Maths MCQs P 2

HN PHYSICS

Sequences and Series


1. Sequence is same as progression.
a) True
b) False
View Answer

Answer: b
Explanation: Sequence and progression are different things. When sequence follow a specified pattern, it is said to be a progression.

2. Complete 2,3,5,7, _____________
a) 8
b) 9
c) 10
d) 11
View Answer

Answer: d
Explanation: Since 2,3,5 and 7 all are consecutive prime numbers so, it is a sequence of prime numbers. Prime number next to 7 is 11. So, 2,3,5,7,11.


3. Complete 2, 4, 6, 8, _____________
a) 10
b) 9
c) 13
d) 11
View Answer

Answer: a
Explanation: Since 2,4,6 and 8 are even numbers so it is a sequence of even numbers. Even number next to 8 is 10. So, 2,4,6,8,10.

4. Which of the following is finite sequence?
a) 48,24,12, ………….
b) 1,2,3, …………
c) 2,4,6,8,10
d) 2,3,5,7,11,13, ……………………
View Answer

Answer: c
Explanation: Since sequence 2,4,6,8,10 contains limited number of terms so, it is finite sequence. Rest all are infinite sequences.

5. Which of the following relation gives Fibonacci sequence?
a) an = an-1 + an-2
b) an-1 = an + an-2
c) an-2 = an + an-1
d) an = an+1 + an-2
View Answer

Answer: a
Explanation: an = an-1 + an-2, n>2.
This is a recurrence relation which gives Fibonacci sequence.

6. 1,1,2,3,5, ………… is a Fibonacci Sequence.
a) True
b) False
View Answer

Answer: a
Explanation: Yes, 1,1,2,3,5, ………… is a Fibonacci Sequence because it follows the recurrence relation
an = an-1 + an-2, n>2.

7. What is the first term of Fibonacci sequence?
a) 0
b) 1
c) 2
d) 3
View Answer

Answer: b
Explanation: a1=1 and a2=1.
an = an-1 + an-2, n>2.
This is a recurrence relation which gives the Fibonacci sequence.

8. What is the third term of Fibonacci sequence?
a) 0
b) 1
c) 2
d) 3
View Answer

Answer: c
Explanation: a1=1 and a2=1.
an = an-1 + an-2, n>2.
This is a recurrence relation which gives Fibonacci sequence.
=>a3=a1+a2=1+1=2.

9. If an = 4n+6, find 15th term of the sequence.
a) 6
b) 10
c) 60
d) 66
View Answer

Answer: d
Explanation: an = 4n+6 and n=15
=>a15 = 4*15 + 6 = 60+6 = 66.

10. a1 = a2 = 2, an = an – 1–1, n > 2. Find a5.
a) 2
b) -1
c) 1
d) 0
View Answer

Answer: b
Explanation: an = an – 1–1, n > 2
=> a3 = a2 – 1 = 2 – 1 = 1
=> a4 = a3 – 1 = 1 – 1 = 0
=> a5 = a4 – 1 = 0 – 1 = -1.

Straight Lines


1. What is the distance between (1, 3) and (5, 6)?
a) 3 units
b) 4 units
c) 5 units
d) 25 units
View Answer

Answer: c
Explanation: We know, distance between two points (x1, y1) and (x2, y2) is (𝑥1−𝑥2)2+(𝑦1−𝑦2)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√.
So, distance between (1, 3) and (5, 6) is (1−5)2+(3−6)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=(4)2+(3)2‾‾‾‾‾‾‾‾‾‾√ = 5 units.

2. What is the distance of (5, 12) from origin?
a) 6 units
b) 8 units
c) 10 units
d) 13 units
View Answer

Answer: d
Explanation: We know, distance between two points (x1, y1) and (x2, y2) is (𝑥1−𝑥2)2+(𝑦1−𝑦2)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√.
So, distance between (5, 12) from origin (0, 0) is (5−0)2+(12−0)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=(5)2+(12)2‾‾‾‾‾‾‾‾‾‾‾√ = 13 units.

3. The coordinates of a point dividing the line segment joining (1, 2) and (4, 5) internally in the ratio 2:1 is ____________________
a) (3, 4)
b) (4, 3)
c) (5, 4)
d) (5, 3)
View Answer

Answer: a
Explanation: The coordinates of a point dividing the line segment joining (x1, y1) internally in the ratio m: n is (𝑚𝑥2+𝑛𝑥1𝑚+𝑛,𝑚𝑦2+𝑛𝑦1𝑚+𝑛).
So, the coordinates of a point dividing the line segment joining (1, 2) and (4, 5) internally in the ratio 2:1 is (2∗4+1∗12+1,2∗5+1∗22+1) = (3, 4).
4. In which ratio (3, 4) divides the line segment joining (1, 2) and (4, 5) internally?

a) 1:2
b) 2:1
c) 3:4
d) 4:3
View Answer

Answer: b
Explanation: The coordinates of a point dividing the line segment joining (x1, y1) and (x2, y2) internally in the ratio m: n is (𝑚𝑥2+𝑛𝑥1𝑚+𝑛,𝑚𝑦2+𝑛𝑦1𝑚+𝑛).
Let the ratio be k: 1.So, the coordinates of a point dividing the line segment joining (1, 2) and (4, 5) internally in the ratio k: 1 is (𝑘∗4+1∗1𝑘+1,𝑘∗5+1∗2𝑘+1)
=> (𝑘∗4+1∗1𝑘+1,𝑘∗5+1∗2𝑘+1) is same as (3, 4).
=> (4k+1)/(k+1) = 3
=> 4k+1 = 3k+3
=> k = 2
So, ratio is 2:1.

5. The coordinates of a point dividing the line segment joining (1, 2) and (4, 5) externally in the ratio 2:1 is ____________________
a) (4, 5)
b) (6, 8)
c) (7, 8)
d) (8, 6)
View Answer

Answer: c
Explanation: The coordinates of a point dividing the line segment joining (x1, y1) and (x2, y2) externally in the ratio m: n is (𝑚𝑥2−𝑛𝑥1𝑚−𝑛,𝑚𝑦2−𝑛𝑦1𝑚−𝑛).
So, the coordinates of a point dividing the line segment joining (1, 2) and (4, 5) externally in the ratio 2:1 is (2∗4−1∗12−1,2∗5−1∗22−1) = (7, 8).

6. _____________ is the midpoint of (1, 2) and (5, 8).
a) (2, 5)
b) (3, 5)
c) (5, 2)
d) (5, 3)
View Answer

Answer: b
Explanation: We know, midpoint of (x1, y1) and (x2, y2) is (𝑥1+𝑥22,𝑦1+𝑦22).
So, midpoint of (1, 2) and (5, 8) is ((1+5)/2, (2+8)/2) is (3, 5).

7. What is the area of triangle whose vertices are (-4, -4), (-3, 2), (3, -16)?
a) 24 sq. units
b) 27 sq. units
c) 32 sq. units
d) 37 sq. units
View Answer

Answer: b
Explanation: We know, area of triangle joining vertices (x1, y1), (x2, y2) and (x3, y3) is (1/2)* determinant ⎛⎝⎜⎜−4−33−42−16111⎞⎠⎟⎟ is 12{(-4)(2+16) – (-4)(-3-3) + (1)(48-6)} = 12|(-72)+(-24)+42| = 27 square units.

8. If area of triangle formed by three points is zero then the three points must be collinear.
a) True
b) False
View Answer

Answer: a
Explanation: Area of triangle formed by three points is zero then the three points must be collinear i.e. they must lie on the same line.

9. Angle made by line with ____________ measured anticlockwise is called inclination of the line.
a) positive x-axis
b) negative x-axis
c) positive y-axis
d) negative y-axis
View Answer

Answer: a
Explanation: We know, inclination of line is always measured with positive x-axis in anticlockwise direction.

10. Slope of a line is given by _________ if inclination of line is α.
a) sinα
b) cosα
c) tanα
d) cotα
View Answer

Answer: c
Explanation: Slope of a line is given by tanα if inclination of line is α. Slope is denoted by tangent of the inclination angle.

11. Find slope of line if inclination made by the line is 60°.
a) 1/2
b) 1/√3
c) √3
d) 1
View Answer

Answer: c
Explanation: Slope of a line is given by tanα if inclination of line is α. If inclination is 60° the slope is tan 60° = √3.

12. What is the inclination of a line which is parallel to x-axis?
a) 0°
b) 180°
c) 45°
d) 90°
View Answer

Answer: a
Explanation: If a line is parallel to x-axis then angle formed by it with x-axis is zero. So, its inclination is zero.

13. What is the inclination of a line which is parallel to y-axis?
a) 0°
b) 180°
c) 45°
d) 90°
View Answer

Answer: d
Explanation: If a line is parallel to y-axis then angle formed by it with x-axis is 90°. So, its inclination is 90°.

14. What is the slope of a line which is parallel to x-axis?
a) -1
b) 0
c) 1
d) Not defined
View Answer

Answer: b
Explanation: If a line is parallel to x-axis then angle formed by it with x-axis is zero. So, its inclination is zero. Hence slope = tan 0° = 0.

15. What is the slope of a line which is parallel to y-axis?
a) -1
b) 0
c) 1
d) Not defined
View Answer

Answer: d
Explanation: If a line is parallel to y-axis then angle formed by it with x-axis is zero. So, its inclination is 90°. Hence slope = tan 90° which is not defined.

Conic Sections


1. Find the equation of circle with center at origin and radius 5 units.
a) x2+y2=25
b) x2+y2=5
c) x2=25
d) y2=25
View Answer

Answer: a
Explanation: Equation of circle with center at (a, b) and radius r units is
(x-a)2+(y-b)2=r2
So, equation of circle is (x-0)2+(y-0)2=52 => x2+y2=25.

2. Find the equation of circle with center at (2, 5) and radius 5 units.
a) x2+y2+4x-10y+4=0
b) x2+y2-4x-10y+4=0
c) x2+y2+4x+10y+4=0
d) x2+y2+4x-10y-4=0
View Answer

Answer: b
Explanation: Equation of circle with center at (a, b) and radius r units is
(x-a)2+(y-b)2=r2
So, equation of circle is (x-2)2+(y-5)2=52 => x2+y2-4x-10y+4=0.

3. Find the center of the circle with equation x2+y2-4x-10y+4=0.
a) (-2, 5)
b) (-2, -5)
c) (2, -5)
d) (2, 5)
View Answer

Answer: d
Explanation: Comparing the equation with general form x2+y2+2gx+2fy+c=0, we get
2g=-4 => g=-2
2f=-10 => f=-5
c=4
Center is at (-g, -f) i.e. (2, 5).

4. Find the radius of the circle with equation x2+y2-4x-10y+4=0.
a) 25 units
b) 20 units
c) 5 units
d) 10 units
View Answer

Answer: c
Explanation: Comparing the equation with general form x2+y2+2gx+2fy+c=0, we get
2g=-4 => g=-2
2f=-10 => f=-5
c=4
Radius = 𝑔2+𝑓2−𝑐‾‾‾‾‾‾‾‾‾‾‾√=4+25−4‾‾‾‾‾‾‾‾‾‾√=5.

5. Find the equation of circle which pass through (5, 9) and center at (2, 5).
a) x2+y2+4x-10y+4=0
b) x2+y2-4x-10y+4=0
c) x2+y2+4x+10y+4=0
d) x2+y2+4x-10y-4=0
View Answer

Answer: b
Explanation: Equation of circle with center at (a, b) and radius r units is
(x-a)2 + (y-b)2 = r2
(5-2)2 + (9-5)2 = r2 => r2=32+42 => r=5.
So, equation of circle is (x-2)2+(y-5)2=52 => x2+y2-4x-10y+4=0.

6. If a circle pass through (2, 0) and (0, 4) and center at x-axis then find the radius of the circle.
a) 25 units
b) 20 units
c) 5 units
d) 10 units
View Answer

Answer: c
Explanation: Equation of circle with center at x-axis (a, 0) and radius r units is
(x-a)2+(y)2=r2
=>(2-a)2+(0)2=r2
And (0-a)2+(4)2=r2
=>(a-2)2=a2+42 => (-2)(2a-2) =16 => a-1=-4 => a=-3
So, r2 = (2+3)2=52
r=5 units.

7. If a circle pass through (4, 0) and (0, 2) and center at y-axis then find the radius of the circle.
a) 25 units
b) 20 units
c) 5 units
d) 10 units
View Answer

Answer: c
Explanation: Equation of circle with center at y-axis (0, b) and radius r units is
(x)2+(y-b)2=r2
=>(4)2+(-b)2=r2
And (0)2+(2-b)2=r2
=>(b-2)2=b2+42 => (-2)(2b-2)=16 => b-1=-4 => b=-3
So, r2=42+32=52 => r=5 units.

8. The point (1, 4) lie ___________ the circle x2+y2-2x-4y+2=0.
a) inside circle
b) outside circle
c) on the circle
d) either inside or outside
View Answer

Answer: b
Explanation: Circle has equation x2+y2-2x-4y+2=0.
12+42-2*1-4*4+2 = 1+16-2-16+2 =1 > 0 so, point is outside the circle.

9. The point (0, 0) lie ___________ the circle x2+y2-2x-4y=0.
a) inside circle
b) outside circle
c) on the circle
d) either inside or outside
View Answer

Answer: c
Explanation: Circle has equation x2+y2-2x-4y=0.
02+02-2*0-4*0+0 = 0 so, point is on the circle.

10. The point (6, 2) lie ___________ the circle x2+y2-2x-4y-36=0.
a) inside circle
b) outside circle
c) on the circle
d) either inside or outside
View Answer

Answer: a
Explanation: Circle has equation x2+y2-2x-4y-36=0.
62+22-2*6-4*2-36 = 36+4-12-8-36 =-16<0 so, point is inside the circle.

Three Dimensional Geometry

1. The point (4, 0, 0) lie on _____________

a) X-axis
b) Y-axis
c) Z-axis
d) Y-Z plane
View Answer

Answer: a
Explanation: In 3d coordinate system, a point with y and z coordinate zero and x-coordinate having non-zero value must lie on x-axis. So, (4, 0, 0) lie on x-axis.

2. The point (0, 0, 3) lie on ____________
a) X-axis
b) Y-axis
c) Z-axis
d) X-Y plane
View Answer

Answer: c
Explanation: In 3d coordinate system, a point with x and y coordinate zero and z-coordinate having non-zero value must lie on z-axis. So, (0, 0, 3) lie on z-axis.

3. The point (0, 2, 0) lie on _________
a) X-axis
b) Y-axis
c) Z-axis
d) X-Y plane
View Answer

Answer: b
Explanation: In 3d coordinate system, a point with x and z coordinate zero and y-coordinate having non-zero value must lie on y-axis. So, (0, 2, 0) lie on y-axis.

4. The point (0, 2, 4) lie on _________
a) X-Y plane
b) Y-Z plane
c) X-Z plane
d) X-axis
View Answer

Answer: b
Explanation: In 3d coordinate system, a point with x-coordinate zero and y & z coordinate having non-zero value must lie on Y-Z plane. So, (0, 2, 4) lie on Y-Z plane.

5. The point (4, 2, 0) lie on _________
a) X-Y plane
b) Y-Z plane
c) X-Z plane
d) X-axis
View Answer

Answer: a
Explanation: In 3d coordinate system, a point with z-coordinate zero and x & y coordinate having non-zero value must lie on X-Y plane. So, (4, 2, 0) lie on X-Y plane.

6. The point (3, 0, 4) lie on _________
a) X-Y plane
b) Y-Z plane
c) X-Z plane
d) X-axis
View Answer

Answer: c
Explanation: In 3d coordinate system, a point with y-coordinate zero and x & z coordinate having non-zero value must lie on X-Z plane. So, (3, 0, 4) lie on X-Z plane.

7. Find the distance of point (2, 3, 5) from X-Y plane.
a) 2 units
b) 3 units
c) 5 units
d) 1 unit
View Answer

Answer: c
Explanation: We know, distance of a point from X-Y plane is equal to the value of its z-coordinate.
So, distance of point (2, 3, 5) from X-Y plane is 5 units.

8. Find the distance of point (2, 3, 5) from Y-Z plane.
a) 2 units
b) 3 units
c) 5 units
d) 1 unit
View Answer

Answer: a
Explanation: We know, distance of a point from Y-Z plane is equal to the value of its x-coordinate.
So, distance of point (2, 3, 5) from Y-Z plane is 2 units.

9. Find the distance of point (2, 3, 5) from X-Z plane.
a) 2 units
b) 3 units
c) 5 units
d) 1 unit
View Answer

Answer: b
Explanation: We know, distance of a point from X-Z plane is equal to the value of its y-coordinate.
So, distance of point (2, 3, 5) from X-Z plane is 3 units.

10. 2-D geometry has ______________ quadrants.
a) 1
b) 2
c) 4
d) 8
View Answer

Answer: c
Explanation: 2-D geometry can have 2 coordinates each with positive or negative value.
Total quadrants = 2*2 = 4.

11. 3-D geometry has ______________ octants.
a) 1
b) 2
c) 4
d) 8
View Answer

Answer: d
Explanation: 3-D geometry can have 3 coordinates each with positive or negative value.
Total octants = 2*2*2 = 8.

12. In which octant does the point (1, 5, 7) lies?
a) 1st
b) 2nd
c) 6th
d) 7th
View Answer

Answer: a
Explanation: Since the point with all positive coordinates i.e. of the form (+, +, +) so lie in 1st octant.
So, (1, 5, 7) lies in 1st octant.

13. In which octant does the point (-1, – 5, -7) lies?
a) 1st
b) 2nd
c) 6th
d) 7th
View Answer

Answer: d
Explanation: Since the point with all negative coordinates i.e. of the form (-, -, -) lie in 7th octant.
So, (-1, – 5, -7) lies in 7th octant.

14. In which octant does the point (-1, 5, 7) lies?
a) 1st
b) 2nd
c) 6th
d) 7th
View Answer

Answer: b
Explanation: Since the point with only x coordinate negative i.e. of the form (-, +, +) lie in 2nd octant.
So, (-1, 5, 7) lies in 2nd octant.

15. In which octant does the point (-1, 5, -7) lies?
a) 1st
b) 2nd
c) 6th
d) 7th
View Answer

Answer: c
Explanation: Since the point with only y coordinate positive i.e. of the form (-, +, -) lie in 6th octant.
So, (-1, 5, -7) lies in 6th octant.

 Limits and Derivatives

1. What is the value of 

lim𝑦→2𝑦2−4𝑦−2?
a) 2
b) 4
c) 1
d) 0
View Answer

Answer: b
Explanation: y2 – 4 = (y – 2)(y + 2)
Therefore the fraction becomes, (y + 2)
As y tends to 2, the fraction becomes 4

2. What is the value of lim𝑦→∞2𝑦?
a) 0
b) 1
c) 2
d) Infinity
View Answer

Answer: a
Explanation: Any number divided by infinity gives us 0.
Here, since the number 2 is divided by y, as y approaches infinity, we get 0

3. What is the value of lim𝑥→4𝑥2−2𝑥−8𝑥−4?
a) 0
b) 2
c) 8
d) 6
View Answer

Answer: d
Explanation: The denominator becomes 0, as x approaches 4.
lim𝑥→4𝑥2−2𝑥−8𝑥−4 Here, if we factorize the numerator we get:
lim𝑥→4(𝑥–4)(𝑥+2)𝑥–4
We can now cancel out (x – 4) from both the numerator and denominator.
We get, lim𝑥→4(x + 2) = 6

4. What is the value of lim𝑥→3𝑥2−9𝑥–3?
a) 0
b) 3
c) Infinity
d) 6
View Answer

Answer: d
Explanation: When x tends to 3, both the numerator and the denominator become 0 and it becomes of the form, 00.
Therefore, we use L’Hospital’s rule, which states the we differentiate the numerator and the denominator, until a definite answer is reached.
On differentiating once we get,
lim𝑥→32𝑥1
Since, this not an indeterminate form now, we can substitute the value of x.
= 2 x 3
= 6

5. What is the value of lim𝑥→∞𝑥2−9𝑥2–3𝑥+2?
a) 1
b) 2
c) 0
d) Limit does not exist
View Answer

Answer: a
Explanation:
Since it is of the form ∞∞, we use L’Hospital’s rule and differentiate the numerator and denominator
L = lim𝑥→∞𝑥2−9𝑥2–3𝑥+2
On differentiating once, we get lim𝑥→∞2𝑥2𝑥
Which is equal to, lim𝑥→∞ ⁡1 = 1.

6. Which of the following limits does not yield 1?
a) lim𝑥→0⁡ 1
b) lim𝑥→∞x-2 + x-1 + 1
c) lim𝑥→∞1𝑒𝑥 + 1
d) lim𝑥→∞𝑥3+𝑥2+32𝑥+1𝑥2–3𝑥+2
View Answer

Answer: d
Explanation: lim𝑥→0⁡ 1 = 1 (Since no x term is present)
When the denominator is infinity, the value of the fraction is 0, provided the numerator is not infinity.
lim𝑥→∞x-2 + x-1 + 1 = 0 + 0 + 1 = 1
lim𝑥→∞1𝑒𝑥 + 1 = 1 ( e-∞ = 0)
lim𝑥→∞𝑥3+𝑥2+32𝑥+1𝑥2–3𝑥+2 (Use L’Hospital’s rule and differentiate the numerator and denominator until a rational form is obtained)
lim𝑥→∞𝑥3+𝑥2+32𝑥+1𝑥2–3𝑥+2 = lim𝑥→∞3𝑥2+2𝑥+322𝑥–3 = lim𝑥→∞3𝑥2 = ∞

7. What is the value of lim𝑦→4 f(y)? It is given that f(y) = y2 + 6y (y ≥ 2) and f(y) = 0 (y < 2).
a) 40
b) 16
c) 0
d) 30
View Answer

Answer: a
Explanation: lim𝑦→4f(y) = y2 + 6y
f(4) = 42 + 6(4)
f(4) = 16 + 24
f(4) = 40

8. What is the value of the limit f(x) = 𝑥2+2𝑥√𝑥2−4𝑥 if x approaches infinity?
a) 0
b) 2
c) 1/2
d) 4
View Answer

Answer: a
Explanation: This is of the form ∞∞, therefore we use L’Hospital’s rule and differentiate the numerator and denominator.
= lim𝑥→∞2𝑥+2/𝑥√2𝑥–4
= lim𝑥→∞√2 x-3/2
= 0

9. What is the value of the lim𝑥→532𝑥+1𝑥2–5𝑥?
a) 6.2
b) 6.4
c) 6.3
d) 6.1
View Answer

Answer: b
Explanation: Use L’Hospital’s Rule, and differentiate the numerator and denominator.
lim𝑥→5322𝑥–5
= 325
= 6.4

10. What is the value of the limit lim𝑥→4𝑥2−4−3𝑥𝑥−3?
a) 0
b) 4
c) 1
d) Limit does not exist
View Answer

Answer: a
Explanation: lim𝑥→4𝑥2−4−3𝑥𝑥−3
= 42−4−3(4)4−3
= 01
= 0.

Mathematical Reasoning


1. A sentence is called statement if it is __________________
a) always true
b) always false
c) either true or false but not both
d) both true and false
View Answer

Answer: c
Explanation: A sentence is called mathematically acceptable statement if it is either true or false but not both.

2. Which of the following is a statement?
a) Women are more intelligent than men
b) Two plus two is three
c) Open the door
d) Shut your mouth
View Answer

Answer: b
Explanation: A sentence is called mathematically acceptable statement if it is either true or false but not both.
“Two plus two is three” is false so it is a statement. Rest we cannot decide whether they are true or false.

3. Which of the following is not a statement?
a) Two and two makes four
b) A prime number is always odd
c) Sum of a and b is 5
d) Elephant is heavier than ant
View Answer

Answer: c
Explanation: “Two and two makes four” and “Elephant is heavier than ant” are true so they are statements. “A prime number is always odd” is false as prime number may be even so it is a statement. “Sum of and b is 5” is not a statement as it can be true or false based on the values of a and b taken.
4. Which of the following is a statement?

a) Today is Monday
b) Tomorrow will be holiday
c) If today is Tuesday then tomorrow will be Sunday
d) There will be full moon tonight
View Answer

Answer: c
Explanation: “Today is Monday”, “Tomorrow will be holiday”, “There will be full moon tonight” are not the statements because we are not sure which day or night we are talking about.
“If today is Tuesday then tomorrow will be Sunday” is a statement because we are sure that it is false.
Wednesday come after Tuesday so if today is Tuesday then tomorrow will be Wednesday.

5. Which of the following is a statement?
a) There are 27 days in this month
b) February has 28 days
c) February has 29 days
d) There are 32 days in this month
View Answer

Answer: d
Explanation: When we talk about this, that, here, there, we are not sure about what we are talking about so “There are 27 days in this month” is not a statement.
“February has 28 days” and “February has 29 days” both are not statements because February may have 28 days or 29 das based on the year. “There are 32 days in this month” is a statement as it is false. We cannot have 32 days in a month.

6. Is “How far is Delhi from here” a statement?
a) True
b) False
View Answer

Answer: b
Explanation: “How far is Delhi from here” is not a statement as we cannot decide what is “here” and from where we are going to measure the distance to Delhi.

7. Is “History is a boring subject” a statement?
a) True
b) False
View Answer

Answer: b
Explanation: “History is a boring subject” is a not a statement as it all depends on reader whether he like History or not.

8. Which of the following is not a statement?
a) Product of 1 and 2 is -4
b) Squares are always positive
c) Give me a cup of tea
d) Sum of 2 and 3 is 9
View Answer

Answer: c
Explanation: “Product of 1 and 2 is -4” is a statement as it is false. We know, product of 1 and 2 is 2.
“Squares are always positive” is a statement as it is true. “Sum of 2 and 3 is 9” is a statement as it is false. But “Give me a cup of tea” is not a statement as it is an order so it is imperative sentence.

9. Which of the following is true?
a) Statements generally not use word like today and tomorrow
b) Statements generally not use word like here and there
c) Statements generally not use word like sum and product
d) Statements generally not use word like this and that
View Answer

Answer: c
Explanation: Statements generally not use ambiguous words like here, there, this, that, today, tonight, tomorrow.

10. Which of the following is a statement?
a) Close the door
b) 11 comes after 12
c) India is a beautiful country
d) This is useless
View Answer

Answer: b
Explanation: “Close the door” is not a statement as it is an imperative sentence. “11 comes after 12”
is a statement as it is true. “India is a beautiful country” is not a statement as opinion of beautifulness vary from person to person. “This is useless” is not a statement as it involves this which doesn’t give any idea about what we are talking.

Statistics


1. Find the mean deviation about the median of the scores of a batsman given below.

InningsScores
120
256
30
484
511
6120

a) 10
b)10.5
c) 11
d) 9
View Answer

Answer: b
Explanation: Mean deviation = 1𝑛[Σi = n |xI – A|], where A is median or AM
From the given data, Median, A = (20 + 56)/2 = 38
⇒ Mean deviation = 1/6 x (63) = 10.5.

2. What is the mean deviation from the mean for the following data?

117156206198223

a) 0

b) 3

c) 1
d) ½
View Answer

Answer: a
Explanation: Mean = (117 + 156 + 206 + 198 + 223)/5 = 180

Xi117156206198223
Xi – mean-63-24261843

Mean deviation = 1𝑛[Σi = 5 |xI – mean|] = 1/5 x [(-63) + (-24) + 26 + 18 + 43] = 1/5 x [0] = 0.

3. The mean deviation of an ungrouped data is 150. If each observation is increased by 3.5%, then what is the new mean deviation?
a) 153.5
b) 3.5
c) 155.25
d) 150
View Answer

Answer: c
Explanation: If x1, x2, …, xn are the observations, then the new observations are (1.035) x1, (1.035) x2, ……, (1.035) xn.
Therefore, the new mean is (1.035) x̄
Now, Mean deviation = 1𝑛[Σi = n |xI – mean|]
⇒ New mean deviation = 1𝑛[Σi = n|(1.035)xI – (1.035) x̄|] = (1.035) × 1𝑛[Σi = n |xI – mean|] = 1.035 x 150 = 155.25.

4. Find the mean deviation about mean from the following data:

xi35202527
fi51220815

a) 7.7
b) 15
c) 8.7
d) 6.2
View Answer

Answer: a
Explanation: From the given data,

xififixi|xi-18|fi|xi-18|
35151575
5126013156
2020400240
258200756
27154059135
Σ fi = 60Σ fixi = 1080Σ fi|xi – 15| = 462

Now, Mean = 1𝑛 Σ fixi = 1080/60 = 18
⇒ Mean deviation = 1𝑛 Σ fi|xi – 18| = 462/60 = 7.7.

5. What is the geometric mean of 5,52, ….,5n?
a) 5n/2
b) 5(n+1)/2
c) 5n(n+1)/2
d) 5n
View Answer

Answer: b
Explanation: Geometric Mean = (5 x 52 x …… x 5n)1/n = [5(1+2+…+n)]1/n = [5n(n+1)/2]1/n = 5(n+1)/2.

6. In a class there are 20 juniors, 15 seniors and 5 graduate students. If the junior averaged 65 in the midterm exam, the senior averaged 70 and the graduate students averaged 91, then what is the mean of the centre class approximately?
a) 71
b) 74
c) 70
d) 72
View Answer

Answer: c
Explanation: Combined mean = (Σ xini)/(Σ ni) = (20 × 65 + 15 × 70 + 5 × 91)/(20 + 15 + 5) = 70.

7. Find the mean deviation from mean of the observations: a, a+d, …., (a+2nd).
a) n(n + 1)d2/3
b) n(n + 1)d2/2
c) a + n(n + 1)d2/2
d) n(n + 1)d/(2n + 1)
View Answer

Answer: d
Explanation: Mean = 1𝑛 Σ xi = 12𝑛+1 [a + (a + d) + … + (a + 2nd)] = a + nd
⇒ Mean Deviation = 12𝑛+1 [2 × d × (1 + 2 + … + n)] = [n (n + 1) (d)]/(2n + 1).

Probability


1. Probability is __________________________
a) Number of outcomes in favour of event
b) Total number of possible outcomes
c) Ratio of number of outcomes in favour to total number of outcomes
d) Ratio of total number of outcomes to number of outcomes in favour
View Answer

Answer: c
Explanation: Probability is chance of an outcome to appear. It is the ratio of number of outcomes in favour to total number of outcomes.

2. Probability of getting head on an unbiased coin is ________
a) 1/4
b) 1
c) 0
d) 1/2
View Answer

Answer: d
Explanation: An unbiased coin can have head or tail as outcome i.e. there are two possible outcomes.
So, probability of getting head on an unbiased coin is 1/2.

3. Probability of getting tail on an unbiased coin is ________
a) 1/4
b) 1
c) 0
d) 1/2
View Answer

Answer: d
Explanation: An unbiased coin can have head or tail as outcome i.e. there are two possible outcomes.
So, probability of getting tail on an unbiased coin is 1/2.

4. Probability of getting an even number on dice is ___________
a) 1
b) 1/2
c) 1/3
d) 0
View Answer

Answer: b
Explanation: There are six possible outcomes on dice i.e. 1 to 6.
Even numbers on dice are 2,4,6 i.e. three outcomes in favour of the event.
So, probability of getting an even number on dice is 3/6 = 1/2.

5. Probability of getting an odd number on dice is ___________
a) 1
b) 1/2
c) 1/3
d) 0
View Answer

Answer: b
Explanation: There are six possible outcomes on dice i.e. 1 to 6.
Odd numbers on dice are 1,2,3 i.e. three outcomes in favour of the event.
So, probability of getting an odd number on dice is 3/6 = 1/2.

6. Probability of getting prime number on dice is ___________
a) 1/2
b) 1/4
c) 1/3
d) 1
View Answer

Answer: a
Explanation: There are six possible outcomes on dice i.e. 1 to 6.
Prime numbers on dice are 2,3,5 i.e. three outcomes in favour of the event.
So, probability of getting a prime number on dice is 3/6 = 1/2.

7. Probability of getting composite number on dice is ___________
a) 1/2
b) 1/4
c) 1/3
d) 1
View Answer

Answer: c
Explanation: There are six possible outcomes on dice i.e. 1 to 6.
Composite numbers on dice are 4,6 i.e. two outcomes in favour of the event.
So, probability of getting a composite number on dice is 2/6 = 1/3.

8. Probability of getting 7 on a dice is ________
a) 1/2
b) 0
c) 1
d) 1/3
View Answer

Answer: b
Explanation: There are six possible outcomes on dice i.e. 1 to 6.
7 does not appear on a dice so probability of getting 7 on a dice is zero.

9. If two coins are tossed simultaneously what are total number of possible outcomes?
a) 2
b) 4
c) 6
d) 8
View Answer

Answer: b
Explanation: If two coins are tossed simultaneously total number of possible outcomes are 4.
{HH, TT, HT, TH}

10. If two coins are tossed simultaneously what is the probability of getting exactly one head?
a) 1/2
b) 1/3
c) 1/4
d) 3/4
View Answer

Answer: a
Explanation: If two coins are tossed simultaneously total number of possible outcomes are 4.
{HH, TT, HT, TH} out of which {HT, TH} favour the event.
So, probability of getting exactly one head = 2/4 = 1/2.

11. If two coins are tossed simultaneously what is the probability of getting exactly one tail?
a) 1/2
b) 1/3
c) 1/4
d) 3/4
View Answer

Answer: a
Explanation: If two coins are tossed simultaneously total number of possible outcomes are 4.
{HH, TT, HT, TH} out of which {HT, TH} favour the event.
So, probability of getting exactly one tail = 2/4 = 1/2.

12. If two coins are tossed simultaneously what is the probability of getting at least one head?
a) 1/2
b) 1/3
c) 1/4
d) 3/4
View Answer

Answer: d
Explanation: If two coins are tossed simultaneously total number of possible outcomes are 4.
{HH, TT, HT, TH} out of which {HH, HT, TH} favour the event.
So, probability of getting at least one head = 3/4.

13. If two coins are tossed simultaneously what is the probability of getting at most one head?
a) 1/2
b) 1/3
c) 1/4
d) 3/4
View Answer

Answer: d
Explanation: If two coins are tossed simultaneously total number of possible outcomes are 4.
{HH, TT, HT, TH} out of which {HT, TH, TT} favour the event.
So, probability of getting at most one head = 3/4.

14. If two coins are tossed simultaneously what is the probability of getting all heads?
a) 1/2
b) 1/3
c) 1/4
d) 3/4
View Answer

Answer: c
Explanation: If two coins are tossed simultaneously total number of possible outcomes are 4.
{HH, TT, HT, TH} out of which {HH} favour the event.
So, probability of getting all heads = 1/4.

15. If two coins are tossed simultaneously what is the probability of getting no heads?
a) 1/2
b) 1/3
c) 1/4
d) 3/4
View Answer

Answer: c
Explanation: If two coins are tossed simultaneously total number of possible outcomes are 4.
{HH, TT, HT, TH} out of which {TT} favour the event.
So, probability of getting no heads = 1/4.

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