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The value of a for which the equation 2x² + 2√6x + a = 0 has equal roots, is

1) 3 2) 4 3) 2 4) √3 5) √2 Solution: (1) 3 The equation 2x2 + 2√6x + a... View Article

The quadratic equations x² + 15 |x| + 14 = 0 has

1) only positive solutions 2) only negative solutions 3) no solution 4) both positive and negative solutions Solution: (3) no... View Article

The number of real values of x which satisfy the equation |x / (x + 1)| + |x| = x / |x – 1|, is

1) 2 2) 1 3) infinite 4) Zero Solution: (2) 1 |x / (x + 1)| + |x| = x... View Article

If one of the roots of 2x² – cx + 3 = 0 is 3 and another equation 2x² – cx + d = 0 has equal roots, where c and d are real numbers, then d is equal to

1) 3 2) 49/8 3) 8/49 4) – 3 Solution: (2) 49/8 Let α and 3 be the roots of... View Article

If a, b and c are real numbers, such that a + 2b + 4c = 0. Then, the equation ax² + bx + c = 0

1) has both the roots complex 2) has its roots lying within – 1 < x < 0 3) has... View Article

The number of integral values of b, which the equation x² + bx – 16 has integral roots, is

1) 2 2) 3 3) 4 4) 5 5) 6 Solution: (1) 2 In this equation, b is an even... View Article

Let α and β be real and z be a complex number. If z² + αz + β = 0 has two distinct roots on the line Re(z) = 1, then it is necessary that

1) β ϵ (-1, 0) 2) |β| = 1 3) β ϵ [1, ∞) 4) β ϵ (0 , 1)... View Article

If a, b and c are in arithmetic progression, then the roots of the equation ax² – 2bx + c = 0 are

1) 1 and c / a 2) – 1 / a and – c 3) – 1 and – c... View Article

The number of real solutions of the equation sin e^x = 5^x + 5^-x is

1) 1 2) 0 3) 2 4) None of these Solution: (2) 0 5x + 5-x = 5x + (1... View Article

The real number K for which the equation, 2x³ + 3x + k = 0 has two distinct real roots in [0,1]

1) lies between 1 and 2 2) lies between 2 and 3 3) lies between – 1 and 0 4)... View Article

Solve the equation x² – √3x + 1 = 0

1) x = (-√3 ± 2i)/2 2) x = (-√3 ± i)/2 3) x = (-√3 ± i) 4) x... View Article

If 9√x = √12 + √147, then the value of x is

1) – 2 2) 2 3) 3 4) – 3 Solution: (3) 3 9√x = √12 + √147 9√x =... View Article

The number of solution(s) of the equation √x + 1 – √x – 1 = √4x – 1 is / are

1) 2 2) 0 3) 3 4) 1 Solution: (2) 0 √x + 1 – √x – 1 = √4x... View Article

If α and β are the roots of the quadratic equation x² + px + q = 0, then the values of α³ + β³ and α⁴ + α²β² + β⁴ are respectively

1) 3pq – p3 and p4 – 3p2q + 3q2 2) -p (3q – p2) and (p2 – q) (p2... View Article

In ∆ABC, tan A and tan B are the roots of pq (x² + 1) = r²x. Then ∆ABC is

1) a right-angled triangle 2) acute-angled triangle 3) an obtuse-angled triangle 4) an equilateral triangle Solution: (1) a right-angled triangle... View Article

The equation whose roots are the squares of the roots of the equation 2x² + 3x + 1 = 0, is

1) 4x2 + 5x + 1 = 0 2) 4x2 – x + 1 = 0 3) 4x2 – 5x... View Article

The value of x such that 3^2x – 2(3^x+2) + 81 = 0 is

1) 1 2) 2 3) 3 4) 4 5) 5 Solution: (2) 2 The given equation is 32x – 2(3x+2)... View Article

If α and β are the roots of the equation px² + qx + r = 0, p ≠ 0. If p, q and r are in AP and 1 / α + 1 / β = 4, then the value of |α -β|is

1) √61/9 2) 2√17/9 3) √34/9 4) 2√13/9 Solution: (4) 2√13/9 Since ɑ + β = – q / p... View Article

The sum of the roots of the equation ax² + bx + c = 0 is equal to the sum of the reciprocal of their squares, then bc², ca², ab² will be in

1) AP 2) GP 3) HP 4) None of these Solution: (1) AP Let p and q be the roots... View Article

If the sum of two roots of x³ + px² – qx + r = 0 is zero, then pq is equal to

1) – r 2) r 3) 2r 4) – 2r Solution: (1) – r Let ɑ, – ɑ, β be... View Article

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