Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-3)

Theory of Equation and Inequations

Total Questions: 50

1. A boat goes 28 km upstream and 39 km downstream in 7 hours. In 9hours, it can go 35 km upstream and 52 km downstream. Determine the speed of the boat in still water. [OAVS TGT 2021 ]

Correct Answer: (a) 10 km/h
Solution:


2. If sum of squares of zeros of the quadratic polynomial f(𝓍) = 𝓍² - 8𝓍 + k is 40, then the value of k is: [OAVS TGT 2019]

Correct Answer: (a) 12
Solution:

3. If y = 8 +10 cos2𝓍 then which of the following is satisfied: [OAVS TGT 2019]

Correct Answer: (a) -2≀y ≀ 18
Solution:

4. If Ξ± and Ξ² are the zeros of the quadratic polynomial f(𝓍) = 𝓍² - p𝓍 + q, then the value of Β² + BΒ² is: [OAVS TGT 2019]

Correct Answer: (a) pΒ²-2q
Solution:

5. The value of k for which the equation has equal roots (k-12)𝓍² + 2(k-12)𝓍 + 2 = 0 is: [OAVS TGT 2019]

Correct Answer: (d) k = 14
Solution:

If any quadratic equation has equal roots then discriminant will be zero.

6. The number of real roots of 2sin𝓍 = 2Λ£ +2⁻ˣ is: [OAVS TGT 2019]

Correct Answer: (a) 0
Solution:


7. The equation √(𝓍+1)-√(𝓍-1)=√(4𝓍-1) has: [OAVS TGT 2019]

Correct Answer: (a) one solution
Solution:

8. The values of a and b so that 𝓍⁴ + 𝓍³ + 8𝓍² + a𝓍 + b is divisible by 𝓍² + 1 is equal to: [OAVS TGT 2019]

Correct Answer: (a) a = 1; b = 7
Solution:

9. Solve the following equation: [OAVS TGT 2019]

Correct Answer: (b) √(b/a)
Solution:

10. If the angle A of a triangle ABC is given by the equation 3 cosA + 2 = 0, then find the quadratic equation whose roots are sin A and tanA? [OAVS TGT 2019]

Correct Answer: (d) 6𝓍² +√5𝓍-5=0
Solution: