If a vertical pole of length 7.5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow 24 m long, then the height of the tower is:
- A20 m
- B40 m
- C60 m
- ✓36 m
Answer: D.
View full solution →Question types
Maths (Standard) - 2024 (30-5-1) Set-1 question types
44 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
44
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
18 Q→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
8 Q→055 Marks Questions
6 Q→06Case study (4 Marks)
3 Q→Sample Questions
Maths (Standard) - 2024 (30-5-1) Set-1 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the given figure, in $\triangle ABC , DE \| BC$. If $AD =2-4 cm, DB =4 cm$ and $AE =2 cm$, then the length of AC is :
- A$\frac{10}{3} cm$
- B$\frac{3}{10} cm$
- ✓$\frac{16}{3} cm$
- D1.2 cm
Answer: C.
View full solution →In the given figure, RJ and RL are two tangents to the circle. If $\angle RJL =42^{\circ}$, then the measure of $\angle JOL$ is :
- A$42^{\circ}$
- ✓$84^{\circ}$
- C$96^{\circ}$
- D$138^{\circ}$
Answer: B.
View full solution →If $\alpha$ and $\beta$ are the zeroes of the polynomial $p(x)= kx ^2-30 x +45 k$ and $\alpha+\beta=\alpha \beta$, then the value of k is :
- A$-\frac{2}{3}$
- B$-\frac{3}{2}$
- C$\frac{3}{2}$
- ✓$\frac{2}{3}$
Answer: D.
View full solution →If the product of two co-prime numbers is 553 , then their HCF is :
- ✓1
- B553
- C7
- D79
Answer: A.
View full solution →Assertion (A) : Degree of a zero polynomial is not defined.
Reason (R) : Degree of a non-zero constant polynomial is 0.
Reason (R) : Degree of a non-zero constant polynomial is 0.
- ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- ✓Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- CAssertion (A) is true, but Reason (R) is false.
- DAssertion (A) is false, but Reason (R) is true.
Answer: B.
View full solution →Assertion (A) : ABCD is a trapezium with $DC \| AB . E$ and F are points on AD and BC respectively, such that $EF \| AB$. Then $\frac{ AE }{ ED }=\frac{ BF }{ FC }$.
Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.
Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.
- ✓Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- CAssertion (A) is true, but Reason (R) is false.
- DAssertion (A) is false, but Reason (R) is true.
Answer: A.
View full solution →A carton consists of 60 shirts of which 48 are good, 8 have major defects and 4 have minor defects. Nigam, a trader, will accept the shirts which are good but Anmol, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. Find the probability that it is acceptable to Anmol.
Prove that the points $(3,0),(6,4)$ and $(-1,3)$ are the vertices of an isosceles triangle.
View full solution →Find the ratio in which the point $P (-4,6)$ divides the line segment joining the points $A (-6,10)$ and $B (3,-8)$.
View full solution →If $\alpha, \beta$ are zeroes of the polynomial $p(x)=5 x^2-6 x+1$, then find the value of $\alpha+\beta+\alpha \beta$.
View full solution →Evaluate :
$\frac{2 \tan 30^{\circ} \cdot \sec 60^{\circ} \cdot \tan 45^{\circ}}{1-\sin ^2 60^{\circ}}$
View full solution →$\frac{2 \tan 30^{\circ} \cdot \sec 60^{\circ} \cdot \tan 45^{\circ}}{1-\sin ^2 60^{\circ}}$
An arc of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding major sector. (Use $\pi=3 \cdot 14$ )
View full solution →Three unbiased coins are tossed simultaneously. Find the probability of getting :
(i) at least one head.
(ii) exactly one tail.
(iii) two heads and one tail.
(i) at least one head.
(ii) exactly one tail.
(iii) two heads and one tail.
Prove that:
$
\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}=1+\sec A \operatorname{cosec} A
$
View full solution →$
\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}=1+\sec A \operatorname{cosec} A
$
Prove that the parallelogram circumscribing a circle is a rhombus.
The first term of an $A.P.$ is $5,$ the last term is $45$ and the sum of all the terms is $400 .$ Find the number of terms and the common difference of the $A.P.$
View full solution →A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 5.8 cm and its base is of radius 2.1 cm , find the total surface area of the article.
Sides $A B$ and $A C$ and median $A D$ of a $\triangle A B C$ are respectively proportional to sides PQ and PR and median PM of another $\triangle PQR$. Show that $\triangle ABC \sim \triangle PQR$.
View full solution →In the given figure, $\triangle FEC \cong \triangle GDB$ and $\angle 1=\angle 2$. Prove that $\triangle ADE \sim \triangle ABC$.
View full solution →From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are $30^{\circ}$ and $60^{\circ}$ respectively. If the bridge is at a height of $4 m$ from the banks, find the width of the river.
View full solution →The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be $4$ years more than three times the age of his son. Find their present ages.
View full solution →Activities like running or cycling reduce stress and the risk of menta disorders like depression. Running helps build endurance. Childrer develop stronger bones and muscles and are less prone to gain weight The physical education teacher of a school has decided to conduct an inte school running tournament in his school premises. The time taken by group of students to run 100 m , was noted as follows:
Based on the above, answer the following questions:
(i) What is the median class of the above given data ?
(ii) (a) Find the mean time taken by the students to finish the race.
OR
(b) Find the mode of the above given data.
(iii) How many students took time less than 60 seconds?
| Time (in seconds) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Number of students | 8 | 10 | 13 | 6 | 3 |
(i) What is the median class of the above given data ?
(ii) (a) Find the mean time taken by the students to finish the race.
OR
(b) Find the mode of the above given data.
(iii) How many students took time less than 60 seconds?
A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of $1 m$ from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above situation, the gardener took help from the students of class $10$. They made a chart for it which looks like the given figure.
Based on the above, answer the following questions :
$(i)$ If $A$ is taken as origin, what are the coordinates of the vertices of $\triangle PQR$ ?
$(ii) \ (a)$ Find distances $PQ$ and $QR$ .
OR
$(b)$ Find the coordinates of the point which divides the line segment joining points $P$ and $R$ in the ratio $2: 1$ internally.
$(iii)$ Find out if $\triangle PQR$ is an isosceles triangle.
View full solution →Based on the above, answer the following questions :
$(i)$ If $A$ is taken as origin, what are the coordinates of the vertices of $\triangle PQR$ ?
$(ii) \ (a)$ Find distances $PQ$ and $QR$ .
OR
$(b)$ Find the coordinates of the point which divides the line segment joining points $P$ and $R$ in the ratio $2: 1$ internally.
$(iii)$ Find out if $\triangle PQR$ is an isosceles triangle.
Essel World is one of India's largest amusement parks that offers a diverse range of thrilling rides, water attractions and entertainment options for visitors of all ages. The park is known for its iconic "Water Kingdom" section, making it a popular destination for family outings and fun$-$filled adventure. The ticket charges for the park are $₹ 150$ per child and $₹ 250$ per adult.
On a day, the cashier of the park found that $300$ tickets were sold and an amount of $₹ 55,000$ was collected.
Based on the above, answer the following questions :
$(i)$ If the number of children visited be $x$ and the number of adults visited be $y$, then write the given situation algebraically.
$(ii) (a)$ How many children visited the amusement park that day?
OR
$(b)$ How many adults visited the amusement park that day?
$(iii)$ How much amount will be collected if $250$ children and $100$ adults visit the amusement park?
View full solution →On a day, the cashier of the park found that $300$ tickets were sold and an amount of $₹ 55,000$ was collected.
Based on the above, answer the following questions :
$(i)$ If the number of children visited be $x$ and the number of adults visited be $y$, then write the given situation algebraically.
$(ii) (a)$ How many children visited the amusement park that day?
OR
$(b)$ How many adults visited the amusement park that day?
$(iii)$ How much amount will be collected if $250$ children and $100$ adults visit the amusement park?
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