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Class 10 · Mathematics · Medium

If A ⊆ B in a universal set U, which of the following relations is always true?

Class 10 · Mathematics · Easy

If U = {1,2,3,4,5,6,7,8}, A = {1,2,3,4}, and B = {5,6,7,8}, what is the relation between B and A?

Class 10 · Mathematics · Medium

What is the sum of the squares of the roots of the equation \(x^2-9x+14=0\)?

Class 10 · Mathematics · Medium

If the roots of the equation \(x^2+ax+25=0\) are \(5\) and \(5\), what is the value of \(a\)?

Class 10 · Mathematics · Medium

What are the roots of the quadratic equation \(x^2-14x+45=0\)?

Class 10 · Mathematics · Medium

One root of the equation \(x^2-15x+54=0\) is \(6\). What is the other root?

Class 10 · Mathematics · Medium

Which quadratic equation has −3 and 6 as its roots?

Class 10 · Mathematics · Medium

For the quadratic equation \(x^2-14x+49=0\), what are the sum and product of its roots, respectively?

Class 10 · Mathematics · Medium

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, and Aᶜ ⊆ B ⊆ U, what is the smallest possible set B?

Class 10 · Mathematics · Medium

If Aᶜ ⊆ Bᶜ, which of the following conclusions is correct?

Class 10 · Mathematics · Easy

Which monic quadratic equation has sum of roots 10 and product of roots 21?

Class 10 · Mathematics · Medium

If the product of two real roots is positive and their sum is positive, how must both roots be?

Class 10 · Mathematics · Easy

One root of the equation \(x^2-11x+30=0\) is \(5\). What is the other root?

Class 10 · Mathematics · Easy

Which equation has roots 2 and 5?

Class 10 · Mathematics · Expert

If the roots of \(x^2+px+q=0\) are \(p+2\) and \(q-2\), and \(p+q=8\), what is the value of \(p\)?

Class 10 · Mathematics · Medium

If α and β are the roots of x² − 8x − 33 = 0, what is αβ + 5α + 5β?

Class 10 · Mathematics · Medium

If one root of x² + ax + 54 = 0 is 6, what are the other root and the value of a?

Class 10 · Mathematics · Medium

If α and β are roots of x² − 7x − 30 = 0, what is αβ + 4α + 4β?

Class 10 · Mathematics · Expert

If the roots of the quadratic equation \(x^2+bx+c=0\) are \(-5\) and \(11\), what is the value of \(b+c\)?

Class 10 · Mathematics · Medium

If one root of x² + ax + 40 = 0 is 5, what are the other root and a?

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