Bihar PGT Mathematics Mock Test - 9 - Bihar PGT/TGT/PRT MCQ

'ऑंसू - ऑँसुओं' युग्म गलत है। आँसू हमेशा बहुवचन में ही प्रयोग होता है।

सदैव बहुवचन में प्रयुक्त होने वाले अन्य शब्द-प्राण, दर्शन, होश, बाल, हस्ताक्षर आदि हैं।

चाँदनी के पर्यायवाची शब्द है - चन्द्रिका, कौमुदी, ज्योत्स्ना, चन्द्रमरीचि, उजियारी, चन्द्रप्रभा, जुन्हाई आदि।

मयंक, चांद का पर्यायवाची है।

"पर + अधीन" शुद्ध सन्धि विच्छेद है। जिसके मेल होने पर पराधीन शब्द बनेगा।

इसमें 'अ + आ = आ' का सूत्र प्रयोग हुआ है। इसमें दीर्घ सन्धि है।

सामान्य - मामूली, साधारण

श्रेष्ठ - अति उत्तम, उत्कृष्ट

सर्वज्ञ - सबकुछ जाननेवाला

साधारण - सब जगह पाया जानेवाला, आम, साधारण दृश्य, साधारण पहनावा, सामान्य, मामूली

विशिष्ट - विशेषता युक्त, असाधारण

प्रकाशन वर्ष की दृष्टी से काव्यकृतियों का सही अनुक्रम-3 आँसू, पल्लव, स्वप्न, साकेत है। 

आँसू- 1925 ई. में जयशंकर प्रसाद द्वारा रचित काव्य है। पल्लव सुमित्रानंदन पन्त का तीसरा कविता संग्रह है जो 1928 में प्रकाशित हुआ था। स्वप्न 1929 में रामनरेश त्रिपाठी द्वारा रचित काव्य है। साकेत मैथिलिशरण गुप्त द्वारा रचित महाकाव्य का नाम है। इसका प्रथम प्रकाशन सन् 1931 में हुआ था। 

The logic followed is:

Abduct and Kidnap are synonyms.

Similarly,

Fierce and Violent are synonyms.

Hence, the correct answer is "Violent".

The pattern followed is:

Top right number = multiplication of top left number and bottom number 

In fig 1:

729 = 81 × 9

729 = 729

In fig 2:

512 = 64 × 8

512 = 512

Similarly,

In fig 3:

? = 49 × 7

? = 343 

Hence, the correct answer is "343".

Given:

x + y + 1 = 0

Concept Used:

(a + b )³ = a³ + b³ + 3ab (a + b)

Calculations:

x + y + 1 = 0

⇒ x + y = -1

Cubing on both sides we get

(x + y)³ = ( -1 )³

⇒ x³ + y³ + 3xy( x + y ) = -1

⇒ x³ + y³ + 3xy ( -1) = -1

∵ x + y = -1

⇒ x³ + y³ - 3xy = -1

∴ required value = -1

The logic followed here is:

1) Intact and Unflawed are synonyms meaning not damaged and perfect.

2) Entire and Partial are antonyms.

3) Bright and Luminous are synonyms.

4) Pure and Perfect are synonyms.

Both the words are synonyms in all the options except option 2, where the given words are antonyms.

Hence, the correct answer is "Entire : Partial".

Persons: A, B, C, D, E and F

1) E is sitting immediate left to the B.

2) A is sitting fourth right to the B.

3) F is sitting between A and D.

4) Final Sitting arrangement.

Hence, “C” is sitting immediate left to the D.

The correct answer is the Helium nucleus.

• Helium nucleus was the source of alpha particles in the Rutherford scattering experiment.
• Ernest Rutherford, a British scientist conducted an experiment and proposed the atomic structure of elements.

Key Points

• Rutherford conducted an experiment by bombarding a thin sheet of gold with α-particles.
• He then analysed the trajectory of these particles after their interaction with the gold foil.
• Since very few α-particles were deflected back, and only a few α-particles had nearly 180^o angle of deflection.
• Hence he concluded that the volume occupied by the positively charged particles in an atom is very small as compared to the total volume of an atom.

• First schedule contains the list of states and union territories.
• First schedule comprises
• Indian constitution has 12 schedules.

How to remember 12 schedules?

Trick: TEARS OF OLD PM

1^st Schedule: T – Territory

2^nd Schedule: E – Enrolment

3^rd Schedule: A – Affirmations/Oaths

4^th Schedule: R – Rajya Sabha

5^th Schedule: S – Scheduled Areas

6^th Schedule: O – Other Scheduled Areas

7^th Schedule: F – Federal Structure

8^th Schedule: O – Official Languages

9^th Schedule: L – Land Reforms

10^th Schedule: D – Defection

11^th Schedule: P – Panchayats

The correct answer is Virtual and erect.

Key Points

• A plane mirror is a mirror with a flat reflective surface.
  • For light rays striking a plane mirror, the angle of reflection equals the angle of incidence.
  • The angle of the incidence is the angle between the incident ray and the surface normal.
  • The image formed by a plane mirror is always virtual and erect.​
  • The image formed by the plane mirror is virtual and erect i.e. image cannot be projected or focused on a screen.
  • The distance of the image 'behind' the mirror is the same as the distance of the object in front of the mirror.
  • The size of the image formed is the same as the size of the object.

Additional Information

• A convex mirror or diverging mirror is a curved mirror in which the reflective surface bulges towards the light source.
  • Convex mirrors reflect light outwards, therefore they are not used to focus light.
  • The image is smaller than the object but gets larger as the object approaches the mirror.
• A concave mirror is called a converging mirror because it converges the Ray of light incident parallels to the mirror into a point called the focus.

If l₁, m₁, n₁ and l₂, m₂, n₂ are the direction cosines of two lines; and θ is the acute angle between the two lines; then the cosine of the angle between these two lines is given by : 

A = {x : x = 2ⁿ, n ≤ 6}
For (n = 1,2,3,4,5,6) {2,4,8,16,32,64}
B = {x : x = 4ⁿ, n ≤ 2}
For (n = 1,2) {4,8}
A - B = {2, 8, 32, 64}

When x= 0 and y = - 2 ,we have : c = 2,

We have : 

The Required point is the radical centre of the three given circles. The radical axes of the three circles taken in pairs are 3x - 24 = 0,16y + 120 = 0 and - 3x + 16y + 80 = 0. On solving, the required point is (8, -15/2).

  represents a circle of radius p having centre at (0, 2 √3) and arg z = π/6 is a line making an angle of 300 with OX and lying in 1st quadrant.  
Let CM be perpendicular from C on OA.  Then, 

Now, the two curves will intersect if CM ≤ P  i.e., 3 ≤ P ⇒ P ≥ 3
Hence, the least value of p is 3 

n. n! = [(n + 1) – 1]n! = (n + 1)! – n!
∴ 1 + 2! – 1! + … + (n + 1)! – n! = (n + 1)!

Out of 20 professors, excluding the principal and vice-principal, 18 professors are left.
No. of ways of selecting 5 professors out of 18 = ¹⁸C₅

Given that 


Similarly, we can find the values of F(3), F (4), F (5) as  respectively..

From this we can say that every term except [F(1)], of the series [F(1)] + [F (2)] + .... + [F (50)] is equal to 1 as for 'n' > 0, F (n) lies between 1 and 2.
Therefore, [F (1)] + [F (2)] + .... +  [F (50)] = 51.
Hence, option (a) is the correct choice.

a,b,c are in H.P
∴1/a , 1/b , 1/care in A.P
∴2/b= 1/a+1/c_______ (1)
∴ x/a+y/b+1/c=0 ________ (2)
∴ From (1)
1/a+1/c−2/b=0 ______ (3)
∴ From (2) & (3)
We infer that,
(x=1,y=−2)
∴ Point is (1,−2)

As n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
But in case of disjoint sets, n(A ∩ B) = 0
∴ n(A ∪ B) = n(A) + n(B)

(A) The  radical axis of the circle x² + y² = 1 and the circle given in is x = -2, which is | | to y-axis 
(B) is y = 2, which is | | to x-axis
(C) is x = 0, which is y-axis 
The radical axis with circle in (A) | | to y-axis and the given circle intersect circle given in A orthogonally. 

(n - 2r)² = n + 2

Slope of OP x slope of OQ = -1 
⇒ 4t₁.4t₂ = -1
Eq of tangent at 

Eq of tangent at 

Let (x₁ , y₁) is the point of intersection