Maths (Standard) - 2024 (30-1-1) Set-1 - CBSE STD 10 Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is :

✓
consistent with unique solution.
B
consistent with infinitely many solutions.
C
inconsistent.
D
inconsistent but can be made consistent by extending these lines.

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark

The centre of a circle is at $(2,0)$. If one end of a diameter is at $(6,0)$, then the other end is at :

A
$(0,0)$
B
$(4,0)$
C
$(-2,0)$
D
$(-6,0)$

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Q 3M.C.Q (1 Marks)1 Mark

Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2,3 or 5 , is :

A
$\frac{7}{36}$
B
$\frac{11}{36}$
C
$\frac{5}{36}$
D
$\frac{4}{9}$

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Q 4M.C.Q (1 Marks)1 Mark

The volume of the largest right circular cone that can be carved ou from a solid cube of edge 2 cm is :

A
$\frac{4 \pi}{3} cu cm$
B
$\frac{5 \pi}{3} cu cm$
C
$\frac{8 \pi}{3} cu cm$
D
$\frac{2 \pi}{3} cu cm$

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Q 5M.C.Q (1 Marks)1 Mark

The middle most observation of every data arranged in order is called:

A
mode
B
median
C
mean
D
deviation

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Q 6Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A) : If the graph of a polynomial touches $x$-axis at only one point, then the polynomial cannot be a quadratic polynomial.
Reason (R): A polynomial of degree $n(n>1)$ can have at most $n$ zeroes.

A
Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
B
Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is true.

Answer: D.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A) : The tangents drawn at the end points of a diameter of a circle, are parallel.
Reason (R): Diameter of a circle is the longest chord.

A
Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
✓
Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer: B.

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Q 82 Marks Questions2 Marks

Show that the number $5 \times 11 \times 17+3 \times 11$ is a composite number.

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Q 92 Marks Questions2 Marks

Prove that $5-2 \sqrt{3}$ is an irrational number. It is given that $\sqrt{3}$ is an irrational number.

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Q 102 Marks Questions2 Marks

In the given figure, $\text{ABCD}$ is a quadrilateral. Diagonal $BD$ bisects $\angle B$ and $\angle D$ both. Prove that :
$(i) \triangle \text{ABD} \sim \triangle CBD$
$(ii) \text{AB = BC}$

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Q 112 Marks Questions2 Marks

If $A=60^{\circ}$ and $B=30^{\circ}$, verify that :
$\sin (A+B)=\sin A \cos B+\cos A \sin B$

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Q 122 Marks Questions2 Marks

Evaluate : $2 \sqrt{2} \cos 45^{\circ} \sin 30^{\circ}+2 \sqrt{3} \cos 30^{\circ}$

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Q 133 Marks Question3 Marks

The difference between the outer and inner radii of a hollow right circular cylinder of length $14 \ cm$ is $1 \ cm$ . If the volume of the metal used in making the cylinder is $176 \ cm^3$, find the outer and inner radii of the cylinder.

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Q 143 Marks Question3 Marks

A circle with centre $O$ and radius $8 \ cm$ is inscribed in a quadrilateral $\text{ABCD}$ in which $\text{P , Q , R , S}$ are the points of contact as shown. If $AD$ is perpendicular to $DC , BC =30 \ cm$ and $BS =24 \ cm$, then find the length $DC .$

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Q 153 Marks Question3 Marks

In the given figure, $\text{AB}$ is a diameter of the circle with centre $\text{O . AQ , BP}$ and $\text{PQ}$ are tangents to the circle. Prove that $\angle POQ =90^{\circ}$.

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Q 163 Marks Question3 Marks

Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?

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Q 173 Marks Question3 Marks

Prove that : $\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}=1+\sec \theta \operatorname{cosec} \theta$

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Q 185 Marks Questions5 Marks

A pole $6 m$ high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point $P$ on the ground is $60^{\circ}$ and the angle of depression of the point $P$ from the top of the tower is $45^{\circ}$. Find the height of the tower and the distance of point $P$ from the foot of the tower. $($Use $\sqrt{3}=1.73)$

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Q 195 Marks Questions5 Marks

In the given figure $PA , QB$ and $RC$ are each perpendicular to $AC$ . If $AP =x, BQ =y$ and $CR =z$, then prove that $\frac{1}{x}+\frac{1}{z}=\frac{1}{y}$

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Q 205 Marks Questions5 Marks

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

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Q 215 Marks Questions5 Marks

In an A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine the first term and common difference of A.P. Also, find the sum of all the terms of the A.P.

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Q 225 Marks Questions5 Marks

The sum of first and eighth terms of an $A.P.$ is $32$ and their product is $60$ . Find the first term and common difference of the $A.P.$ Hence, also find the sum of its first $20$ terms.

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Q 23Case study (4 Marks)4 Marks

A backyard is in the shape of a triangle $\text{ABC}$ with right angle at $B$. $AB =7 m$ and $BC =15 m$. A circular pit was dug inside it such that it touches the walls $A C, B C$ and $A B$ at $P, Q$ and $R$ respectively such that $AP =x m$.

Based on the above information, answer the following questions:
$(i)$ Find the length of $AR$ in terms of $x$.
$(ii)$ Write the type of quadrilateral $\text{BQOR} $.
$(iii) \ (a)$ Find the length $PC$ in terms of $x$ and hence find the value of $x$.
OR
$(b)$ Find $x$ and hence find the radius $r$ of circle.

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Q 24Case study (4 Marks)4 Marks

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.

Numbers announced	Number of times
0-15	8
15-30	9
30-45	10
45-60	12
60-75	9

Based on the above information, answer the following:
(i) Write the median class.
(ii) When first ball was picked up, what was the probability of calling out an even number?
(iii) (a) Find median of the given data.
OR
(b) Find mode of the given data.

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Q 25Case study (4 Marks)4 Marks

A rectangular floor area can be completely tiled with $200$ square tiles. If the side length of each tile is increased by $1$ unit, it would take only $128$ tiles to cover the floor.

$(i)$ Assuming the original length of each side of a tile be $x$ units, make a quadratic equation from the above information.
$(ii)$ Write the corresponding quadratic equation in standard form.
$(iii) (a)$ Find the value of $x$, the length of side of a tile by factorisation.
OR
$(b)$ Solve the quadratic equation for $x$, using quadratic formula.

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Maths (Standard) - 2024 (30-1-1) Set-1 question types

Maths (Standard) - 2024 (30-1-1) Set-1 questions

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Maths (Standard) - 2024 (30-1-1) Set-1 question types

Maths (Standard) - 2024 (30-1-1) Set-1 questions

Generate a Maths (Standard) - 2024 (30-1-1) Set-1 paper free