Holiday Home work
Chapter 1 Real Numbers
- Ravi and Shikha drive around a circular sports field . Ravi takes 16 minutes to take one round while Shikha completes the round in 20 minutes. If both start from the same point, at the same time and go in the same direction, after how much time will they meet at the starting point ?
- If HCF of 144 and 180 is expressed in the form 13 m – 16. Find the value of m.
- The HCF of two numbers is 116 and their LCM is 1740, if one number is 580 , find the other.
- Find the largest number which divides 129 and 545, leaving remainders 3 and 5 respectively.
- What is the smallest number that , when divided by 35, 56 and 91 leaves remainder of 7 in each case .
- On a morning walk 3 persons step off together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance and complete steps?
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- Chapter 2 Polynomials
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- Find zeroes of the quadratic polynomial 4x² – 4 x-3 and verify the relation between the zeroes and its coefficients.
- Form a quadratic polynomial of which one zero is 2 – √5 and the sum of its zeros is 4.
- Find the polynomial whose zeroes are 5 + √19 and 5 -√19.
- Find k so that the difference between the zeros of the quadratic polynomial x²- 4x + k is 2.
- Find the value of k such that the polynomial x²– (k+6)x + 2(2k-1) has sum of its zeroes equal to half of their product.
- If p and q are zeroes of the polynomial x² – 2x – 15, then form a quadratic polynomial whose zeroes are 2p and 2q.
- Chapter 3 Pair of Linear equations in two variables
- Determine the value of k so that the following Linear equations have no solution.(3k+1)x + 3y-2=0(k²+1)x + (k-2)y-5=0
- For what value of k will the following pair of linear equations have infinitely many solutions. kx+3y-(k-3)=0 , 12x+ky-k=0
- Solve the following pair of linear equations 21x+47y=110 , 47x+21y=162
- The sum of a two digit number and the number obtained by reversing the order of its digits is 121 , and the two digits differ by 3. Find the number.
- 10 years ago father was 12 times as old as his son and 10 years hence, he will be twice as old as his son will be. Find their present ages.
- The taxi charges in a city comprise of a fixed charge together with the charge for the distance covered. For a journey of 10 km the charge paid is rupees 75 and for a journey of 15 km the charge paid is rupees 110. What will a person have to pay for travelling a distance of 25 km ?
- 37 pens and 53 pencils together cost rupees 320 , while 53 pens and 37 pencils together cost rupees 400. Find the cost of a pen and that of a pencil.
- Chapter 4 Quadratic equations
- Find the roots of the quadratic equation 3x²-2√6x+2=0.
- Find the discriminant of the quadratic equation 2x²-4x+3 , and hence find the nature of its roots.
- For what value of m, will the following equation have real and equal roots. x²-2x(1+3m)+7(3+2m)=0
- The sum of the squares of two numbers is 233 and one of the number is 3 less than twice the other. Find the numbers.
- The perimeter of a rectangular field is 82 cm and its area is 400 m². Find the breadth of the rectangle.
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