mathematics ONLINE TEST 0% 12th Maths – Chapter-1 & 3 (Full) Wish you all the Best ! 1 / 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 2 / 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? 5π / 6 2π / 3 3π / 4 π / 4 3 / 25 If α, β, γ are the roots of the equation x³ – 3x + 11 = 0, then α+ β + γ is______? -11 zero -3 3 4 / 25 If A is a 3×3 non-singular matrix such that AAᵀ = Aᵀ A and B = A¯¹ Aᵀ, then BBᵀ =? I₃ A Bᵀ B 5 / 25 If |adj(adjA)| = |A|⁹, then the order of the square matrix A is? 4 3 2 5 6 / 25 The equation 4ax² + 3bx + 2x = 0 where a, b, c are real and a + b+ c = has? One + ve & one – ve 2 – ve roots Two real roots Two imaginary roots 7 / 25 Let a > 0, b > 0, c > 0. Then both the roots of the equation ax² + bx + c = 0 are? Real and negative Rational numbers Real and positive None 8 / 25 The homogenous system of linear equations A x = 0 has the trivial solution if? |A| ≠ 0 |A| = 2 |A| = 1 |A| = x 9 / 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 (iii) and (iv) (ii) and (iii) Only (i) (i), (ii) and (iv) 10 / 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? 3 2 zero 1 11 / 25 The polynomial x³ + 2x + 3 has? no zeros three real zeros one negative and two imaginary zeros one positive and two imaginary zeros 12 / 25 If A,B and C are invertible matrices of some order, then which one of the following is not true? adj A = |A| A¯¹ adj (AB) = (adj A) (adj B) (ABC)¯¹ = C¯¹ B¯¹ A¯¹ det A¯¹ = (det A)¯¹ 13 / 25 If ρ (A) = ρ ([A| B]) , then the system AX = B of linear equations is? Inconsistent Consistent and has infinitely many solution Consistent Consistent and has a unique solution 14 / 25 The homogenous system of linear equations Ax = 0 has a non trivial solution if ? |A| ≠ 0 |A| = 0 |A| = 1 |A| = x 15 / 25 If Aᵀ A¯¹ is symmetric, then A² =? Aᵀ (A¯¹)² A¯¹ (Aᵀ)² 16 / 25 A polynomial equation in x of degree n always has? n complex roots n distinct roots n real roots at most one root. 17 / 25 Suppose m < n, then there are more number of unknowns then the number of equations, we get ? ρ(A) = ρ(A/0) > n ρ(A) = ρ(A/0) ≤ n ρ(A) = ρ(A/0) < n None of the above 18 / 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 19 / 25 The equation √(x + 1) – √(x – 1) = √(4x – 1) has? One solution More than one solution No solution Two solution 20 / 25 The number of real numbers in [0, 2π] satisfying sin⁴ x − 2sin² x +1 is? 1 4 2 ∞ 21 / 25 The polynomial x³ − kx² + 9x has three real zeros if and only if, k satisfies? |k| > 6 |k| ≤ 6 |k| ≥ 6 k = 0 22 / 25 According to the rational root theorem, which number is not possible rational zero of 4x⁷ + 2x⁴ −10x³ − 5 ? 5 / 4 -1 5 4 / 5 23 / 25 If the roots of the equation x³ + bx² + cx – 1 = 0 form an increasing G.P, then? One of the roots is -1 One of the roots is – 2 One of the roots is 2 One of the roots is 1 24 / 25 If f(x) = 0 has n roots, then f ‘(x) = 0 has ___ roots? (n – r) n -1 n + 1 n 25 / 25 A zero of x³ + 64 is? -4 4i 4 zero 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.
