AWES TGT Maths Mock Test - 7 - AWES TGT/PGT MCQ

• The Union Cabinet cleared the Cinematograph (Amendment) Bill, 2023 which has provisions for harsher punishments for film piracy and the introduction of new age categories for classifying films.
• The Bill will be introduced in the upcoming Monsoon Session of Parliament, as per the Information and Broadcasting Minister Anurag Thakur.

The world's first wooden satellite, named LignoSat, is set to be launched by NASA and the Japan Aerospace Exploration Agency (JAXA) in 2024.

Jyothi Yarraji secured the gold medal in the 60m hurdles event at the Asian Indoor Athletics Championship in Tehran. She achieved this feat with a timing of 8.12 seconds, breaking her national record set in the previous edition of the championship.

The field theory of learning in children, in which the learner perceives and responds to the whole situation, comes under Kohler's theory of understanding.

The associative theory of learning in children is described on the basis of stimulus response. In this, a relationship is established between the stimulus response. It is also called stimulus response or S-R principle.

′+′ signs can be put in a row in one way creating seven gaps shown as arrows:
Now 4′−′ signs must be kept in these gaps. So, no tow ′−′ signs should be together.
Out of these 7 gaps 4 can be chosen in 7C4 ways.

If A = {5, 10, 15}, B = ϕ
B - A will have those elements which are in B but not in A.
B - A = ϕ

 (1+x)ⁿ= nC0+ nC1x+ nC2x²+...+ nC0xⁿ ....(1)
(1−x)ⁿ= nC0 − nC1x+ nC2x²−...+ nC0 xⁿ....(2)
⇒(1+x)ⁿ−(1−x)ⁿ = nC0+ nC1x+ nC2x²+...+ nC0xⁿ− nC0+ nC1x− nC2x²+...+ nC0xⁿ
 =2(nC1x+nC3x³+....+xⁿ)

Given: n=60 and put x=1
⇒(1+1)⁶⁰−(1−1)⁶⁰
 =2⁶⁰
⇒2⁶⁰=2(nC1x+nC3x³+....+xⁿ)

∴Sum of odd powers of x in the expansion is = nC1x+nC3x³+....+xⁿ =2⁶⁰−1 =2⁵⁹

 are any three vectors then the correct expression for distributivity of scalar product over addition is :

The point (2 cosθ, 2 sinθ) lies on the circle x² + y2 = 4. From the figure, it  is  obvious that 



Hence no solution

The correct option is C 
a=c=1/4, b=1/2
y=x is a tangent
∴ slopes are equal.
dy/dx=2ax+b
⇒1=2a+b at (1,1)⋯(1)
Also, the parabola passes through (1,1)
⇒a+b+c=1⋯(2)
The parabola passes through (−1,0)
⇒0=a−b+c⋯(3)
Solving (1),(2),(3), we get -
∴a=c=1/4
and b=1/2

an = ar^(n-1)
 Given, a = √3, r = 3/√3
​r = √3
a₅₀ = ar^(n-1)
= (√3)(√3)^(50-1)
= (√3)(√3)⁴⁹
= (√3)⁵⁰

Vector equation of a line that passes through the given point whose position vector is and parallel to a given vector is given by : 

AB = 0 does not necessarily imply that either A or B is a null matrix 
- Both matrices need not be null matrices.

Radius of the given circle = |g|. For perpendicular tangents origin should lie on the director circle, i.e. distance of origin from the centre of the given circle  

a = 5, c = 3
angle c = 60^o
cos b = (a² + c² - b²)/2ca
= 1/2 = (25 + 9 - b²)/30
=> 15 = 34 - b²
=> b² = 19
=> b = (19)1/2
=> b = 4.35

Squaring on both sides,you get sin^2x + 2sinxcosx + cos^2x = 1

which gives 1 + 2sinxcosx = 1 {since sin^2x +cos^2x = 1 for all x}

which means,2sinxcosx =0

which means either sinx =0 or cosx=0

so,the general solution is that for sinx=0 union cosx=0

r = d

A linear equation with one variable consists of numbers or constants and multiplies of a variable. The standard form of such an equation is ax+b=0, where a and b are constants and x is the variable.
Hence, 2x+7=8  is a linear equation in one variable.

Let BD be the whole height of the tree

The tree breaks at point C and makes ΔABC as given into the figure such that

AC = CD

In rt. ΔABC 

Height of lighthouse =75m
Angles are 30 and 60
Let x be the distance between the ships and y be the distance between the foot of the lighthouse and closer ship.
So tan 60= 

Tan 30 = 
x = 

Assertion: Consider the given polynomial x² + 4x + 5
as its discriminant is negative b² -4ac = 16 - 20 = -4 so it dont have real roots ,
∴ x² + 4x + 5 has no zeroes.
∴ Assertion is false.
Reason: Clearly, Reason is true.
Since Assertion (A) is false but reason (R) is true.

1, ∵ It is a sure event.