Quantitative and Numerical Ability Test

Result

Quantitative and Numerical Ability Test - 3

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

If Φ is the acute angle between the two straight lines represented by 3y = 9x + 5 and 3y = 7x + 9, then what is value of tanΦ ?

A
1/12

B
2/7

C
1/8

D
1/6

E
3/8

Solution
Question 2
1 / -0

The sum of the areas of two circles, which touch each other externally, is 153π. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.

A
4

B
2

C
3

D
1

E
None of these

Solution
Question 3
1 / -0

A 180-metre-long train crosses a platform of equal length in 18 seconds. What is the speed of the train?

A
22 m/sec

B
10 m/sec

C
15 m/sec

D
18 m/sec

E
None of these

Solution

When the train crosses the platform , It covers its own lenth as well as lenth of platform, Therefore total length becomes - 180+180

Time taken is 18 seconds.

The required speed =

180+180 / 18 = 20m/sec

Therefore, the correct answer is option E.
Question 4
1 / -0

Find the equation of the line parallel to the line passing through (5, 7) and (2, 3) and having x intercept as -4.

A
2y = 3x +16

B
3y = 4x +16

C
3y = 4x - 16

D
3y = 2x +16

E
5y = 4x +16

Solution

Slope of the given line = (7 – 3) / (5 – 2) = 4/3. So the slope of the required line is also 4/3. One point on this line is (-4, 0). Hence the equation of the line is y – 0 = 4/3 (x + 4) ⇒ 3y = 4x +16.
Question 5
1 / -0

What is the equation of a straight line passing through the points A (-2, 6) and B (4, -3)?

A
2y = 3x + 6

B
2x = 3y - 6

C
3y = 2x + 6

D
2y + 3x = 6

E
2y = 3x - 6

Solution

The equation of the straight line passing through the points A (-2, 6) and B (4, -3) is

y-6=-3-6 / 4+2 (x+2}

⇒ 2y + 3x = 6.
Question 6
1 / -0

The respective ratio between the speed of the boat downstream and the speed of the boat upstream is 27: 17. By what percent is the speed of the boat downstream more than the speed of the boat in still water?

A
26.4%

B
31.4%

C
22.7%

D
19.8%

E
29.3%

Solution
Question 7
1 / -0

A
12 m

B
9 m

C
18 m

D
6 m

E
7 m

Solution
Question 8
1 / -0

If (2 + 4 + 6 + ... 50^th terms)/(1 + 3 + 5 + ... n^th terms) = 51/2, then find the value of n.

A
12

B
13

C
9

D
10

E
8

Solution
Question 9
1 / -0

What is the equation of tangent to the circle x² + y² = 625 at point P (24, -7)?

A
24y + 7x = 625

B
24x = 7y-625

C
24x - 7y = 625

D
7y + 24x + 625 = 0

E
7x -24y = 625

Solution

The equation of the circle is x²+ y² = 625. The equation of the tangent at point (24, -7) is 24x – 7y = 625.
Question 10
1 / -0

If 2x² - 15x + 28 = 0 and 2y² - 21y + 54 = 0, then which of the following is true?

A
x < y

B
x ≤ y

C
x > y

D
x ≥ y

E
x = y

Solution

We have 2x² - 15x + 28 = 0 ⇒ (2x – 7) (x – 4) = 0 ⇒ x = 7/2 or 4.

And 2y² - 21y + 54 = 0 ⇒ (2y – 9) ( y – 6) = 0 ⇒ y = 9/2 or 6.

Hence x < y.