Mathematics (Basic) Test 1

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Mathematics (Basic) Test 1

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Question 1
1 / -0

A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square like 4,9….is

A
\(\frac1{45}\)

B
\(\frac{2}{15}\)

C
\(\frac4{45}\)

D
\(\frac19\)

Solution

P(perfect Square)=\(\frac5{45}=\frac19\)
Question 2
1 / -0

In a circle of diameter 42cm ,if an arc subtends an angle of \(60^{\circ}\) at the centre where \(\pi\) =22/7,then the length of the arc is

A
22/7 cm

B
11 cm

C
22 cm

D
44 cm

Solution

Length of the arc= \(\frac{\theta}{360^{\circ}}(2\pi r)\)

=\(\left(\frac{60^{\circ}}{360^{\circ}}\right)\times2\times\frac{22}7\times21\) = 22cm
Question 3
1 / -0

If sin \(\theta\) = x and sec \(\theta\) = y , then tan \(\theta\) is

A
xy

B
\(\frac{\text x}y\)

C
\(\frac{y}{\text x}\)

D
\(\frac1{\text xy}\)

Solution

Tan \(\theta\) = \(\frac{sin\,\theta}{cos\,\theta}\) = sin \(\theta\) xsec \(\theta\) = xy
Question 4
1 / -0

The pair of linear equations y = 0 and y =-5 has

A
One solution

B
Two solutions

C
Infinitely many solutions

D
No solution

Solution

The lines are parallel hence.
Question 5
1 / -0

A fair die is thrown once. The probability of even composite number is

A
0

B
1/3

C
3/4

D
1

Solution

P(even composite no) =2/6=1/3
Question 6
1 / -0

8 chairs and 5 tables cost Rs.10500, while 5 chairs and 3 tables cost Rs.6450. The cost of each chair will be

A
Rs. 750

B
Rs.600

C
Rs. 850

D
Rs. 900

Solution

Let the cost of one chair=Rs. x

Let the cost of one table=Rs. y

8x + 5y=10500

5x + 3y = 6450

Solving the above equations

Cost of each chair= x= Rs. 750
Question 7
1 / -0

If \(cos\,\theta\) + \(cos^2\theta \) =1,the value of \(sin^2\theta+sin^4\theta\) is

A
-1

B
0

C
1

D
2

Solution

\(cos\,\theta=I-cos^2\theta=sin^2\theta\)

Therefore \(sin^2\theta+sin^4\theta=cos\,\theta+cos^2\theta=1\)
Question 8
1 / -0

The decimal representation of \(\frac{23}{2^3\times5^2}\) will be

A
Terminating

B
Non-terminating

C
Non-terminating and repeating

D
Non-terminating and non-repeating

Solution

Terminating
Question 9
1 / -0

The LCM of \(2^3\times3^2\) and \(2^2\times3^2\) is

A
\(2^3\)

B
\(3^3\)

C
\(2^3\times3^3\)

D
\(2^2\times3^2\)

Solution

\(2^3\times3^3\)
Question 10
1 / -0

The HCF of two numbers is 18 and their product is 12960. Their LCM will be

A
420

B
600

C
720

D
800

Solution

\(1^{st}\) No. \(\times\) \(2^{nd}\) No. = HCF \(\times\) LCM

12960 = 18 \(\times\) LCM

LCM = 720
Question 11
1 / -0

The co-ordinates of the point P dividing the line segment joining the points A (1,3) and B (4,6) internally in the ratio 2:1 are

A
(2,4)

B
(4,6)

C
(4,2)

D
(3,5)

Solution

\(\frac{(2\times4+1\times1)}3\), \(\frac{(2\times6+1\times3)}3\)

= (3,5)
Question 12
1 / -0

The prime factorisation of 3825 is

A
\(3\times5^2 \times21\)

B
\(3^2\times5^2\times35\)

C
\(3^2\times5^2\times17\)

D
\(3^2\times25\times17\)

Solution

\(3825=3^2\times5^2\times17\)
Question 13
1 / -0

In an isosceles triangle ABC, if AC = BC and \(AB^2=2AC^2\), then the measure of angle C will be

A
\(30^\circ\)

B
\(45^\circ\)

C
\(60^\circ\)

D
\(90^\circ\)

Solution

\(AB^2=AC^2+AC^2\)

\(=AC^2+BC^2\)

Hence, angle C = \(90^\circ\)
Question 14
1 / -0

If -1 is a zero of the polynomial p(x)=\(\text x^2\) -7x-8 , then the other zero is

A
-8

B
-7

C
1

D
8

Solution

Let the zeroes be a and b

Then, a = -1 , a + b=-(-7)/1

Hence, b = 7 + 1 = 8
Question 15
1 / -0

In a throw of a pair of dice, the probability of the same number on each die is

A
\(\frac16\)

B
\(\frac13\)

C
\(\frac12\)

D
\(\frac56\)

Solution

P(same no on each die) = \(\frac6{36}=\frac16\)
Question 16
1 / -0

The mid-point of (3p,4) and (-2,2q) is (2,6) . Find the value of p+q

A
5

B
6

C
7

D
8

Solution

(2,6)=\(\left(\frac{(3p-2)}2,\frac{(4+2q)}2\right)\)

3p - 2 = 4, 4 + 2q = 12

P = 2, q = 4

hence p + q = 6
Question 17
1 / -0

The decimal expansion of \(\frac{147}{120}\) will terminate after how many places of decimals?

A
1

B
2

C
3

D
4

Solution

\(\frac{147}{120}= \frac{49}{40}=\frac{49}{2^3 \times 5}\)

Three decimal places
Question 18
1 / -0

The perimeter of a semicircular protractor whose radius is ‘r’ is

A
\(\pi\) + 2r

B
\(\pi\) + r

C
\(\pi\)r

D
\(\pi\)r + 2r

Solution

Perimeter of protractor=Circumference of semi-circle + 2 \(\times\) radius

= \(\pi\)r+2r
Question 19
1 / -0

If P (E) denotes the probability of an event E, then

A
0< P(E) \(\le\)1

B
0 < P(E) < 1

C
0 \(\le\) P(E) \(\le\) 1

D
0 \(\le\) P(E) <1

Solution

0\(\le\) P( E) \(\le\)1
Question 20
1 / -0

In \(\triangle\)ABC, \(\angle\)B = \(90^{\circ}\) and BD \(\perp\) AC. If AC = 9cm and AD = 3 cm then BD is equal to

A
\(2\sqrt2\) cm

B
\(3\sqrt2\) cm

C
\(2\sqrt3\) cm

D
\(3\sqrt3\) cm

Solution

\(\frac{CD}{BD}=\frac{BD}{AD}\)

\(BD^2=CD\times AD=6\times3\)

BD=3\(\sqrt2\) cm
Question 21
1 / -0

The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 do not have a solution if

A
K = 5

B
K = 10

C
K \(\neq\) 10

D
K \(\neq\) 5

Solution

\(\frac36=\frac{5}{k}\)

\(\Rightarrow\) K=10
Question 22
1 / -0

If the circumference of a circle increases from 2\(\pi\) to 4\(\pi\) then its area _____ the original area.

A
Half

B
Double

C
Three times

D
Four times

Solution

\(\frac{C1}{C2}=\frac{2\pi r}{2\pi R}\)

\(\frac{2\pi}{4\pi}=\frac{2\pi r}{2\pi R}\)

\(\frac{r}{R}=\frac12\)

\(\frac{A1}{A2}=\frac{\pi r^2}{\pi R^2}=(\frac{r}R)^2=(\frac12)^2=\frac14\)

A2=4A1

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Re-Attempt Weekly Quiz Competition

Mathematics (Basic) Test 1

Result

Mathematics (Basic) Test 1

Score

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SHARING IS CARING

Question 1

\(\frac1{45}\)

\(\frac{2}{15}\)

\(\frac4{45}\)

\(\frac19\)

Solution

Question 2

22/7 cm

11 cm

22 cm

44 cm

Solution

Question 3

xy

\(\frac{\text x}y\)

\(\frac{y}{\text x}\)

\(\frac1{\text xy}\)

Solution

Question 4

One solution

Two solutions

Infinitely many solutions

No solution

Solution

Question 5

0

1/3

3/4

1

Solution

Question 6

Rs. 750

Rs.600

Rs. 850

Rs. 900

Solution

Question 7

-1

0

1

2

Solution

Question 8

Terminating

Non-terminating

Non-terminating and repeating

Non-terminating and non-repeating

Solution

Question 9

\(2^3\)

\(3^3\)

\(2^3\times3^3\)

\(2^2\times3^2\)

Solution

Question 10

420

600

720

800

Solution

Question 11

(2,4)

(4,6)

(4,2)

(3,5)

Solution

Question 12

\(3\times5^2 \times21\)

\(3^2\times5^2\times35\)

\(3^2\times5^2\times17\)

\(3^2\times25\times17\)

Solution