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All questions of Mathematics for Class 9 Exam

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In the adjoining figure, the value of ∠A +  ∠B + ∠C + ∠D + ∠E + ∠F is
  • a)
    360°
  • b)
    270°
  • c)
    540°
  • d)
    180°
Correct answer is option 'A'. Can you explain this answer?

Arvind Singh answered
In △ACE, By angle Sum property of triangle
∠A+∠C+∠E=180degree     ...(1)
Similarly, in △BDF∠B+∠D+∠F=180degree     ...(2)
Adding (1) and (2), 
we get∠A+∠B+∠C+∠D+∠E+∠F=360degree

In the given figure, ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are joined. If ∠CAD = 40° and ÐBDC = 25°. Find ∠BCD.
  • a)
    85°
  • b)
    120°
  • c)
    115°
  • d)
    95°
Correct answer is option 'C'. Can you explain this answer?

Swati Verma answered
Given- O is the centre of a circle. AOC&BOD  are two diameters. ∠CAD=60o.
To find out ∠BCD=?
Solution- We join AC &  BD &  BC. Now OA, OC & OD, OB are radii of the given circle since  they belong to the diameters AC &  BD respectively.
∴OA=OC=OD=OB.
Again, BC subtends ∠CDB &  ∠CAB to the circumference of the given circle. ∴∠CAB=∠CDB=25o since angles, subtended by a chord of a  circle to its circumference, are equal. Now ABCD is a cyclic quadrilateral.
∴∠DAB+∠DCB=180o
∴∠BCD=950

The exterior angle of a triangle is equal to the sum of two
  • a) 
    interior angles
  • b) 
    exterior angles
  • c) 
    interior opposite angles
  • d) 
    alternate angles.
Correct answer is option 'C'. Can you explain this answer?

Arjun Sharma answered
An exterior angle of a triangle is equal to the sum of the opposite interior angles. For more on this see Triangle external angle theorem. If the equivalent angle is taken at each vertex, the exterior angles always add to 360deg In fact, this is true for any convex polygon, not just triangles.

The base of a right angled triangle is 5 metres and hypotenuse is 13 metres. Its area will be:
  • a)
    25 m2
  • b)
    28 m2
  • c)
    30 m2
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Rochana Singh answered
Solution:

Given, base = 5m and hypotenuse = 13m

Let height be h.

Using Pythagoras theorem, we have:

$$(\text{hypotenuse})^2 = (\text{base})^2 + (\text{height})^2$$

$$(13)^2 = (5)^2 + h^2$$

$$h^2 = 169 - 25$$

$$h^2 = 144$$

$$h = 12 \text{m}$$

Therefore, the height of the triangle is 12m.

Area of the triangle = 1/2 × (base) × (height)

$$\text{Area} = \frac{1}{2} \times 5 \times 12$$

$$\text{Area} = 30 \text{m}^2$$

Hence, the area of the triangle is 30 m². Therefore, the correct option is (c).

If the decimal number is a fraction then its binary equivalent is obtained by ________ the number continuously by 2.
  • a)
    Dividing
  • b)
    Multiplying
  • c)
    Adding
  • d)
    Subtracting
Correct answer is option 'B'. Can you explain this answer?

Aniket Yadav answered
On multiplying the decimal number continuously by 2, the binary equivalent is obtained by the collection of the integer part. However, if it’s an integer, then it’s binary equivalent is determined by dividing the number by 2 and collecting the remainders.

Which of the following is not an improper fraction :-
  • a)
    4/3
  • b)
    3/2
  • c)
    5/3
  • d)
    7/11
Correct answer is option 'D'. Can you explain this answer?

Hridoy Verma answered
Improper Fractions

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 4/3 and 5/3 are both improper fractions.

Proper Fractions

A proper fraction is a fraction where the numerator is less than the denominator. For example, 3/2 is a proper fraction.

Answer

The correct answer is option 'D' which is 7/11. This is because 7/11 is a proper fraction, as the numerator (7) is less than the denominator (11). The other options, 4/3, 3/2, and 5/3, are all improper fractions.

If ax = b, by = c and cz = a, then the value of xyz is :-
  • a)
    0
  • b)
    1
  • c)
    1/3
  • d)
    1/2
Correct answer is option 'B'. Can you explain this answer?

Tanvi choudhary answered
From the following, we need to find the values of x,y, and z:
a x =b , b y =c , c z =a
From ax =  b, we get x  =b/a -------------------------- (i)
From by = c, we get y  =c/b ---------------------------(ii)
From cz = a, we get z = c/a ---------------------------(iii)
Multiplying the left hand sides and right hand sides of (i), (ii) and (iii) we get
xyz=(b/a)*(c/b)*(c/a)
When we simplify, we find that xyz=1. Hence proved.

In Δ PQR, side QR = 10 cm and height PM = 4.4 cm. If PR = 11 cm, then altitude QN equals :
  • a)
    4 cm
  • b)
    5 cm
  • c)
    5.5 cm
  • d)
    5.6 cm
Correct answer is option 'A'. Can you explain this answer?

Bibek Chaudhary answered
The context of computer science, a loop is a programming construct that allows a set of instructions to be repeated multiple times. It is used to automate repetitive tasks and to control the flow of a program.

There are several types of loops commonly used in computer programming:

1. While loop: This loop continues executing a block of code as long as a specified condition is true. The condition is checked before each iteration.

2. For loop: This loop executes a block of code a specified number of times. It consists of an initialization, a condition, and an increment or decrement.

3. Do-while loop: This loop is similar to a while loop, but the condition is checked at the end of each iteration. This guarantees that the block of code will be executed at least once.

Loops are useful for iterating over arrays, processing collections of data, and performing calculations. They can also be nested within each other to create more complex patterns of repetition.

When using loops, it is important to ensure that there is a condition that will eventually become false, otherwise the loop may run indefinitely, leading to a program crash or an infinite loop.

The point P(3, 0) lies
  • a)
    in II Quadrant
  • b)
    in III Quadrant
  • c)
    in IV Quadrant
  • d)
    on the x-axis
Correct answer is option 'D'. Can you explain this answer?

Preet answered
Point P(3,0) Will lie on the x-axis As U Know: If 'X-coOrdinate of any Point Is Any Integer And Y-coOrdinate is 0' ; Then,It will always lie on thex-axis.

In the given figure, O is the centre of the circle. Find the value of x.
  • a)
    30°
  • b)
    45°
  • c)
    60°
  • d)
    75°
Correct answer is 'D'. Can you explain this answer?

Hitanshi answered
Angle BDC = angle BAC. ( Angles on same segment)
In ∆BDC, by angle sum property of a triangle,
angle( DBC + BDC + DCB) = 180′
60' + 45' + 40' + angle OCD = 180'
145' + angle OCD = 180'
angle OCD = 180' - 145'
angle OCD = 35'

Angle BCD = 35' + 40'
x = 75'

The difference of two complementary angles is 40°. Then the angles are :-
  • a)
    65°, 25°
  • b)
    70°, 20°
  • c)
    70°, 30°
  • d)
    60°, 30°
Correct answer is option 'A'. Can you explain this answer?

Srijita answered
Let 1 angle be = xthe other angle = 90-xA/q90 - x - x = 4090 - 2x = 4090 - 40 = 2x50 = 2xx = 50/2 = 251 angle = x = 252 angle = 90 - x = 90 - 25degree = 65degree.

If pqr = 1, then     is equal to :-
  • a)
    0
  • b)
    1/pq
  • c)
    pq
  • d)
    1
Correct answer is option 'D'. Can you explain this answer?

Srijita answered
Dear Sreyansh, hope it helps pqr = 1 r = 1/pq 1/r = pq (1/1+p+q-1) + (1/1+q+r-1) + (1/1+r+p-1) (1/(1+p+1/q) + (1/(1+q+pq) + (1/(1+1/pq+1/p) (1/(q+pq+1/q) + (1/(q+pq+1) + (1/(q+pq+1/pq) (q/q+pq+1) + (1/q+pq+1) + (pq/q+pq+1) (q+pq+1) / (q+pq+1) = 1

The value of x in   is :-
  • a)
    33
  • b)
    44
  • c)
    55
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Sanjana answered
(4x -7 )^1/3 -5 =0 = (4x -7)^1/3 = 5 = 4x -7 = 5 ³ = 4x -7 =125 = 4x = 125 +7 = 4x = 132 = x = 132/4 = x = 33

Can you explain the answer of this question below:

If 2x = 3y = 6-z, then  is equal to :-

 

  • A:

    0

  • B:

    1

  • C:

    3/2

  • D:

    -1/2

The answer is a.

Prachi Rathore answered
LET 2^x=3^y=(1/6)^z=k,Therefore,K^(1/x)=2,K^(1/y)=3,K^(1/z)=(1/6),Multiply these 3 equations to get:K^[(1/x)+(1/y)+(1/z)]=1Hence we can conclude that either k=1 ( which is totally false) or power is equal to “0”.The correct answer is : [(1/x)+(1/y)+(1/z)]=0

In the adjoining figure, it is given that ∠A = 60°, CE || BA and ∠ECD = 65° then ∠ ACB = _______ .
  • a)
    60°
  • b)
    55°
  • c)
    70°
  • d)
    90°
Correct answer is 'B'. Can you explain this answer?

Sonal Sinha answered
AngleBAC=angleACE....(alt interior angle) So, Angle ACE=65 dgree Angle ACB+ angleACE + angle ECD= 180 degree....(linear pair) Angle ACB+65 degree + 60 degree=180 dgree Angle BCA=(180-125) degree Angle BCA=55 degree (Ans).

ABCD is a parallelogram and 'O' is the point of intersection of its diagonals AC and BD . If the
area of ΔAOD = 8 cm2 the area of the parallelogram is
  • a)
    2 cm2
  • b)
    4 cm2
  • c)
    16 cm2
  • d)
    32 cm2
Correct answer is option 'D'. Can you explain this answer?

Tia Shah answered
The area of a parallelogram is given by the formula:

Area = base * height

In this case, we know that the base is the length of one of the sides of the parallelogram, and the height is the perpendicular distance between the base and the opposite side.

Since ABCD is a parallelogram, we can use the length of AB as the base. Let's call AB = b.

To find the height, we need to find the perpendicular distance between AB and the line passing through O. Let's call this distance h.

Since O is the point of intersection of the diagonals AC and BD, we can use the fact that the diagonals of a parallelogram bisect each other to find the length of AO and BO.

Since AO is a diagonal, it is equal in length to CO. Similarly, BO is equal in length to DO.

Let's call AO = CO = x and BO = DO = y.

Now, we can use the fact that the diagonals of a parallelogram bisect each other to find the length of AB in terms of x and y.

Since AO and BO bisect AC and BD respectively, we can write:

AC = 2 * AO = 2x
BD = 2 * BO = 2y

Since ABCD is a parallelogram, AC is parallel to BD. Therefore, AC and BD have the same length.

2x = 2y

x = y

Now, we can use the fact that the diagonals of a parallelogram bisect each other to find the length of AB in terms of x.

Since AC and BD bisect each other at O, we can write:

AB = AO + BO = x + y

Since x = y, we can simplify this to:

AB = 2x

Now, we can substitute this value for AB into the formula for the area of a parallelogram:

Area = base * height
Area = AB * h

Area = (2x) * h

So, the area of the parallelogram is given by 2xh.

However, we don't have enough information to find the value of x or h, so we cannot determine the exact area of the parallelogram.

Find the least number which will leaves remainder 5 when divided by 8, 12, 16 and 20.
  • a)
    240
  • b)
    245
  • c)
    265
  • d)
    235
Correct answer is option 'B'. Can you explain this answer?

Ananya Das answered
We have to find the Least number, therefore we find out the LCM of 8, 12, 16 and 20.
8 = 2*2*2;
12 = 2*2*3;
16 = 2*2*2*2;
20 = 2*2*5;
LCM = 2*2*2*2*3*5 = 240;
This is the least number which is exactly divisible by 8, 12, 16 and 20.
Thus,
required number which leaves remainder 5 is,
240+5 = 245.

Can you explain the answer of this question below:

If   = 4, then  is equal to :-

 

  • A:

    196

  • B:

    194

  • C:

    192

  • D:

    190

The answer is b.

Study Buddy answered
(x+1/x)² = (4)² x²+1/x²+2 =16 x²+1/x² = 14 (x²+1/x²)² = (14)² x⁴ +1/x⁴ +2 = 196 x⁴+1/x⁴ = 194

If a + b + c = 0, then a2 + b2 + c2 is :-
  • a)
    –4(ab + bc + ca)
  • b)
    –2(ab + bc + ca)
  • c)
    0
  • d)
    2a2 – 2bc
Correct answer is option 'B'. Can you explain this answer?

Wahid Khan answered
Putting formula of (a+b+c)² = a² + b² + c² + 2(ab + bc + ca).... Now, value of a²+b²+c² is zero so .....0 = a² + b² + c² + 2(ab + bc + ca)..... next if we do side change we get a² + b² + c² = -2(ab + bc +ca)

Let N = 1421*1423*1425. What is the remainder when N is divided by 12?
  • a)
    0
  • b)
    9
  • c)
    3
  • d)
    6
Correct answer is option 'C'. Can you explain this answer?

Deepika Mehta answered
Solution:
We have to find the remainder when N is divided by 12.

Prime factorization of 12 = 2^2 * 3

Let's find the remainders when N is divided by 2^2 and 3 separately.

Remainder when N is divided by 2^2:

Since 1424 is divisible by 4, we only need to consider the remainders when 1421, 1423, and 1425 are divided by 4.

1421 ≡ 1 (mod 4)
1423 ≡ 3 (mod 4)
1425 ≡ 1 (mod 4)

Multiplying these three congruences, we get:

1421 * 1423 * 1425 ≡ 1 * 3 * 1 ≡ 3 (mod 4)

Therefore, the remainder when N is divided by 4 is 3.

Remainder when N is divided by 3:

Since the sum of the digits of N is equal to the sum of the remainders when the factors are divided by 3, we have:

N ≡ 1 + 4 + 2 + 1 + 1 + 4 + 2 + 3 + 1 + 4 + 2 + 5 ≡ 30 ≡ 0 (mod 3)

Therefore, the remainder when N is divided by 3 is 0.

Using the Chinese Remainder Theorem, we can combine the remainders when N is divided by 2^2 and 3 to find the remainder when N is divided by 12:

N ≡ 3 (mod 4)
N ≡ 0 (mod 3)

Solving this system of congruences, we get:

N ≡ 3 * 3 * 2 ≡ 18 ≡ 6 (mod 12)

Therefore, the remainder when N is divided by 12 is 6.

Hence, option 'C' is the correct answer.

The number of surfaces in right circular cylinder is :
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?

Jyoti Kapoor answered
A right circular cylinder is a three-dimensional object with two congruent circles as parallel bases and a lateral surface consisting of a rectangle.

An exterior angle of a triangle is equal to the sum of two _________ angles :-
  • a)
    Exterior opposite
  • b)
    Interior opposite
  • c)
    Interior
  • d)
    Opposite
Correct answer is option 'B'. Can you explain this answer?

Ananya Sharma answered
A related theorem. Because an exterior angle is equal to the sum of the opposite interior angles, it follows that it must be larger than either one of them. Stated more formally: Theorem: An exterior angle of a triangle is always larger then either opposite interior angle.

Cards each marked with one of the numbers 4, 5, 6,...., 20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Then, the probability of getting an even prime number is
  • a)
    1
  • b)
    0
  • c)
    1/2
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Milan Chawla answered
Solution:
Given that there are cards marked with numbers 4, 5, 6,...., 20 in a box.

To find: the probability of getting an even prime number.

Prime numbers between 4 to 20 are 5, 7, 11, 13, 17, and 19.

Out of these prime numbers, only 2 is an even number.

Thus, the probability of getting an even prime number is 1/6.

But, the question asks for the probability of getting an even prime number from the given numbers 4, 5, 6,...., 20.

Out of these numbers, even numbers are 4, 6, 8, 10, 12, 14, 16, 18, and 20.

There are no even prime numbers in this list.

Therefore, the probability of getting an even prime number is 0.

Hence, the correct answer is (B) 0.

In a quadrilateral, the angles are in the ratio 3 : 4 : 5 : 6. Then the difference between the greatest and the smallest angle is:
  • a)
    60°
  • b)
    54°
  • c)
    40°
  • d)
    45°
Correct answer is option 'A'. Can you explain this answer?

Soumya answered
Let the all angles of quadrilateral be 3x,4x,5x,6x. sum of all angles of quadrilateral = 360 3x + 4x + 5x + 6x = 360 18x = 360 x = 360÷18 x = 20 Angles of triangle will be - 3x = 3*20 = 60 4x = 4*20 = 80 5x = 5*20 = 100 6x = 6*20 = 120 The greatest angle = 120 The smallest angle = 60 So, the difference between the greatest and smallest angle = 120-60 = 60....

The graph of the line x = 4 passes through
  • a)
    (4, 3)
  • b)
    (3, 4)
  • c)
    (0, 4)
  • d)
    (-1, 4)
Correct answer is option 'A'. Can you explain this answer?

Akshat Ghosh answered
Explanation:

The equation x = 4 represents a vertical line passing through the point (4, 0) on the x-axis. Therefore, the line intersects the y-axis at (0, 0) and all points on the line have an x-coordinate of 4.

To check which point lies on this line, we can substitute x = 4 in the coordinates of each given point and see if we get a valid point on the line.

a) (4, 3): Since x = 4 and y = 3, this point lies on the line.
b) (3, 4): Since x ≠ 4, this point does not lie on the line.
c) (0, 4): Since x ≠ 4, this point does not lie on the line.
d) (-1, 4): Since x ≠ 4, this point does not lie on the line.

Therefore, the only point that lies on the line x = 4 is (4, 3).

Answer: Option A (4, 3)

What is the sum of all two digit numbers that gives a remainder of 3 when they are divided by 7?
  • a)
    666
  • b)
    676
  • c)
    683
  • d)
    777
Correct answer is option 'B'. Can you explain this answer?

Anita Menon answered
The two digit number which gives a remainder of 3 when divided by 7 are:
10, 17, 24 94.
Now, these number are in AP series with 
1st Term, a = 10; 
Number of Terms, n = 13;
Last term, L = 94 and
Common Difference, d = 7.
Sum,
= n*(a+L)/2
= 13*52 = 676.

The factors of (x3 – 5x2 + 8x – 4) are :-
  • a)
    (x + 2) (x – 2) (x – 1)
  • b)
    (x + 1) (x + 2) (x – 2)
  • c)
    (x – 2)2 (x – 1)
  • d)
    (x – 2)2 (x + 1)
Correct answer is option 'C'. Can you explain this answer?

Saroj Mor answered
X³ - 5x² + 8x - 4 -: x - 1= 0 x= 1 p(1)= 1³ - 5 × 1² + 8 × 1 - 4 = 1 - 5 + 8 - 4 = - 4 + 4 = 0 -: divide x³ - 5x² + 8x - 4 by x - 1 then quotient will be = x² - 4x + 4 (x-1)(x³ - 5x² + 8x - 4)then factorise it by splitting the middle term. =x² - 4x + 4 = sum = 4 prod.=4x² - (2+2)x + 4= x² - 2x - 2x + 4 x(x - 2) - 2(x - 2) = (x - 2) ( x - 2) ( x - 1)= (x - 2)² ( x - 1).

Solution set of the equation |x – 2| = 5 is :-
  • a) 
    {3, -7}
  • b) 
    {-3, 7}
  • c) 
    {3, 6}
  • d) 
    None of these
Correct answer is option 'B'. Can you explain this answer?

Raghavendra Chawla answered
The given equation is:

|x - 5| > 2

To solve this inequality, we need to consider two cases:

Case 1: (x - 5) > 2

Solving for x, we get:

x > 7

Case 2: (x - 5) < />

Solving for x, we get:

x < />

Therefore, the solution set of the inequality is:

x < 3="" or="" x="" /> 7

This can also be written as:

(-∞, 3) ∪ (7, ∞)

where (∞ means infinity).

Two circles intersect in A and B. Quadrilaterals PCBA and ABDE are inscribed in these circles such that PAE and CBD are line segment. If ∠P = 95° and ∠C = 40°. Find the value of Z.
  • a)
    65°
  • b)
    105°
  • c)
    95°
  • d)
    85°
Correct answer is option 'D'. Can you explain this answer?

Dark Bot answered
In square ABCP, angle ABC = 85. as opposite angle of a cyclic quadrilateral are supplementary.

in square ABDE , angle ABD = 95 as CD is a line and angle ABC and angle ABD forms a linear pair

in square ABDE , angle AED i.e Z = 85 as opposite angle of the cyclic quadrilateral are supplementary.

thnx

The number of line segments determined by three given non-collinear points is :
  • a) 
    three
  • b) 
    two
  • c) 
    four
  • d) 
    infinitely many
Correct answer is option 'A'. Can you explain this answer?

Jyoti Kapoor answered
If the lines are non collinear 
if line should be pass through all three points then answer is none because non collinear means the points which not lie in a line if it must contain only two points then number of line will be three ..because we can draw a triangle.

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