Mix Test

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Mix Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following values of x and y represents the solution of the pair of equations 3x + 7y = 20 and 2x + 3y = 10?

A
x = 2, y = 2

B
x = – 4, y = – 6

C
x = – 2, y = 14/3

D
x = – 2, y = 2

Solution

3x + 7y = 20 …. (I) 2
2x + 3y = 10 …. (II) 3
On subtracting II from I, we get
5y = 10

y = 2
Now, putting the value of y in (I), we get
3x + 7 (2) = 20
3x = 20 – 14
x = = 2
x = 2 and y = 2
Question 2
1 / -0

Which of the following expressions is always true?

A
a² + b² > 3ab

B
a²+ b² < ab

C
a² + b² 2ab

D
a² + b² > 4ab

Solution

As (a – b)² is always non-negative,
a² + b ² – 2ab 0
a² + b² 2ab
Question 3
1 / -0

If one root of the equation x² + px + q = 0 is double the other, then p²/q is equal to

A
1

B
1/2

C
2/9

D
9/2

Solution

Let the two roots of the given equation be α and 2α.
Sum of roots = α + 2α = -p or 3α = -p or α = -p/3 ... (1)
Product of roots = 2α² = q ... (2)
From equations (1) and (2), we get
2 × = q
⇒
Question 4
1 / -0

If the points A (2, 5), B (– 7, 2) and C (a, 3) are collinear, then find the value of a.

A
4

B
3

C
– 4

D
– 1

Solution

Since the point A, B and C are collinear, slope of AB = (5 – 2)/(2 + 7) = 1/3 = slope of BC = (3 - 2)/(a + 7).
a = – 4
Question 5
1 / -0

The circumference of a circle is 88 cm. What will be the length of an arc that subtends an angle of at the centre of the circle?

A
33 cm

B
cm

C
cm

D
cm

Solution

If r is the radius of the circle and is the angle subtended by an arc at the centre of the circle, then the length of that arc =
Thus, the length of the given arc =
Question 6
1 / -0

What values of x satisfy < – ?

A
– 3 < x < 3

B
x < – 3

C
– 3 < x < 6

D
– 3 < x < 1

Solution

From the question, we get
2x - 4 < - x²- 1
So, x² + 2x - 3 < 0
Or (x + 3)( x - 1) < 0
Or - 3 < x < 1

So, option (4) is the answer.
Question 7
1 / -0

Equation of a straight line is 3x + y + 3 = 0. If B is the point where the line crosses the y-axis, then find the coordinates of B.

A
B(0, - 1)

B
B(0, 3)

C
B(0, - 3)

D
B(0, - 7)

Solution

Equation of line is 3x + y + 3 = 0.
3x + y + 3 = 0 (Subtracting 3 from both sides)
3x + y + 3 - 3 = 0 - 3
3x + y = - 3
3x + y = - 3 (Subtracting 3x from both sides)
3x - 3x + y = - 3 - 3x
y = - 3x - 3
General equation for straight line is y = mx + c.
Comparing the above equation with general equation, we get
c = - 3
For y-intercept, x-coordinate is always '0'. Thus, coordinates of point B are (0, - 3).
Question 8
1 / -0

A brick measures 20 cm x 10 cm x 7 cm. How many such bricks will be required to build a wall that is 25 m long, 2 m high and m thick?

A
20000

B
24000

C
25000

D
30000

Solution

Number of bricks required = (Volume of the wall)/(Volume of one brick) = (2500 200 75)/(20 10 7.5) = 25000
Question 9
1 / -0

Mrs. Sharma earns one-third of what her husband earns. Her husband earns Rs. 6600 per month. How much does Mrs. Sharma earn in two months?

A
Rs. 6000

B
Rs. 6600

C
Rs. 5220

D
Rs. 4400

Solution

Mrs. Sharma's husband earns = Rs. 6600
Mrs. Sharma's earning = of 6600
= Rs. 2200
Hence, Mrs. Sharma earns in 2 months = 2 x 2200 = Rs. 4400
Question 10
1 / -0

The sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 square metres. The total cost of fencing the park at 50 paise per metre is

A
Rs. 312.50

B
Rs. 375

C
Rs. 187.50

D
Rs. 125

Solution

Assume that the sides of the rectangle are 3a and 2a.
Area = 3a × 2a = 6a² = 3750 square metres
a² = 625 a = 25 m
Perimeter = 2 × (3a + 2a) = 2 × 5a = 2 × 5 × 25 = 250 m
Total cost of fencing = 250 × = Rs. 125
Question 11
1 / -0

Which of the following statements is true about an exterior angle of a triangle?

A
It will always be greater than or equal to 90°.

B
It will never be a right angle.

C
It is always equal to the sum of two interior opposite angles of the triangle.

D
It is always less than any of the two interior opposite angles.

Solution

An exterior angle of a triangle is always equal to the sum of two interior opposite angles of the triangle.
Question 12
1 / -0

In a fraction X, if thrice the denominator is decreased by 30% and twice the numerator is increased by 10%, then the resultant fraction is 22% of 26/21. Find the fraction X.

A

B

C

D

Solution

Let the fraction X be .
New fraction: =
= =
Hence, option (2) is the correct answer.
Question 13
1 / -0

Ram has 3 more oranges than Shyam, Krishna has 4 more oranges than Rajiv and Rajiv has 3 times the number of oranges as that of Ram. Find the number of oranges that Krishna has when Ram and Shyam give their oranges to him. Assume that the total number of oranges is 33.

A
4

B
5

C
12

D
21

Solution

Let the number of oranges with Ram = x
Let the number of oranges with Shyam = y
Let the number of oranges with Krishna = z
Let the number of oranges with Rajiv = t
According to question,
x = 3 + y …………… (1)
z = 4 + t …………… (2)
t = 3x …………… (3)
and x + y + z + t = 33 …………… (4)
Substituting values of x, z & t in equation (4), we get
(3 + y) + y + (4 + 3x) + (3x) = 33
2y + 6x + 7 = 33
2y + 6x = 26 ………………. (5)
Substitute the value of x in equation (5), we get
y + 3x = 13
y + 3(3 + y) = 13
y + 9 + 3y = 13
4y + 9 = 13
y = 1
x = 3 + 1 = 4, t = 3 x 4 = 12 & z = 4 + 12 = 16
Adding equation (1) and (5)
x – y + 3x + y = 13 +3
4x = 16
x = 4
I 4 = 3 + y
y = 1
Number of oranges with Krishna = z = 16
Ram & Shyam give their 4 + 1 = 5 oranges to Krishna.
Number of oranges with Krishna = 16 + 5 = 21
Question 14
1 / -0

Nidhi arranged to pay off a debt of Rs. 3,600 to CASA bank in 40 annual installments in the form of an AP. When 30 installments had been repaid, she died, leaving one-third of the debt unpaid. What was the value of the first installment (in Rs.)?

A
45

B
47

C
49

D
51

Solution

If Rs. a is the first installment and the common difference is Rs. d, then sum of all installments
= S₄₀ = [2.a + (40 – 1) d] = total debt = 3600 2a + 39d = 180 …(1)
Also, S₃₀ = [2.a + (30 – 1) d] = of the total debt = 2400
2.a + 29d = 160 …(2)
Subtracting (2) from (1), we get 10d = 20. d = 2
a = Rs. 51
Question 15
1 / -0

For the given figure, which of the following options is not true?

A
1 = 6

B
3 = 6

C
3 + 6 = 180^o

D
4 = 8

Solution

1 = 6 is true. (corresponding angles)
3 = 6 is false. (angles on same side of transversal cannot be equal)
3 + 6 = 180^ois true. (supplementary angles)
4 = 8 is true. (corresponding angles)