/4]

Q5. For what values of ‘k’,the given equation hai real and equal roots,

(k-12)x²+2(k-12)x+2=0 [Ans. K=12,14]

Q6. Rs.250 was divided equally among a certain number of children,each would have received 50 paise less.Find the no. of children.[ans.100]

Q7. The sum of ages of a man and his son is 45 years.Five years ago,the product of their ages was four times the man’s age at that time.Find their present ages.  [36yrs.,9yrs.]

Q8. The difference of two numbers is 5 and the difference of their reciprocals is ⅟10.Find the numbers. [Ans.10,5 &-5,-10]

Q9. A train covers a distance of 90km. at uniform speed.If the speed of the train is increased by 15km an hour,the journey would have taken 30 minutes less.Find the original speed of the train.     [45km/hr.]

Arithmetic Progession

Q1. Find the 105^th term of the A.P.

4,4¹/₂,5,5¹/₂,… [Ans.56]

Q2. Is 51 a term of  A.P.

5,8,11,14?

Q3. Which term of an A.P. 24,21,18,15,---- is the first negative term?

Q4. If the p^th,q^th & r^th terms of an A.P. be a,b,c respectively,then show that a(q-r)+b(r-p)+c(p-q)=0

Q5. If the n^th term of a progression be a linear expression in n, then prove that this progression is an A.P.

Q6. The first and the last terms of an A.P. are a and l respectively.Show that the sum of the n^th term from 
the beginning and the n^th term from the end is (a+l).

Q7. Divide 24 into three parts such that they are in A.P. and their product is 440. (5,8,11)

Q8.Find the sum of all three digit natural numbers which are multiples of 7 [Ans.70336]

Q9. The sum of n terms of an A.P. is (5n²-3n). Find the A.P. Hence,find its 10^th term. [Ans.T₁₀=92]

Q10. If the sum of first n,2n and 3n terms of an A.P. be S₁,S₂ and S₃ respectively,then prove that S₃=2(S₂-S₁).

Areas related to circles

Q1. Three horses are tied with 7m. long ropes at three corners of triangular field having sides 20m.,34m,42m.Find the area of the plot,which remains ungrazed.  [Ans. 77m²,259m²]

Q2.The minute hand of a clock is 12cm. long.Find the area of the face of the clock described by the minute hand in 35 minutes.  [Ans. 264m2]

Q3. The perimeter of a sector of a circle of radius 5.6cm is 27.2cm.Find the area of the sector. [Ans.44.8cm2]

Q4. Three circles,each of radius 6cm touches the other two. Find the area enclosed between them. [π=3.14,√3=1.732]  [Ans.5.76cm2]

Coordinate Geometry

Q1. Show that the points A(1,2),B(5),C(3,8) and D(-1,6) are the vertices of a square.

Q2. Find the coordinates of the circumcentre of a triangle,whose vertices are A(4,6),B(0,4) and C(6,2).Also find the circumcentre. [Ans. (3,3) and r=√10 units.]

Q3.Find the lengths of the medians of a triangle ABC,having vertices at A(0,-1),B(2,1) and C(0,3).

Q4. Find the coordinates of the centroid of a triangle ABC whose vertices are (6,-2),B(4,-3),C(-1,-4)  [Ans. G(3,-3)]

Q5. Find the area of the rhombus whose vertices taken in order are the points A(3,0),B(4,5),C(-1,4) and D(-2,-1)          [Ans. 24sq. units]

Probability

Q1. A box contains 19 balls bearing numbers 1,2,3 ----- 19 respectively.A ball is drawn at random from the box.Find the probability that the number on the ball is:

(i.)A prime number

(ii.)Divisible by 3 or 5

(iii.)Neither divisible by 5 nor by 10

(iv.)An even number

Q2. Tickets numbered 2,3,4,5----100,101 are placed in a box and mixed thoroughly.One ticket is drawn at random from the box.Find the probability that the number on the ticket is:

(i.)   An even number

(ii.)   A number less than 16

(iii.)  A number which is a perfect square.

(iv.)  A prime number less than 40.

Q3. One card is drawn from a well shuffled deck of 52 cards. Find the probability of drawing:

(i.)   An ace

(ii.)  A  ‘4’ of spades

(iii.)  A ‘9’ of black suit

(iv.)  A red king

Q4. Find the probability of getting 53 Fridays in a leap year.

Q5. The king,the queen,the jack and 10,all of spades are lost from a pack of 52 playing cards. A card is drawn at random from the remaining well shuffled pack. Find the probability of getting:

(i.)        Red card

(ii.)       King

(iii.)      Black card

Area related to circles(02-01-2012)

Surface areas and Volumes(02-01-2012)

Mathematics Assignment - Arithmetic Progression(11-11-11)

Mathematics Assignment Chapter: Introduction to Trignometric

Maths Assignment: Chapter - Application of trignometric

Maths Assignment: Chapter - Quadratic Equations Part 1

Maths Assignment: Chapter - Quadratic Equations Part 2

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