mathematics ONLINE TEST 0% 12th Maths – Chapter-1 & 3 (Full) Wish you all the Best ! 1 / 25 The number of real numbers in [0, 2π] satisfying sin⁴ x − 2sin² x +1 is? ∞ 4 2 1 2 / 25 If α, β, γ are the roots of the equation x³ – 3x + 11 = 0, then α+ β + γ is______? -11 -3 zero 3 3 / 25 The equation 4ax² + 3bx + 2x = 0 where a, b, c are real and a + b+ c = has? 2 – ve roots Two imaginary roots One + ve & one – ve Two real roots 4 / 25 The rank of the coefficient matrix is equal to the rank of the augmented matrix and is loss then 3, the determinant of the coefficient matrix should be? zero 1 3 2 5 / 25 The polynomial x³ − kx² + 9x has three real zeros if and only if, k satisfies? k = 0 |k| > 6 |k| ≥ 6 |k| ≤ 6 6 / 25 The homogenous system of linear equations Ax = 0 has a non trivial solution if ? |A| ≠ 0 |A| = 0 |A| = x |A| = 1 7 / 25 A polynomial equation in x of degree n always has? at most one root. n distinct roots n complex roots n real roots 8 / 25 If a, b,c ϵ Q p + √q (p,q ϵ Q) is an irrational root of ax² + bx + c = 0 then the other root is? – p – √q p – √q p – iq – p + √q 9 / 25 Let a > 0, b > 0, c > 0. Then both the roots of the equation ax² + bx + c = 0 are? Real and negative Real and positive Rational numbers None 10 / 25 Suppose that m > n, then there are more number of equations then the number of unknowns, reducing the system by elementary transformations, we get? ρ(A) = ρ(A/0) > n ρ(A) = ρ(A/0) ≤ n ρ(A) = ρ(A/0) < n ρ(A) = ρ(A/0) = n +1 11 / 25 The polynomial x³ + 2x + 3 has? one positive and two imaginary zeros no zeros three real zeros one negative and two imaginary zeros 12 / 25 Which of the following is/are correct? (i) Adjoint of a symmetric matrix is also a symmetric matrix. (ii) Adjoint of a diagonal matrix is also a diagonal matrix. (iii) If A is a square matrix of order n and λ is a scalar, then adj( A) = n adj(A) . (iv) A(adjA) = (adjA)A =| A| I (i), (ii) and (iv) Only (i) (iii) and (iv) (ii) and (iii) 13 / 25 A zero of x³ + 64 is? 4i 4 -4 zero 14 / 25 According to the rational root theorem, which number is not possible rational zero of 4x⁷ + 2x⁴ −10x³ − 5 ? 5 / 4 4 / 5 5 -1 15 / 25 Suppose m < n, then there are more number of unknowns then the number of equations, we get ? ρ(A) = ρ(A/0) > n None of the above ρ(A) = ρ(A/0) < n ρ(A) = ρ(A/0) ≤ n 16 / 25 If A is a 3×3 non-singular matrix such that AAᵀ = Aᵀ A and B = A¯¹ Aᵀ, then BBᵀ =? B A I₃ Bᵀ 17 / 25 If ρ (A) = ρ ([A| B]) , then the system AX = B of linear equations is? Consistent and has a unique solution Consistent Consistent and has infinitely many solution Inconsistent 18 / 25 The homogenous system of linear equations A x = 0 has the trivial solution if? |A| = 1 |A| = x |A| ≠ 0 |A| = 2 19 / 25 If A,B and C are invertible matrices of some order, then which one of the following is not true? (ABC)¯¹ = C¯¹ B¯¹ A¯¹ adj (AB) = (adj A) (adj B) det A¯¹ = (det A)¯¹ adj A = |A| A¯¹ 20 / 25 If the roots of the equation x³ + bx² + cx – 1 = 0 form an increasing G.P, then? One of the roots is – 2 One of the roots is 2 One of the roots is -1 One of the roots is 1 21 / 25 The equation √(x + 1) – √(x – 1) = √(4x – 1) has? No solution Two solution More than one solution One solution 22 / 25 If 0≤ θ ≤ π and the system of equations x + (sinθ) y -(cosθ) z =0, (cos θ) x – y + z =0, (sin θ) x + y – z =0, has a non-trivial solution then θ is? 2π / 3 π / 4 5π / 6 3π / 4 23 / 25 If f(x) = 0 has n roots, then f ‘(x) = 0 has ___ roots? n + 1 (n – r) n -1 n 24 / 25 If |adj(adjA)| = |A|⁹, then the order of the square matrix A is? 4 2 3 5 25 / 25 If Aᵀ A¯¹ is symmetric, then A² =? (A¯¹)² Aᵀ A¯¹ (Aᵀ)² Your score is 0% Note: Once you start the test, you are not allowed to go back. Results won’t be generated if you quit the test. Complete the test within the given time. Once the time is over, the test will be submitted automatically. You can verify your answers at the result page.
