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Maths (Standard) 2024 Compartment Exams Set-1 Maths - Maths (Standard) 2024 Compartment Exams Set-1

CBSE - STD 10 - Maths (CBSE - English Medium). 45 questions in this chapter.

Question types

Maths (Standard) 2024 Compartment Exams Set-1 question types

45 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

45
Questions
6
Question groups
5
Question types
Sample Questions

Maths (Standard) 2024 Compartment Exams Set-1 questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
Two dice are thrown at the same time and the product of the numbers appearing on them is noted. The probability that the product of the numbers lies between 8 and 13 is :
  • ✓
    $\frac{7}{36}$
  • B
    $\frac{5}{36}$
  • C
    $\frac{2}{9}$
  • D
    $\frac{1}{4}$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
If the length of the shadow on the ground of a pole is $\sqrt{3}$ times the height of the pole, then the angle of elevation of the Sun is :
  • ✓
    $30^{\circ}$
  • B
    $45^{\circ}$
  • C
    $60^{\circ}$
  • D
    $90^{\circ}$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
If the length of an arc of a circle subtending an angle $60^{\circ}$ at its centre is 22 cm , then the radius of the circle is :
  • A
    $\sqrt{21} cm$
  • ✓
    21 cm
  • C
    $\sqrt{42} cm$
  • D
    42 cm

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
If $\tan ^2 \theta+\cot ^2 \alpha=2$, where $\theta=45^{\circ}$ and $0^{\circ} \leq \alpha \leq 90^{\circ}$, then the value of $\alpha$ is :
  • A
    $30^{\circ}$
  • ✓
    $45^{\circ}$
  • C
    $60^{\circ}$
  • D
    $90^{\circ}$

Answer: B.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A):TA and TB are two tangents drawn from an external point T to a circle with centre ' O '. If $\angle TBA =75^{\circ}$ then $\angle ABO =25^{\circ}$.
Image
Reason (R) : The tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.
  • A
    Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true. Reason (R) does not give correct explanation of (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is not true but Reason (R) is true.

Answer: D.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A) : If the graph of a polynomial intersects the x -axis at exactly two points, then the number of zeroes of that polynomial is 2 .
Reason $(R)$ : The number of zeroes of a polynomial is equal to the number of points where the graph of the polynomial intersects x -axis.
  • ✓
    Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true. Reason (R) does not give correct explanation of (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is not true but Reason (R) is true.

Answer: A.

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Q 92 Marks Questions2 Marks
PQRS is a trapezium with $P Q \| S R$. If $M$ and $N$ are two points on the non-parallel sides PS and QR respectively, such that MN is parallel to PQ , then show that $\frac{ PM }{ MS }=\frac{ QN }{ NR }$.
Image
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Q 122 Marks Questions2 Marks
In the given figure, PAQ and PBR are tangents to the circle with centre ' $O$ ' at the points $A$ and $B$ respectively. If T is a point on the circle such that $\angle QAT =45^{\circ}$ and $\angle TBR =65^{\circ}$, then find $\angle ATB$.
Image
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Q 133 Marks Question3 Marks
A school has invited $42$ Mathematics teachers, $56$ Physics teachers and $70$ Chemistry teachers to attend a Science workshop. Find the minimum number of tables required, if the same number of teachers are to sit at a table and each table is occupied by teachers of the same subject.
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Q 153 Marks Question3 Marks
The sum of the digits of a $2 -$digit number is $12$ . Seven times the number is equal to four times the number obtained by reversing the order of the digits. Find the number.
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Q 173 Marks Question3 Marks
In the given figure, two concentric circles have radii $3 \ cm$ and $5 \ cm$ . Two tangents $TR$ and $TP$ are drawn to the circles from an external point $T$ such that $TR$ touches the inner circle at $R$ and $TP$ touches the outer circle at $P$. If $T R=4 \sqrt{10} \ cm$, then find the length of $T P$.
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Q 185 Marks Questions5 Marks
A solid toy is in the form of a hemisphere surmounted by a right circular cone. Ratio of the radius of the cone to its slant height is $3: 5$. If the volume of the toy is $240 \pi cm^3$, then find the total height of the toy.
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Q 195 Marks Questions5 Marks
The largest possible hemisphere is drilled out from a wooden cubical block of side $21 \ cm$ such that the base of the hemisphere is on one of the faces of the cube. Find:
$(i)$ the volume of wood left in the block,
$(ii)$ the total surface area of the remaining solid.
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Q 205 Marks Questions5 Marks
A shopkeeper buys a number of books for $₹ 1,800$ . If he had bought $15$ more books for the same amount, then each book would have cost him $₹ 20$ less. Find how many books he bought initially.
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Q 215 Marks Questions5 Marks
If Nidhi were $7$ years younger than what she actually is, then the square of her age $($in years$)$ would be $1$ more than $5$ times her actual age. What is her present age ?
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Q 225 Marks Questions5 Marks
An age$-$wise list of number of literate people in a block is prepared in the following table. There are total $100$ people and their median age is $41.5$ years. Information about two groups are missing, which are denoted by $x$ and $y.$ Find the value of $x$ and $y.$
Age $($in years$)$ Number of literate people
$10-20$ $15$
$20-30$ $X$
$30-40$ $12$
$40-50$ $20$
$50-60$ $Y$
$60-70$ $8$
$70-80$ $10$
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Q 23Case study (4 Marks)4 Marks
Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of the city from where bank, hospital, post office and supermarket can be easily accessed. In the graph, the bank is plotted as A(9, 5), hospital as B(-3,1) and supermarket as C(5,5) such that A, B, C form a triangle.
Image
Based on the above given information, answer the following questions:
(i) Find the distance between the bank and the hospital.
(ii) In between the bank and the supermarket, there is a post office plotted at E which is their mid-point. Find the coordinates of E.
(iii) (a) In between the hospital and the supermarket, there is a bus stop plotted as D, which is their mid-point. If Partha wants to reach the bus stand from the bank, then how much distance does he need to cover ?
OR
(b) P and Q are two different garment shops lying between the bank and the hospital, such that $BP = PQ = QA$. If the coordinates of P and Q are $(1, a)$ and $(b, 3)$ respectively, then find the values of ' $a$ ' and ' $b$ '.
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Q 24Case study (4 Marks)4 Marks
A school has decided to plant some endangered trees on $51^{\text {st }}$ World Environment Day in the nearest park. They have decided to plant those trees in few concentric circular rows such that each succeeding row has $20$ more trees than the previous one. The first circular row has $50$ trees.
Image
Based on the above given information, answer the following questions:
$(i)$ How many trees will be planted in the $10^{\text {th }}$ row?
$(ii)$ How many more trees will be planted in the $8^{\text {th }}$ row than in the $5^{\text {th }}$ row ?
$(iii)\  (a)$ If $3200$ trees are to be planted in the park, then how many rows are required ?
OR
$(b)$ If $3200$ trees are to be planted in the park, then how many trees are still left to be planted after the $11^{\text {th }}$ row ?
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Q 25Case study (4 Marks)4 Marks
Due to short circuit, a fire has broken out in New Home Complex. Two buildings, namely $X$ and $Y$ have mainly been affected. The fire engine has arrived and it has been stationed at a point which is in between the two buildings. A ladder at point $O$ is fixed in front of the fire engine. The ladder inclined at an angle $60^{\circ}$ to the horizontal is leaning against the wall of the terrace $($top$)$ of the building $Y$. The foot of the ladder is kept fixed and after some time it is made to lean against the terrace $($top$)$ of the opposite building $X$ at an angle of $45^{\circ}$ with the ground. Both the buildings along with the foot of the ladder, fixed at $' O \ '$ are in a straight line.
Image
Based on the above given information, answer the following questions :
$(i)$ Find the length of the ladder.
$(ii)$ Find the distance of the building $Y$ from point $'O\ '$, i.e. $OA$.
$(iii)\ (a)$ Find the horizontal distance between the two buildings.
OR
$(b)$ Find the height of the building $X$.
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