FORMATIVE TEST 2 GUESS PAPER CLASS 10 MATHS

Section -A

CBSE GUESS

1.The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have

(A) a unique solution (B) exactly two solutions        (C) infinitely many solutions (D) no solution

2. If a pair of linear equations is consistent, then the lines will be

(A) parallel      (B) always coincident             (C) intersecting or coincident             (D) always intersecting

3. The pair of equations y = 0 and y = –7 has

(A) one solution          (B) two solutions        (C) infinitely many solutions              (D) no solution

4.If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is

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

5. Given that sinα =1/2 and cosβ =1/2 , then the value of (α + β) is

(A) 0°              (B) 30°                                    (C) 60°                                                           (D) 90°

Section - B

1.For which values of p and q, will the following pair of linear equations have infinitely many solutions?

4x + 5y = 2    and            (2p + 7q) x + (p + 8q) y = 2q – p + 1.

2. In a competitive examination, one mark is awarded for each correct answer while1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly

3. Given that α + β = 90°, show that  = sinα

4. A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number

5.An aeroplane leaves an Airport and flies due North at 300 km/h. At the same time, another aeroplane leaves the same Airport and flies due West at 400 km/h. How far apart the two aeroplanes would be after 1and 1/2  hours?       Or,

In an equilateral triangle ABC, D is a point on side BC such that BD =1/3 BC. Prove that 9 AD²= 7 AB².

6. Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.

7. Show that tan⁴θ + tan²θ = sec⁴θ – sec²θ.

8. If sin θ + cos θ = √3 , then prove that tan θ + cot θ = 1

9. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians

10. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.