10th Maths Objective type Questions
Chapter 1
Q1. Choose the correct option:
1) The LCM of `6` and `20` is
a) `60` b) `2` c) `1` d) `5`
2) The HCF of `96` and `404` is
a) `120` b) `4` c) `10` d) `7`
3) The LCM of `96` and `404` is
a) `9696` b) `9797` c) `9898` c) `9897`
4) The LCM of `6, 72,` and `120` is
a) `430` b) `360` c) `260` d) `250`
5) The HCF of `6, 72.` and `120`
a) `7` b) `8` c) `5` d) `6`
Answer:
`1) a` `2) b` `3) a` `4) b` `5) 6`
Chapter 2
Q1. Choose the correct option:
1) The zeroes of the polynomial `6x^2 - 3 - 7x` will be
a) `-1/3, 3/2` b) `-2/3, 3/4` c) `-1/2, 2/5` d) `-1/7, 2/5`
2) The zeroes of the polynomial `x^2 - 3` will be
a) `+sqrt3, -sqrt3`
b) `+3, -3`
c) `3`
d) `5`
3) If `alpha` and `beta` are the zeroes of the quadratic polynomial `ax^2+bx+c,` then value of `alpha+beta` is
a) `b/a` b) `-b/a` c) `-a/b` d) `a/b`
4) The zeroes of polynomial `x^2+7x+10`. will be
a) `3, 5` b) `4, 6` c) `-2, -5` d) `7, 8`
5) If `alpha` and `beta` are the zeroes of the quadratic polynomial `ax^2+bx+c,` then value of `alpha times beta` is
a) `b/a` b) `-b/a` c) `-a/b` d) `c/a`
Answer:
`1) a` `2) a` `3) b` `4) c` `5) d`
Chapter 3
Q1. Fill in the blanks:
1) If the system gives no solution, then lines are _____.
2) If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is ______.
3) If the system gives infinitely many solutions, then lines are______.
4) If the system gives the unique solution, then lines are ______.
5) If the lines are parallel, then the pair of equations has no solutions. In this case, the pair of equations is_____.
Answer:
1) Parallel lines 2) consistent 3) Coincident lines 4) Intersecting lines 5) inconsistent
Chapter 4
Q1. Fill in the blanks:
1) The roots of the quadratic equation `6x^2 - x - 2` are _____.
2) A quadratic equation `ax^2 + bx + c = 0` has two _____ roots if `b^2 - 4ac = 0`
3) A quadratic equation `ax^2 + bx + c = 0` has two_______ roots if `b^2-4ac lt 0`
Answer:
1) `2/3, -1/2` 2) equal real 3) no real
Chapter 5
Q1. Fill in the blanks in the following table, given that `a` is the first term, `d` the common difference and `a_n` the `nth` term of the AP ;
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v) |
2) For the `AP : 3/2, 1/2, -1/2, -3/2,`.... the common difference `d` is _____.
3) `30th` term of the `AP: 10, 7, 4, `.... is _____.
Answer:
1. i) `a_n = 28` ii) `d = 2` iii) `a = 46` iv) `n = 10` v) `a_n = 3.5`
Q2. Choose the correct choice is the following:
i) `30^(th)` term of the AP : `10, 7, 4,`...is
A) `97` B) `77` C) `-77` D) `-87`
ii) `11^(th)` term of the AP : `-3, -1/2, 2`,....is :
A) `28` B) `22` C) `-38` D) `-48(1)/2`
Answer:
i) `C` ii) `B`
Chapter 6
Q1. Fill in the blanks using the correct word given in brackets :
i) All circles are______.
ii) All square are______.
iii) All __________ triangles are similar.
iv) Two polygons of the same number of sides are similar, if
(a) their corresponding angles are ______ and
(b) their corresponding sides are _______ .
Answer :
i) similar, ii) similar, iii) equilateral, iv) a) equal, b) proportional.
Q2. Tick the correct answer and justify: In `triangleABC`, `AB=6sqrt3cm` and `BC=6cm`.The angle `B` is:
A) `120^circ` B) `60^circ` C) `90^circ` D) `45^circ`
Answer:
`C`
Chapter 7
Q1. Answer in one word/ sentence.
1) The distance between the pair of points `(2, 3), (4, 1)`.
2) The Area of a triangle whose vertices are `(1, -1), (-4, 6)` and `(-3, -5).`
Answer:
1) `2sqrt2` 2) `24`
Chapter 8.
Q1. State whether the following are true or false, Justify your answer:
i) The value of `tan A` is always less than `1.`
ii) `sec A=12/5` for some value of angle `A.`
iii) `cos A` is the abbreviation used for the cosecant of angle `A.`
vi) `cot A` is the product of `cot` and `A.`
v) `sin theta=4/3` for some angle `theta.`
Answer:
i) false, ii) true iii) false iv) false v) false.
Q.2 Choose the correct option:
i) `(2 tan 30^circ)/(1 + tan^2 30^circ) =`
A) `sin 60^circ` B) `cos 60^circ` C) `tan 60^circ` D) `sin 30^circ`
ii) `(1 - tan^2 45^circ)/(1 + tan^2 45^circ) =`
A) `tan 90^circ` B) `1` C) `sin45^circ` D) `0`
iii) `sin 2A = 2 sin A` is true when `A =`
A) `0^circ` B) `30^circ` C) `45^circ` D) `60^circ`
iv) `(2 tan 30^circ)/(1 - tan^2 30^circ) =`
A) `cos 60^circ` B) `sin 60^circ` C) `tan 60^circ` D) `sin 30^circ`
Answer:
i) `A` ii) `D` iii) `A` iv) `C`
Q3. Choose the correct option.
i) `9 sec^2 A - 9 tan^2 A =`
A) `1` B) `9` C) `8` D) `0`
ii) `(1 + tan theta + sec theta)(1 + cot theta - cosec theta) = `
A) `0` B) `1` C) `2` D) `-1`
iii) `(sec A + tan A)(1 - sin A) =`
A) `sec A` B) sin A C) `cosec A` D) `cos A`
iv) `(1 + tan^2 A)/(1 + cot^2 A) =`
A) `sec^2 A` B) `- 1` C) `cot^2 A` D) `tan^2 A`
Answer:
i) `B` ii) `C` iii) `D` iv) `D`
Q4. Match the column
1) `sin (90^circ - theta)` i) `cot theta`
2) `cos(90^circ -theta)` ii) `sec^2theta`
3) `tan(90^circ- theta)` iii) `cos theta`
4) `cosec 60^circ` iv) `sin theta`
5) `1+tan^2 theta` v) `cot^2theta`
6) `cosec^2 theta -1` vi) `2/sqrt3`
Answer:
1) iii 2) iv 3) i 4) vi 5) ii 6) v
Q5. Match the column
1) `cot(90^circ - theta)` i) `1`
2) `sec(90^circ - theta)` ii) `tan theta`
3) `cosec(90^circ - theta)` iii) `cosec theta`
4) `cos^2A+sin^2A` iv) `sqrt3`
5) `cos30^circ` v) `sec theta`
6) `tan60^circ` vi) `sqrt3/2`
Answer:
1) ii 2) iii 3) v 4) i 5) vi 6) iv
Chapter 10
Q1. How many tangents can a circle have?
Answer:
Infinitely many.
Q2. Fill in the blanks:
i) A tangents to a circle intersects it in _____ point (s).
ii) A line intersecting a circle in two points is called a ______.
iii) A circle can have ______ parallel tangents at the most.
iv) The common point of a tangent to a circle and the circle is called ______.
Answer:
i) `1` ii) secant iii) `2` iv) point of contact.
Q3. A tangent `PQ` at a point `P` of a circle of radius `5 cm` meets a line through the centre `O` at a point `Q` so that `OQ = 12 cm`. Length `PQ` is :
A) `12 cm` B) `13 cm` C) `8.5 cm` D) `sqrt119 cm`
Answer:
D) `sqrt119 cm`
In Q. 4 to 6, choose the correct option and give justification.
4. From a point `Q,` the length of the tangent to a circle is `24 cm` and the distance of `Q` from the centre is `25 cm.` The radius of the circle is
A) `7 cm` B) `12 cm` C) `15 cm` D) `24.5 cm`
5. In the figure, If `TP` and `TQ` are the two tangents to a circle with centre `O` so that `angle POQ = 110^circ`, then `angle PTQ` is equal to
A) `60^circ` B) `70^circ` C) `80^circ` D) `90^circ`
6. If tangents `PA` and `PB` from a point `P` to a circle with centre `O` are each other at angle of `80^circ,` then `anglePOA` is equal to
A) `50^circ` B) `60^circ` C) `70^circ` D) `80^circ`
Answer:
4) A 5) B 6) A
Chapter 12
Q1. Tick the correct answer in the following:
i) If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
A) `2 units` B) `π units` C) `4 units` D) `7 units`
ii) Area of a sector of angle `p` (in degrees) of a circle with radius `R` is
A) `p/180 times 2πR` B) `p/180 times πR^2` C) `p/360 times 2πR` D) `p/720 times 2πR^2`
iii) The area of a sector of a circle with radius `6 cm` if the angle of the sector is `60^circ`
A) `32/7` B) `63/7` C) `78/7` D) `132/7`
Answer:
i) A ii) D iii) D
Chapter 13
Q1. True/ False
1) The slant height of cone `l =sqrt(r^2 + h^2)`
2) Curved Surface Area of hemisphere `4pi r^2`.
Answer:
1) True 2) false.
Chapter 14
Q1. True/false
1) The median is a measure of central tendency which gives the value of the middlemost observation in the data.
2)The commutative frequency distribution is required for calculating medians.
Answer:
1) True 2) True.
Chapter 15
Q1. Complete the following statements:
i) Probability of an event `E +` Probability of the event 'not `E' = `______.
ii) The probability of an event that cannot happen is _______. Such an events is called ______.
iii) The probability if ab event that is certain to happen is _______. Such an event is called ______.
iv) The sum of the probabilities of all the elementary events of an experiment is ________.
v) The probability of an event is greater than or equal to _______ and less than or equal to _______.
Answer:
i) `1` ii) `0,` impossible event iii) `1,` sure or certain event iv) `1` v) `0, 1`
Q2. Which of the following experiments have equally likely outcomes?
i) A driver attempts to start a car. The car starts or does not start.
ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
iii) A trial is made to answer a true-false question. The answer is right or wrong.
iv) A baby is born. It is a boy or a girl.
Answer:
`iii)` and `vi)` have equally likely outcomes.
Q3. Choose the correct options
i) Which of the following cannot be the probability of an event?
A) `2/3` B) `-1.5` C) `15%` D) `0.7`
Answer:
i) B
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