CBSE Class 10 Hots Question bank Database for chapter Application of Derivatives.Based on CBSE and NCERT guidelines. The students should practice these HOTs Questions togain perfection which will help him to get more marks in CBSE examination. Based on CBSE and NCERT guidelines. Based on the same pattern as released by CBSE every year. CBSE releases HOTs Questions every year. These papers are released prior to the CBSE board examinations so that students can do practice. database of 1 marks, 2 marks, 3 marks and 5 marks questions.
Quadratic Equation
1. Find the sum & product of the roots of the equation x2- √3 =0
2. Divide 51 into two parts whose product is378.
3. Determine K, so that the equation x2-4x+k=0 has no real roots.
4. Find the equation whose roots are 5+ √2 and 5- √2
5. For the given equation √3 x2-2 √2 x-2 √3 =0
6. Find the value of a and b such that x=1, and x= -2 are solutions of the quad. Equation x2+ax+b=0
7. Find the value of K for which the following quad. Equation have equal roots
(a). (k-4) x2+2(k-4) x+4=0 (b). kx (x-2) +6=0
8. For what value of ‘P’, the following equations have real roots
(a) Px2r +4x +1=0 (b) 4x2 + 8x-P=0 (c) 2x2+Px +8=0
9. If ∝ and β are the roots of the equation x2 – 4x –5=0. Find ∝-1 + β-1
10. If one root of a quad. Equation is 2 −√3/2 , then what is the other root?
2/3 MARKS
1. Solve the following by factorization method
(a) 2x2+ax-a2=0, a∈ R (b) 4x2-4ax+(a2-b2)=0 (a,b∈ R)
2. Using quadratic formula, solve the following equation for x abx2 + (b2-ac) x-bc=0 (a,b,c ∈ R)
3. Solve for x, x+ 1/x = 25 1/25.
4. If one root of the quadratic equation 2x2 +kx -6 =0 is 2, find the value of k also find the other root
5. If -5 is a root of 2x2 + px-15=0 & the quad. Equation f (x2+x)+k = 0 has equal root find the value of k
6. If the roots of the equation (b-c) x2 +(c-a) x+ (a-b)=0 are equal then prove that 2b= a+c
7. Find two consecutive multiple of three whose product is 270
8. Two no. differ by 4 and their product is 192, find the numbers.
9. Is the following situation possible ?if so determine their present ages The sum of the ages of two friend are 20 years. 4 years ago, the product of their age in years was 48.
10. If the list price of a toy is reduced by Rs 2 a person can by 2 toys more for Rs360.find original price of the toy.
Answers
1 Marks Questions
(1) sum = 0 , Product = -√13
(2) 42,9
(3) K > 4
(4) X2– 10x + 23 = 0
(5) √6 , −√6/3
(6) 4 /3 , −4/ 3
(7) (a) P ≤ 4 (b) P ≥ −8 (c) P ≥ 8 , ≤ −8
(8) −4 /5
(9) 2 + √3/2
2/3 Marks Questions
(1) (a) x = -a , a /2 (b) a ± b/2
(2) X = −b/ a , x = c/ b
(3) 25 , 1/25
(4) 2 , −3/2
(5) P=7 , k = 7/4
(6)
(7) 15,18 ; -15, -18
(8) 12,16
(9) Not possible
(10) Rs.20