Maths TET Paper 2 - Algebra

ప్రశ్న 1: Find the degree of the algebraic expression: 5x³y² - 3x²y⁴ + 7xy - 9.

(A) 3 (B) 5 (C) 6 (D) 4

ప్రశ్న 2: If P = 3x² - 4x + 7 and Q = 2x² + 5x - 3, what is the coefficient of x in (2P - 3Q)?

(A) -23 (B) 7 (C) -1 (D) 23

ప్రశ్న 3: If x = -1 and y = 2, find the value of: 3x³ - 2x²y + 4xy² - 5.

(A) -28 (B) -26 (C) -24 (D) -30

ప్రశ్న 4: Simplify: (81 / 16)^(-3/4) × (25 / 9)^(-3/2)

(A) 8 / 125 (B) 125 / 8 (C) 64 / 125 (D) 27 / 125

ప్రశ్న 5: If 2^(x - 1) + 2^(x + 1) = 320, find the value of x.

(A) 6 (B) 7 (C) 8 (D) 5

ప్రశ్న 6: The standard form (Scientific notation) of 0.00000305 is:

(A) 3.05 × 10^(-5) (B) 3.05 × 10^(-6) (C) 30.5 × 10^(-7) (D) 3.05 × 10^(-7)

ప్రశ్న 7: If x + (1/x) = 5, then find the value of x³ + (1/x³).

(A) 125 (B) 110 (C) 140 (D) 115

ప్రశ్న 8: If a + b + c = 0, what is the value of (a² / bc) + (b² / ca) + (c² / ab)?

(A) 0 (B) 1 (C) 3 (D) -3

ప్రశ్న 9: If x + y + z = 9 and xy + yz + zx = 23, find the value of x² + y² + z².

(A) 35 (B) 81 (C) 45 (D) 58

ప్రశ్న 10: Factorize completely: x⁴ - 16y⁴.

(A) (x² - 4y²)(x² + 4y²) (B) (x - 2y)(x + 2y)(x² + 4y²) (C) (x - 2y)²(x + 2y)² (D) (x - 4y)(x + 4y)(x² + y²)

ప్రశ్న 11: The factors of 6x² + 17x + 5 are:

(A) (2x + 1)(3x + 5) (B) (2x + 5)(3x + 1) (C) (6x + 1)(x + 5) (D) (3x + 2)(2x + 5)

ప్రశ్న 12: Factorize: 8a³ + 27b³.

(A) (2a + 3b)(4a² - 6ab + 9b²) (B) (2a + 3b)(4a² + 6ab + 9b²) (C) (2a - 3b)(4a² + 6ab + 9b²) (D) (2a + 3b)³

ప్రశ్న 13: Solve for x: (3x + 5) / (2x - 3) = 7 / 4.

(A) x = 20 (B) x = -20 (C) x = 41 / 2 (D) x = -41 / 2

ప్రశ్న 14: The graph of the linear equation 3x + 4y = 24 intersects the Y-axis at which point?

(A) (8, 0) (B) (0, 6) (C) (0, 8) (D) (6, 0)

ప్రశ్న 15: For what value of k will the system of equations kx + 3y = k - 3 and 12x + ky = k have infinitely many solutions?

(A) k = 6 (B) k = -6 (C) k = 0 (D) k = 3

ప్రశ్న 16: Ten years ago, a father was 12 times as old as his son. Ten years hence, he will be twice as old as his son. What is the present age of the son?

(A) 12 years (B) 14 years (C) 16 years (D) 18 years

ప్రశ్న 17: If α and β are the zeros of the polynomial p(x) = 2x² - 5x + 7, then find the value of (α² + β²).

(A) -3 / 4 (B) 25 / 4 (C) -11 / 4 (D) 11 / 4

ప్రశ్న 18: The remainder when f(x) = x³ - 3x² + 4x - 5 is divided by (x - 2) is:

(A) -1 (B) 3 (C) -5 (D) 1

ప్రశ్న 19: If (x - 1) is a factor of p(x) = kx³ - 4x² + kx + 6, find the value of k.

(A) -1 (B) 1 (C) 2 (D) -2

ప్రశ్న 20: If a cubic polynomial p(x) is divided by a linear polynomial g(x), what is the degree of the quotient polynomial q(x)?

(A) 1 (B) 2 (C) 3 (D) 0

ప్రశ్న 21: What is the nature of the roots of the quadratic equation 2x² - 4x + 3 = 0?

(A) Real and unequal (B) Real and equal (C) No real roots (Imaginary) (D) Rational and equal

ప్రశ్న 22: Find the positive value of k for which the equation kx² - 6x + 1 = 0 has equal roots.

(A) 3 (B) 6 (C) 9 (D) 12

ప్రశ్న 23: The sum of the squares of two consecutive positive integers is 365. Find the integers.

(A) 11, 12 (B) 12, 13 (C) 13, 14 (D) 14, 15

ప్రశ్న 24: A quadratic equation whose roots are (3 + √5) and (3 - √5) is:

(A) x² - 6x + 4 = 0 (B) x² + 6x + 4 = 0 (C) x² - 6x - 4 = 0 (D) x² + 6x - 4 = 0

ప్రశ్న 25: Find the 20th term of the AP: 3, 8, 13, 18, ...

(A) 95 (B) 98 (C) 103 (D) 100

ప్రశ్న 26: Which term of the AP: 21, 18, 15, ... is -81?

(A) 34th term (B) 35th term (C) 36th term (D) 37th term

ప్రశ్న 27: Find the sum of the first 20 terms of the AP: 5, 9, 13, 17, ...

(A) 860 (B) 840 (C) 920 (D) 880

ప్రశ్న 28: If (k - 1), (2k + 1), and (4k - 1) are three consecutive terms of an AP, find the value of k.

(A) 2 (B) 3 (C) 4 (D) 1

ప్రశ్న 29: Find the 8th term of the GP: 2, 6, 18, 54, ...

(A) 1458 (B) 4374 (C) 2187 (D) 13122

ప్రశ్న 30: In a GP, if the 3rd term is 24 and the 6th term is 192, find the 10th term.

(A) 1536 (B) 3072 (C) 6144 (D) 12288