CBSE Important Questions

CLASS X MATHS (H.W)

1. Find the value of k, for which given value is a zero of the given quadratic polynomial (a) (x²+2kx-3);x = -1/2 (b)x²+4ax-k; x= -a
2. Verify that -1, 1, 2 are zeros of a cubic polynomial x³ - 2x² - x+2 & verify the relationship between the zeros & its coefficients.
3. Form a quadratic polynomial whose (i) zeros are 2 & -3(ii) zeros are -4/5 & 1/3.
4. Solve the equations 15x -6y = 30 ; 17x + 10y =118
5. Solve the equations ax + by = c; bx – ay = 0
6. A fraction becomes 9/11, if 2 is added to both the numerator & denominator. If 3 is added to both the numerator & denominator it becomes 5/6. Find the fraction.
7. Solve(By cross multiplication)  2/u + 3/v = 13 ; 5/u – 4/v = -2
8. Find the values of p & q for which the following system has infinite solutions. 2x + 3y = 7 ; (p + q)x + (2p – q)y = 21.
9. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. How old I am and how old is my son?
10. A and B are friends and their ages differ by two years. A’s father D is twice as old as A, & B is twice as old as his sister C. The ages of D and C differ by 40 years. Find the ages of A and B?
11. Five years hence father’s age will be three times age of his son. Five years ago father was seven times as old as his son. Find their present ages.
12. Five years ago, Neeta was thrice as old as Gita. Ten years later, Neeta will be twice as old Gita. How old are Gita & Neeta now?
13. If two zeroes of the polynomials are x⁴ - 6x³ - 26x² + 138x - 35 are 2±√3, find the other zeroes.
14. On dividing x³ - 3x² + x + 2 by polynomials g(x), the quotient & remainder were x - 2 & - 2x+4 respectively. Find g(x).
15. If the polynomials x⁴ + 2x³ + 8x² + 12x + 18 is divided by another polynomial x²+ 5, the remainder comes out to be p x +q. Find the values of p and q .
16. Prove that √2 is not a rational number.
17. Find the values of  m and n for which the following system of equations has infinitely many solutions: 3x+4y = 12; (m + n)x +2(m-n)y=5m-1
18. Solve for  x & y:  x/a +y/b =1 ;  a(x-a) – b( a + b)=2a²+b²
19. Solve for x & y: b x/a +ay/b = a²+b²;   x+ y =2ab.
20. Solve for  x & y: x/a – y/b = a-b; ax +by = a³ + b³
21. Solve for x & y: 3(2x + y ) = 7xy  ; 3(x +3y) = 11xy.
22. Solve for  x & y:  3/(x + y) + 2/(x – y) =2 ; 9/(x +y) + 4/(x- y) = 1;(x + y) ≠0  (x - y) ≠0
23. A two digit number is obtained by either multiplying the sum of the digits by 8 & adding 1, or by multiplying the difference of the digits by 13 & adding 2. Find the number. How many such numbers are there?
24. The difference between two numbers is 15 &the difference between their squares is 465. Find the numbers.
25. In a rectangle if length is increased by 7 units & breadth is decreased by 3 units or if length is decreased by 7 units & breadth is increased by 5 units, in both the cases the area remains same. Find the dimensions of the rectangle. Also find the area of the rectangle.
26. A fraction is such that if the numerator is multiplied by 3 & denominator is reduced by 3, we get 18/11, but if the numerator is increased by 8 & denominator is doubled, we get 2/5. Find the fraction.
27. Solve(By Cross-Multiplication)
    (a – b) x + (a+ b) y = a² - 2ab - b² ;
    (a + b)( x + y) = a² + b²