class 10 Real Numbers Guess Questions

1) State whether 6/15 will have a terminating decimal expansion or a non-terminating repeating decimal.

2) State whether 35/50 will have a terminating decimal expansion or a non-terminating repeatingdecimal.

3) Find the LCM and HCF of 192 and 8 and verify that LCM × HCF = product of the two numbers.

4) Use Euclid’s algorithm to find the HCF of 4052 and 12576.

5) Show that any positive odd integer is of the form of 4q + 1 or 4q + 3, where q is some integer.

6) Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

7) Prove that 3√2 5 is irrational.

8) Prove that 1/√2 is irrational. (3 marks)

9) In a school there are tow sections- section A and Section B of class X. There are 32 students in section A and 36 students in section B. Determine the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.

10) Express 3825 as a product of its prime factors.

11) Find the LCM and HCF of 8, 9 and 25 by the prime factorization method.

12) Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.

13) State whether 29/343 will have a terminating decimal expansion or a non-terminating repeating decimal.

14) State whether 23/ 23 52 will have a terminating decimal expansion or a non-terminating repeating decimal

15) Find the LCM and HCF of 336 and 54 and verify that LCM × HCF = product of the two numbers

CBSE X Guess questions For 2014 CBSEBoard

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

Thanks to http://www.hansrajmodelschool.org

10th maths Extra score questions chapter Pair of Linear Equation in Two Variable

Pair of Linear Equation in Two Variable HOTS By JSUNIL TUTORIAL

1 mark questions :- 

Q. 1 Is the pair of linear equations consistent: - x + y = 3 ; 3x – 2y = 4 .

Q. 2 Find out whether the lines representing the following pair of linear equations are parallel or coincide:- 6x – 3y +10 = 0 ; 2x – y + 9 = 0

Q. 3 Write the value of k for which the following pair of linear equations has unique solution:-

x + k y + 6 = 0 ; 2x + 3y + 8 = 0

Q. 4 Write the value of k for which the following pair of linear equations has no solution: -

4x +y =11 ; k x + 3y =5

Q. 5 Write the value of k for which the system of equations has infinite solutions:-

2x – 3y +10 = 0 ; 3x – ky +15 = 0

Q. 6 Does (2, –3) lie on the linear equation 3x – 2y + 5 = 0

10th maths Chapter Polynomial extrascore questions

Math Adda  

Chapter: POLYNOMIALS        

LEVEL-I

1. The zeroes of the polynomial 2x²-3x-2 are

a. 1, 2        b. -1/2,1    

c. ½,-2      d. -1/2,2                       [Ans- (d)]

2. If a and b are zeroes of the polynomial 2x²+7x-3, then the value of a² +b² is

a. 49/4                b. 37/4       

c. 61/4                d. 61/2                                                      
Ans-( c ) 

3. If the polynomial 6x³+16x²+px -5 is exactly divisible by 3x+ 5 , then the value of p is

a. -7      b. -5     

c.5        d.7                                                                                  
[Ans- (d )]

4. If 2 is a zero of the polynomials 3x2+ax-14 and 2x3+bx2+x-2, then the value of 2 - 2b is

a. -1       b. 5         

c. 9       d. -9                         

[Ans-( c ) ]

5. A quadratic polynomial whose product and sum of zeroes are 1/3 and √2 respectively is

(a) 3x² – x +3√ 2 (b) 3x² + x - 3√2 (c) 3x² + 3√2x +1 (d) 3x² – 3√2x +1         
[ Ans: (d)]

LEVEL-II

1. If 1 is a zero of the polynomial p(x) = ax² -3(a-1) x -1, then find the value of a.       
Ans: a=1

2. For what value of k, (-4) is zero of the polynomial x² – x – (2k+2)?                          
Ans: k=9

3. Write a quadratic polynomial, the sum and product of whose zeroes are 3 and -2. 
Ans: x² -3x-2

4. Find the zeroes of the quadratic polynomial 2x²-9-3x and verify the relationship between the zeroes and the coefficients.                                   Ans: 3, -3/2

5. Write the polynomial whose zeroes are 2 +√3 and 2 - √3.          Ans: p(x)=x2-4x+1

LEVEL – III

1. Find all the zeroes of the polynomial 2x³+x²-6x-3, if two of its zeroes are -√3 and √3. 
Ans: x=-1/2

2. If the polynomial x⁴ + 2x³ + 8x²+12x+18 is divided by another polynomial x² + 5, the remainder comes out to be  px+q. 

Find the value of p and q.                                                         Ans:p=2,q=3

3. If the polynomial 6x⁴+8x³+17x²+21x+7 is divided by another polynomial 3x²+4x+1, the remainder  comes out to  be (ax+b), find a and b.                      Ans:a=1, b=2

4. If two zeroes of the polynomial f(x)= x³-4x²-3x+12 are √3 and -√3, then find its third zero. Ans: 4

5. If a, b are zeroes of the polynomial x²-2x-15 then form a quadratic polynomial whose zeroes are  (2a) and (2b).              Ans: x²-4x-60

LEVEL – IV

1. Find other zeroes of the polynomial p(x)=2x⁴ +7x³19x²-14x +30 if two of its zeroes are √2 and -
√2.

Ans: 3/2 and -5

2. Divide 30x⁴ +11x³-82x²-12x-48 by (3x² +2x-4) and verify the result by division algorithm.

3. If the polynomial 6x⁴ +8x³-5x²+ax+b is exactly divisible by the polynomial 2x²-5, then find the 
value of a and b.     
Ans: a = -2 0 , b = - 2 5

4. Obtain all other zeroes of 3x⁴ -15x³+13x²+25x-30, if two of its zeroes are and ±√5/3. 
Ans: 
±√5/3,3,2

5. If a, b are zeroes of the quadratic polynomial p(x)=kx²+4x+4 such that a² +b²=24, find the value 
of k.                                                                        
Ans: k=2/3 or k= -1

SELF EVALUATION

1. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find (a) a/b +b/a (b) a² +b²

2. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find the value of a² - b²

3. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find the value of a³ +b³

4. What must be added to 6x⁵+5x⁴+11x³-3x²+x+5 so that it may be exactly divisible by 3x² -2x+4 ?

5. If the square of difference of the zeroes of the quadratic polynomial f(x)= x²+px+45 is equal to 144, 
find the value of p.

Algebra

Math Adda

of the following:
Q. 1. Solve for x and y: x – 4y = 13 and 3x + 2y = – 3.
Q. 2. Find the discriminant of the quadratic equation 3x2 – 5x – 11 = 0.
Q. 3. Find AP, if first term – 1 and common difference is 2.

Q. 4. Write the formula for sum of first n terms of an AP whose first term is a and the last term is l.
Q. 5. Find the value of k, so that the pair of linear equations will have infinite number of solutions: x +
(2k – 1)y = 4 and kx + 6y = k + 6.
Q. 6. Draw the graphs of the equations 4x – y – 8 = 0 and 2x – 3y + 6 = 0. Also determine the vertices
of the triangle formed by the lines and x – axis.
Q. 7. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks
more in Mathematics and 3 marks less in English, the product would have been 210, find her marks in
the two subjects.
Q. 8. If the pthterm of an AP is q and the qthterm is p. Find the rthterm.
Q. 9. Find the zeroes of the quadratic polynomial 8x2 – 4 and verify the relationship between zeroes
and their coefficients.
Q. 10. Solve the following system of linear equations: 2(ax – by) + (a + 4b) = 0 and 2(bx + ay) + (b –
4a) = 0.
Q. 11. Solve for x: 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0
Q. 12. If m times the mth term of an AP is equal to n times its nth term, find its (m + n)th term.

Real number CBSE TEST PAPER-07

Math Adda
                                             CBSE TEST PAPER-07
                                            MATHEMATICS (Class-10)
                                             Chapter 1. Real Numbers



1. What will be the value of 0.+ 0. ?

2. Given that HCF (135, 225) = 45. Find LCM (135, 225).

3. Solve √18x√50. What type of number is it, rational or irrational?

4. What type of decimal expansion will69/60 represent? After how many places will the decimal expansion terminate?

5. Find the H.C.F. of the smallest composite number and the smallest prime number.

6. If a = 4q + r then what are the conditions for a and q. What are the values that rcan take?

7. What is the smallest number by which √5 - √ 3 be multiplied to make it a rational no? Also find the no. so obtained.

8. What is the digit at unit’s place of 96?

9. Find one rational and one irrational no. between √3 and √5.

10. If the no. pn never to end with the digit 0 then what are the possible value (s) ofp?

11. State Euclid’s Division Lemma and hence find HCF of 16 and 28.

12. State fundamental theorem of Arithmetic and hence find the unique fraternization of 120.

13. Prove that 1/(2 - √5) is irrational number.

14. Check whether 5 × 7 × 11 + 6 is a composite number.

15. Check whether 7 × 6 × 3 × 5 + 5 is a composite number.

Real number CBSE TEST PAPER-06

Math Adda


CBSE TEST PAPER-06

MATHEMATICS (Class-10)

Chapter 1. Real Numbers
1. Express each number as a product of its prime factors:

(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

3. Find the LCM and HCF of the following integers by applying the prime factorization method.

(i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25

4. Given that HCF (306, 657) = 9, find LCM (306, 657).

5. Check whether 6n can end with the digit 0 for any natural number n.

6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

7. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

12. Use Euclid’s division lemma to show that the square of any positive integer is of the form 5q, 5q+1,5q+4 for some integer q.

13. Show that any one of the numbers (n + 2), n and (n + 4) is divisible by 3.

14. If 793800 = 2 3 x 3 m x 5 n x 7 2, find the value of m and n. 15. If the HCF of 210 and 55 is expressible in the form 210 × 5 + 55y then find y

Real number

Math Adda

                    CBSE TEST PAPER-05

                            MATHEMATICS (Class-10)

                               Chapter 1. Real Numbers

1. Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255
2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
3. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Sol. Hints: Find the HCF of 616 and 32
4. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]
5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m+ 1 or 9m + 8.
6. Consider the numbers 4n, where n is a natural number. Check whether there is any value of nfor which 4n ends with the digit zero.
7. Find the LCM and HCF of 6 and 20 by the prime factorization method.
8. Find the HCF of 96 and 404 by the prime factorization method. Hence, find their LCM.
9. Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.
10. Find the value of y if the HCF of 210 and 55 is expressible in the form 210 x 5 + 55y
11. Prove that no number of the type 4K + 2 can be a perfect square.

Real Number

Math Adda

                 CBSE TEST PAPER-04

                         MATHEMATICS (Class-10)

                        Chapter 1. Real Numbers

1.    Express 5005 as a product of its prime factors.

2.    Find the LCM and HCF of 24, 36 and 72 by the prime factorization method.

3.    Find the LCM and HCF of 96 and 404 by the prime factorization method

4.    State whether 64/455  will have a terminating decimal expansion or a non-terminating repeating decimal

5.     State whether15/ 1600   will have a terminating decimal expansion or a non-terminating repeating decimal.

6.    Find the LCM and HCF of 510 and 92 and verify that LCM × HCF = product of the two numbers.

7.    Use Euclid’s division algorithm to find the HCF of 196 and 38220 (3 marks)

8.    Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m,9m + 1 or 9m + 8

9.     Show that every positive odd integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer

10.  10. Show that 3√ 2 is irrational.

11.  11. Prove that 3 + 2 √5 is irrational.

12.  A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?

Real Number

Math Adda                                     CBSE TEST PAPER-03

                                   MATHEMATICS (Class-10)

                                    Chapter 1. Real Numbers

1. Express 3825 as a product of its prime factors.

2. Find the LCM and HCF of 8, 9 and 25 by the prime factorization method.

3. Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.

4. State whether 29/343  will have a terminating decimal expansion or a non-terminating repeating decimal.

5. State whether 23/ 2³ 5²will have a terminating decimal expansion or a non-terminating repeating decimal

6. Find the LCM and HCF of 336 and 54 and verify that LCM × HCF = product of the two numbers

7. Use Euclid’s division algorithm to find the HCF of 867 and 255

8. Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.

9. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m,9lm + 1 or 9m + 8.

10. Prove that 7 √5 is irrational.

11. Prove that √5 is irrational.

12. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Real number

Math Adda                            CBSE TEST PAPER-02

                                              MATHEMATICS (Class-10)

                                     Chapter 1. Real Numbers

1. Express 156 as a product of its prime factors.

2. Find the LCM and HCF of 17, 23 and 29 by the prime factorization method.

3. Find the HCF and LCM of 12, 36 and 160, using the prime factorization method.

4. State whether 6/15  will have a terminating decimal expansion or a non-terminating repeating decimal.

5. State whether35/50  will have a terminating decimal expansion or a non-terminating repeating

decimal.

6. Find the LCM and HCF of 192 and 8 and verify that LCM × HCF = product of the two numbers.

7. Use Euclid’s algorithm to find the HCF of 4052 and 12576.

8. Show that any positive odd integer is of the form of 4q + 1 or 4q + 3, where q is some integer.

9. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

10. Prove that 3√2 5 is irrational.

11. Prove that 1/√2   is irrational. (3 marks)

12. In a school there are tow sections- section A and Section B of class X. There are 32 students in section A and 36 students in section B. Determine the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.

Real number

Math Adda

                               CBSE TEST PAPER-01

                                           MATHEMATICS (Class-10)

                                                         Chapter 1. Real Numbers

1.    Express 140 as a product of its prime factors

2.    Find the LCM and HCF of 12, 15 and 21 by the prime factorization method.

3.    Find the LCM and HCF of 6 and 20 by the prime factorization method.

4.    State whether13/3125 will have a terminating decimal expansion or a non-terminating repeating decimal.

5.    State whether 17/8 will have a terminating decimal expansion or a non-terminating repeating decimal.

6.    Find the LCM and HCF of 26 and 91 and verify that LCM × HCF = product of the two numbers.

7.    Use Euclid’s division algorithm to find the HCF of 135 and 225

8.    Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m

9.    Prove that √3 is irrational.

10. Show that 5 – √3 is irrational

11. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, whereq is some integer.

12. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?