Mathematics (Solved Paper 2024 – II) (51 to 100)

Total Questions: 50

1. What is 3α + 2β equal to if

Correct Answer: (a) 36
Solution:

2. Find ?

Correct Answer: (b) 30°
Solution:

3. Find ?

Correct Answer: (a) 0
Solution:

4. Find ?

Correct Answer: (a) -4
Solution:

5. find ?

Select the correct answer using the code given below.

Correct Answer: (c) Both A and B
Solution:

6. The diagonals of a quadrilateral ABCD are along the lines x - 2y = 1 and 4x + 2y = 3 The quadrilateral ABCD may be a

Correct Answer: (d) rhombus
Solution:The Slope of the diagonal along the line x - 2y = 1 is m₁= 1/2

and the slope of the diagonal along the line 4x + 2y = 3 is m₂ = - 2.

Now, m₁ m₂ = 1/2(-2)  = -1 ⇒ m₁ m₂ = -1 .So, Diagonals are prependicular to each others.

⇒ The quadrilateral ABCD is a rhombus.

7. The foci of the ellipse 4x² + 9y² = 1 are at Q and R. If P(x,y) is any point on the ellipse, then what is PQ + PR equal to?

Correct Answer: (b) 1
Solution:Given equation of ellipse, 4x² + 9y ² = 1 Here, a = 1/2 and b = 1/3

Since, P(x,y) is any point on the ellipse.

So, PQ + PR = 2a = 2 × 1/2 = 1

8. If P(2,4), Q(8, 12), R(10, 14) and S(x, y) are vertices of a parallelogram, then what is (x + y) equal to?

Correct Answer: (b) 10
Solution:

9. The equation of a circle is (x² - 4x + 3) + (y² - 6y + 8) = 0 Which of the statements are correct?

A. The end points of a diameter of the circle are at (1, 2) and (3, 4).

B. The end points of a diameter of the circle are at (1, 4) and (3, 2).

C. The end points of a diameter of the circle are at (2, 4) and (4, 2).

Select the answer using the code given below.

Correct Answer: (a) A and B only
Solution:Given, (x² - 4x + 3) + (y² - 6x + 8) = 0

⇒ (x - 3)(x - 1) + (y - 4)(y - 2) = 0

So, all the possible ends of the diameters of given circle are (3, 4), (3, 2),

(1, 4) and (1, 4).

Also, Radius= √2 and center = (2, 3)

So, the required pair of ends of diameters are

(I) (1, 2) & (3, 4) and

(II) (1, 4) and (3, 2).

10. Consider the points P(4k,4k) and Q(4k, - 4k) lying on the parabola y²= 4kx. If the vertex is A, then what is angle <PAQ equal to?

Correct Answer: (b) 90°
Solution: