After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She requires to calculate _____ of marks.
- Amedian
- Bmode
- Cmean
- Drange
Question types
Maths (Standard) - 2024 (30-2-1) 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 (30-2-1) 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, AT is tangent to a circle centred at O . If $\angle CAT =40^{\circ}$, then $\angle CBA$ is equal to
- A$70^{\circ}$
- B$50^{\circ}$
- C$65^{\circ}$
- D$40^{\circ}$
Which term of the A.P. $-29,-26,-23$, ...., 61 is 16 ?
- A$11^{\text {th }}$
- B$16^{ th }$
- C$10^{\text {th }}$
- D$31^{\text {st }}$
XOYZ is a rectangle with vertices $X (-3,0), O (0,0), Y (0,4)$ and $Z (x, y)$. The length of its each diagonal is
- A5 units
- B$\sqrt{5}$ units
- C$x^2+y^2$ units
- D4 units
In the given figure, tangents PA and PB to the circle centred at O , from point $P$ are perpendicular to each other. If $P A=5 cm$, then length of $A B$ is equal to
- A5 cm
- B$5 \sqrt{2} cm$
- C$2 \sqrt{5} cm$
- D10 cm
Assertion (A) : Two cubes each of edge length 10 cm are joined together.The total surface area of newly formed cuboid is $1200 cm^2$.
Reason (R): Area of each surface of a cube of side 10 cm is $100 cm^2$.
Reason (R): Area of each surface of a cube of side 10 cm is $100 cm^2$.
- ABoth Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason (R) are true. Reason (R) does not give correct explanation of (A).
- CAssertion (A) is true but Reason (R) is not true.
- DAssertion (A) is not true but Reason (R) is true.
Assertion (A): If $\sin A =\frac{1}{3}\left(0^{\circ}< A <90^{\circ}\right)$, then the value of $\cos A$ is $\frac{2 \sqrt{2}}{3}$
Reason (R): For every angle $\theta, \sin ^2 \theta+\cos ^2 \theta=1$.
Reason (R): For every angle $\theta, \sin ^2 \theta+\cos ^2 \theta=1$.
- ABoth Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason (R) are true. Reason (R) does not give correct explanation of (A).
- CAssertion (A) is true but Reason (R) is not true.
- DAssertion (A) is not true but Reason (R) is true.
$A (3,0), B (6,4)$ and $C (-1,3)$ are vertices of a triangle ABC . Find length of its median BE.
View full solution →In what ratio is the line segment joining the points $(3,-5)$ and $(-1,6)$ divided by the line $y =x$ ?
View full solution →In the given figure, $AB$ and $CD$ are tangents to a circle centred at $O$ . Is $\angle BAC =\angle DCA$ ? Justify your answer.
View full solution →If $2 \sin (A+B)=\sqrt{3}$ and $\cos (A-B)=1$, then find the measures of angles A and B. $0 \leq A, B,(A+B) \leq 90^{\circ}$.
View full solution →Evaluate : $2 \sin ^2 30^{\circ} \sec 60^{\circ}+\tan ^2 60^{\circ}$.
View full solution →In a $2-$digit number, the digit at the unit's place is $5$ less than the digit at the ten's place. The product of the digits is $36$. Find the number.
View full solution →In a test, the marks obtained by $100$ students $($out of $50)$ are given below:Find the mean marks of the students.
View full solution →| Marks obtained: | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
| Number of students: | $12$ | $23$ | $34$ | $25$ | $6$ |
Prove that $\frac{1+\sec \theta-\tan \theta}{1+\sec \theta+\tan \theta}=\frac{1-\sin \theta}{\cos \theta}$.
View full solution →In the given figure, $\text{AB , BC , CD}$ and $DA$ are tangents to the circle with centre $O$ forming a quadrilateral $\text{A B C D}$.
Show that $\angle AOB +\angle COD =180^{\circ}$
View full solution →Show that $\angle AOB +\angle COD =180^{\circ}$
In the given figure, $PQ$ is tangent to a circle centred at $O$ and $\angle B A Q=30^{\circ}$; show that $\text{B P=B Q}$.
View full solution →The perimeter of a certain sector of a circle of radius $5.6 m$ is $20.0 m$ . Find the area of the sector.
View full solution →From the top of a $45 m$ high light house, the angles of depression of two ships, on the opposite side of it, are observed to be $30^{\circ}$ and $60^{\circ}$. If the line joining the ships passes through the foot of the light house, find the distance between the ships. $($Use $\sqrt{3}=1.73 )$
View full solution →Sides $AB$ and $AC$ and median $AD$ to $\triangle ABC$ 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 →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.
Tara scored $40$ marks in a test, getting $3$ marks for each right answer and losing $1$ mark for each wrong answer. Had $4$ marks been awarded for each correct answer and $2$ marks been deducted for each wrong answer, then Tara would have scored $50$ marks. Assuming that Tara attempted all questions, find the total number of questions in the test.
View full solution →In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey.
Observe the pie chart and answer the following questions:
(i) If one person is selected at random, find the probability that he/she travelled by bus or ship.
(ii) Which is most favourite mode of transport and how many people used it?
(iii) (a) A person is selected at random. If the probability that he did not use train is $4 / 5$, find the number of people who used train.
OR
(iii) (b) The probability that randomly selected person used aeroplane is 7/60. Find the revenue collected by air company at the rate of ₹ 5,000 per person.
View full solution →Observe the pie chart and answer the following questions:
(i) If one person is selected at random, find the probability that he/she travelled by bus or ship.
(ii) Which is most favourite mode of transport and how many people used it?
(iii) (a) A person is selected at random. If the probability that he did not use train is $4 / 5$, find the number of people who used train.
OR
(iii) (b) The probability that randomly selected person used aeroplane is 7/60. Find the revenue collected by air company at the rate of ₹ 5,000 per person.
The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.
A circus tent is cylindrical upto a height of $8 m$ and conical above it. The diameter of the base is $28 m$ and total height of tent is $18.5 m .$
Based on the above, answer the following questions :
$(i)$ Find slant height of the conical part.
$(ii)$ Determine the floor area of the tent.
$(iii) (a)$ Find area of the cloth used for making tent.
OR
$(iii) (b) $Find total volume of air inside an empty tent.
View full solution →A circus tent is cylindrical upto a height of $8 m$ and conical above it. The diameter of the base is $28 m$ and total height of tent is $18.5 m .$
Based on the above, answer the following questions :
$(i)$ Find slant height of the conical part.
$(ii)$ Determine the floor area of the tent.
$(iii) (a)$ Find area of the cloth used for making tent.
OR
$(iii) (b) $Find total volume of air inside an empty tent.
A ball is thrown in the air so that $t$ seconds after it is thrown, its height $h$ metre above its starting point is given by the polynomial $h=25 t-5 t^2$.
Observe the graph of the polynomial and answer the following questions:
$(i)$ Write zeroes of the given polynomial.
$(ii)$ Find the maximum height achieved by ball.
$(iii) (a)$ After throwing upward, how much time did the ball take to reach to the height of $30 m ?$
$\text{OR}$
$(iii) (b)$ Find the two different values of $t$ when the height of the ball was $20 m.$
View full solution →Observe the graph of the polynomial and answer the following questions:
$(i)$ Write zeroes of the given polynomial.
$(ii)$ Find the maximum height achieved by ball.
$(iii) (a)$ After throwing upward, how much time did the ball take to reach to the height of $30 m ?$
$\text{OR}$
$(iii) (b)$ Find the two different values of $t$ when the height of the ball was $20 m.$
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