Maths Mock Test- 2 - Class 10 MCQ

The correct answer is b

Given quadratic polynomial is,

p(x)=x2+ax+b

Let one of the zero of the polynomial is a then the other zero will be −a.

Sum of zeros=a+(−a)= −a / 1

=>0= −a/1

=>a=0

and product of the zeros =a(−a)=b/1

=>−a2=b

=>b=−a2

=>b has to be negative.

(a) Given that, 2x² - 3x + 6 = 0
On comparing with ax² + bx + c = 0, we get
a = 2,  b = -3 and c = 6
∴ Sum of the roots = 
So, sum of the roots of the quadratic equation 2x² - 3x + = 0 is not 3, so it is not the answer
(b) Given that, -x² + 3x - 3 =0
On compare with ax² + bx + c = 0, we get
a = -1, b = 3 and c = -3
∴ Sum of the roots = 
So, sum of the roots of the quadratic equation -x² + 3x - 3 = 0 is 3, so it is the answer.
(c) Given that, 
⇒ 2x² - 3x + √2 = 0
On comparing with ax² + bx + c = 0, we get
a = 2, b = -3 and c = √2
∴ Sum of thee roots = 
So, sum of the roots of the quadratic equation  is not 3, so it is not the answer.
(d) Given that, 3x² - 3x + 3 = 0
⇒ x² - x + 1 = 0
On comparing with ax² + bx + c = 0, we get
a = 1, b = -1 and c = 1
∴ Sum of the roots = 
So, sum of the roots of the quadratic equation 3x² - 3x + 3 = 0 is not 3, so it is not the answer.

Given equation is (x² + 1)² - x² = 0
⇒ x⁴ + 1 + 2x² - x² = 0 [∵ (a + b)² = a² + b² + 2ab]
⇒ x⁴ + x² + 1 = 0
Let x² = y
∴ (x²)² + x² + 1 = 0
y² + y + 1 = 0
On comparing with ay² + by + c = 0, we get
a = 1, b = 1 and c = 1
Discriminant, D = b² - 4ac
= (1)² - 4(1)(1)
= 1 - 4 = -3
Since, D < 0
∴ y² + y + 1 = 0 i.e., x⁴ + x² + 1 = 0 or (x² + 1)² - x² = 0 has no real roots.

Taking LCM

Circumference of a circle = 2πr
= 2*22/7*28
= 2*22*4
= 176
now, perimeter of square = circumference of a circle = 176
Therefore, side of square = perimeter/4
= 176/4
= 44 answer.

Perimeter of circle = 2πr
Area of circle= πr²
Perimeter = Area
2πr= πr²
2= πr²/r
πr gets cancelled
So r = 2 units

∵ OT is radius and PT is tangent
∴ OT ⊥ PT
Now, in ΔOTP,
OP² = PT² + OT²
⇒ 26² = 24² + OT²
⇒ 676 - 576 -OT²
⇒ 100 = OT² ⇒ 10 cm = OT

and the prime numbers in it are {2,3,5}.

Total possible outcomes = 3

Probability of getting a prime = 3/6 = 1/2.

 According to the basic axiom of probability, the sum of the probabilities of all individual outcomes in any experiment is always 1 because the sample space includes every possible outcome. Option A suggests a range that does not include 1, option B presents an invalid inequality, and option D indicates a probability of 0, which contradicts the fundamental principle that probabilities in a complete sample space must total 1.
So option C is correct

(3/5)^2x-3= (5/3)^x-3
(3/5)^2x-3=(3/5)^3-x
2x-3=3-x
2x+x=6
3x=6
x=2

Angle of elevation for Guddi is same for the tree and the mall.

So, the ratio of object height to its shadow will be same for the both subjects.

Therefore by proportionality rule,

Angle of elevation =45 degrees
Base=20 m
Height of the tower=perpendicular
We have tan 45=P/B
1=P/20
P=20 m
Hence the height of the tower  is 20 metres.