Test: Elementary Mathematics - 4 - CDS MCQ

For a number to be divisible by 5, it should have either 0 or 5 at its unit's place.
But in the problem, it is given that the number is a two-digit number and the digits are unequal as well as not equal to 0.
Let us take another number instead of taking 0, i.e. 2 and 5.
Now, two-digit numbers by using 2 and 5 are 25 and 52, from which 25 is divisible by 5, but 52 is not.
Therefore, 5 cannot be the factor of both ab and ba.

2 + 3 + x + 5 + y = 22
x + y = 22 - 5 - 5
x + y = 12

Median = 68
So, median class = 60 - 80
ℓ = lower boundary point of median class = 60
cf = Cumulative frequency of the class preceding the median class = 5 + x
f = Frequency of the median class = 5
h = class length of median class = 20


8/4 = 6 - x
-4 = -x
Or, x = 4 and y = 8

=

We have sides of cuboid :-
length = l and breadth = l and
height = 3.14 l
We know, volume of cuboid = length × breadth × height
Volume = l × l × 3.14l
Volume = 3.14 l³ m³.
Now, to find the volume of the solid on which the cuboid is surmounted:
Volume of cube = (side)³
Volume = l³
Therefore, volume of the whole solid = Vol. Of cuboid + Vol. Of cube
= 3.14 l³ + l³
= 4.14 l³m³

Sum of interior angles = 1080°
Sum of interior angles = (n - 2) x 180°
1080º/180º = n - 2
6 = n - 2
n = 8
Number of sides of regular polygon having sum of interior angles 1080° is 8.

Height of cylinder = 15 m
Radius of cylinder = 3 m
Curved surface area = 2πrh = 90π
Radius of cone = 3 m
Height of cone = 4 m (19 – 15 = 4 m)
Slant height, ℓ = = 5
Curved surface area of cone = πrℓ = 15π
Curved surface area of cone + cylinder
90π + 15π = 105π
= 105 x (22/7) = 330 m²

Distance = 225 m
Train's speed = 30 km/hr and man's speed = 3km/hr
Relative speed = 30 – 3 = 27 km/hr
Speed = 27 km/hr × 5/18 m/s = 15/2 m/s
Time = = 30 seconds

Smallest number made of 5's and divisible by 3 is 555.
Thus, A = 555/3 = 185
B = 1 + 8 + 5 = 14
C = 1 + 4 = 5
Thus, value of C³ = 5³ = 125
Answer: (2).

Comparing both sides, we get
3 + 4x = 23
4x = 20
x = 5
Hence, option (3) is correct.

According to the question:
θ = angle between the two radius and chord
chord length = 2 × r× sin (θ/2)
9.75= 2 × 6.9 × sin (θ/2)
0.7065 = sin (θ/2)
1/√2 = sin (θ/2)
θ/2 = 45°
θ = 90°

Hence, option 2 is correct.

Let n be the number of sides of the polygon.
The sum of its interior angles is given by (n - 2) × 180°. … (i)
Hence, the interior angles form an AP with first term 'a' = 120° and common difference = 5°.
Sum of n terms of AP = S_n = n/2[2 × 120° + (n - 1) × 5°) = n/2[240° + (n - 1)5°] … (ii)
Equating (i) and (ii), we get
(n - 2) × 180° = n/2[240° + (n - 1)5°]
⇒ (n - 2) × 360 = n(240 + 5n - 5) = n(235 + 5n)
⇒ 360n - 720 = 235n + 5n²
⇒ 5n² - 125n + 720 = 0
Or n² - 25n + 144 = 0 or (n - 16)(n - 9) = 0
⇒ n = 16 or n = 9
But when n = 16, last angle = T_n = a + (n - 1)d = 120° + 15(5°) = 120° + 75°
= 195°, which is not possible [∵ Angle > 180°]
Hence, n = 9.
Number of sides of the polygon = 9

We know that if and are the means (average) of n₁, n₂ and n₃ observations, respectively, then the combined mean (average) is

Mean salary =
=

= Rs. 26,666.67
Clearly, workers earning less than the mean salary are category B and C workers. i.e. 5 + 3 = 8.

Let the sum be Rs. P.
The first sum is recovered after x years.
The second is recovered after (x + (1/2))years.
As the amount in each case is the same, the interest received is also the same.
Thus, =
9x = 8x + 4
x = 4 years
So, in the first case, it is recovered after 4 years.
In the second case, it is recovered after 4 + 1/2 = 4(1/2) years.

Let the cost price of one chair be Rs. x and the cost price of one stool be Rs. y.
Then, A.T.Q.
4x + 9y = 1340 ... (i)
Also, 4(10% of x) + 9(20% of y) = 188

... (ii)
On subtracting Eq. (i) from Eq. (ii), we get
9y = 1880 - 1340
Or, 9y = 540
Or, y = 60
On substituting y = 60 in Eq. (i), we get
4x + 540 = 1340
Or, 4x = 1340 - 540
Or, 4x = 800
Or, 4x = 800
Thus, Ram had to pay Rs. 800 for the chairs.

Number of women visiting shopping mall O = 45% of 640 = 288
Number of women visiting shopping mall R = 72% of 650 = 468
Percentage = (288/468) x 100 = 61.54%

+ 3 cos 40° cosec 50° - 2 sec 35° sin 55°
= + 3 cos 40° cosec (90° - 40°) - 2
= + 3 cos 40° sec 40° -
= 1 + 3 1 - 2
= 1 + 3 - 2(1) = 2

Prime factorization of 21 = 3 × 7
Numbers up to 21 : 1, 2, 3, 4, 5, 6, 7 , 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
Now we need to remove the multiples of 3 and 7 from the list above
So, numbers co primes with 21 ( that are less than 21 and greater than 1) = 2, 4, 5, 8, 10, 11, 13, 16, 17,19, 20
Number of the required numbers = 11

Median = +
l = lower boundary point of median class
c.f. = Cumulative frequency of the class preceding the median class
f = Frequency of the median class
n = total number of values or observations
h = class length of median class
⇒ 39.8 = 35 +
⇒ h =
Or, h = (4.8/6) x 10 
⇒ h = 8

4^x + 4^{x - 1} = 4^x (1 + (1/4)) = 20
4^x(5/4) = 20

4^x = 4²
x = 2, x^x = 2² = 4

AC = AP tan α
⇒ (1/2) AB = n AB tan α

⇒ tan α = 1/2n

⇒ 

Women visiting shopping mall M = 45% of 560 = 252
Women visiting shopping mall O = 45% of 640 = 288
Ratio = 252 : 288 = 7 : 8

Clearly, x + 5 = 5
⇒ x = 5 − 5 = 0
{x : x + 5 = 5} = {0}

The ball, after being cut, will have eight parts, each with the same volume and the same surface area.
The ball will look somewhat like figure (1), when seen from the top before cutting.
After cutting, it will look something like figure (2), as shown below:

Now, the surface area of each piece = Area (ACBD) + 2 (Area CODBC).
The darkened surface is nothing but the arc AB from side glance, which means its surface area is one-eighth the area of the sphere, i.e. (1/8) × 4 π r² = (1/2)πr²
Now, CODBC can be seen as a semicircle with radius 4 cm.
Therefore, 2 (Area CODB) = 2[1/2]πr² = πr²
⇒ Surface area (in cm²) of each piece = (1/2)πr² + πr² = (3/2)π4² = 24π