In the given figure, QR is a common tangent to the two given circles touching externally at A . The tangent at A meets QR at P . If $AP =4.2 cm$, then the length of QR is :
- A4.2 cm
- B2.1 cm
- ✓8.4 cm
- D6.3 cm
Answer: C.
View full solution →Question types
Maths (Standard) - 2024 (30-4-1) 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 (30-4-1) Set-1 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
For an event $E$, if $P(E)+P(\bar{E})=q$, then the value of $q^2-4$ is :
- ✓-3
- B3
- C5
- D-5
Answer: A.
View full solution →The fourth vertex $D$ of a parallelogram $A B C D$ whose three vertices are $A (-2,3), B (6,7)$ and $C (8,3)$ is :
- A$(0,1)$
- ✓$(0,-1)$
- C$(-1,0)$
- D$(1,0)$
Answer: B.
View full solution →In the given figure, AB and AC are tangents to the circle. If $\angle ABC =42^{\circ}$, then the measure of $\angle BAC$ is :
- ✓$96^{\circ}$
- B$42^{\circ}$
- C$106^{\circ}$
- D$86^{\circ}$
Answer: A.
View full solution →At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun's altitude at that time is :
- A$30^{\circ}$
- ✓$45^{\circ}$
- C$60^{\circ}$
- D$90^{\circ}$
Answer: B.
View full solution →Assertion (A): If the circumference of a circle is 176 cm, then its radius is 28 cm.
Reason (R): Circumference =$2 \pi$ x radius of a circle.
Reason (R): Circumference =$2 \pi$ x radius of a circle.
- ✓Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- BBoth Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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 →Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1:1.
Reason (R): The ratio in which the point (-3, k) divides the line segment joining the points (-5, 4) and (-2, 3) is 1: 2.
Reason (R): The ratio in which the point (-3, k) divides the line segment joining the points (-5, 4) and (-2, 3) is 1: 2.
- ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- BBoth Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- ✓Assertion (A) is true, but Reason (R) is false.
- DAssertion (A) is false, but Reason (R) is true.
Answer: C.
View full solution →In the given figure, $\triangle AHK \sim \Delta ABC$. If $AK =8 \ cm, BC =3.2 \ cm$ and $HK =6.4 \ cm$, then find the length of $AC .$
View full solution →In the given figure, $O$ is the centre of the circle. If $\angle AOB =145^{\circ}$, then find the value of $x$.
View full solution →If $\sin ( A - B )=\frac{1}{2}, \cos (A+ B )=\frac{1}{2} ; 0< A + B \leq 90^{\circ}, A > B$; find $\angle A$ and $\angle B$.
View full solution →Evaluate : $\frac{5 \cos ^2 60^{\circ}+4 \sec ^2 30^{\circ}-\tan ^2 45^{\circ}}{\sin ^2 30^{\circ}+\sin ^2 60^{\circ}}$
View full solution →Find the length of the arc of a circle which subtends an angle of $60^{\circ}$ at the centre of the circle of radius 42 cm .
View full solution →Prove that the parallelogram circumscribing a circle is a rhombus.
Prove that $\frac{2-\sqrt{3}}{5}$ is an irrational number, given that $\sqrt{3}$ is an irrational number.
View full solution →If $\alpha$ and $\beta$ are the zeroes of the polynomial $x^2+x-2$, then find the value of $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$.
View full solution →Find the zeroes of the polynomial $4 x^2+4 x-3$ and verify the relationship between zeroes and coefficients of the polynomial.
View full solution →Rehana went to a bank to withdraw $₹ 2,000 $. She asked the cashier to give her $₹ 50$ and $₹ 100$ notes only. Rehana got $25$ notes in all. Find how many notes of $₹ 50$ and $₹ 100$ did she receive.
View full solution →The following table shows the ages of the patients admitted in a hospital during a year:
Find the mode and mean of the data given above.
| Age (in years) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |
| Number of patients | 6 | 11 | 21 | 23 | 14 | 5 |
Find the mode and mean of the data given above.
Find the value of ' $c$ ' for which the quadratic equation
$(c+1) x^2-6(c+1) x+3(c+9)=0 ; c \neq-1$
has real and equal roots.
View full solution →$(c+1) x^2-6(c+1) x+3(c+9)=0 ; c \neq-1$
has real and equal roots.
A train travels a distance of $90 \ km$ at a constant speed. Had the speed been $15 \ km / h$ more, it would have taken $30$ minutes less for the journey. Find the original speed of the train.
View full solution →Sides $AB , BC$ and the median $AD$ of $\triangle ABC$ are respectively proportional to sides $PQ , QR$ and the median PM of another $\Delta PQR$. Prove that $\triangle ABC \sim \Delta PQR$.
View full solution →$E$ is a point on the side $AD$ produced of a parallelogram $\text{ABCD}$ and $BE$ intersects $CD$ at $F$ . Show that $\triangle ABE \sim \Delta CFB$.
View full solution →Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.
500 mL milk is packed in a cuboidal container of dimensions $15 cm \times 8 cm \times 5 cm$. These milk packets are then packed in cuboidal cartons of dimensions $30 cm \times 32 cm \times 15 cm$.
Based on the above given information, answer the following questions:
(i) Find the volume of the cuboidal carton.
(ii) (a) Find the total surface area of a milk packet.
OR
(b) How many milk packets can be filled in a carton?
(iii) How much milk can the cup (as shown in the figure) hold?
View full solution →500 mL milk is packed in a cuboidal container of dimensions $15 cm \times 8 cm \times 5 cm$. These milk packets are then packed in cuboidal cartons of dimensions $30 cm \times 32 cm \times 15 cm$.
Based on the above given information, answer the following questions:
(i) Find the volume of the cuboidal carton.
(ii) (a) Find the total surface area of a milk packet.
OR
(b) How many milk packets can be filled in a carton?
(iii) How much milk can the cup (as shown in the figure) hold?
Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize.
While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an $A.P$. If the number on the $n^{\text {th }}$ spot is $20+4 n$, then answer the following questions to help the players in spotting the clues:
$(i)$ Which number is on first spot?
(ii) (a) Which spot is numbered as $112$?
$\text{OR}$
$(b)$ What is the sum of all the numbers on the first $10$ spots?
$(iii)$ Which number is on the $( n -2)^{ th }$ spot?
View full solution →While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an $A.P$. If the number on the $n^{\text {th }}$ spot is $20+4 n$, then answer the following questions to help the players in spotting the clues:
$(i)$ Which number is on first spot?
(ii) (a) Which spot is numbered as $112$?
$\text{OR}$
$(b)$ What is the sum of all the numbers on the first $10$ spots?
$(iii)$ Which number is on the $( n -2)^{ th }$ spot?
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Based on the above, answer the following questions:
(i) Find the mid-point of the segment joining F and G .
(ii) (a) What is the distance between the points A and C ?
OR
(b) Find the coordinates of the point which divides the line segment joining the points A and B in the ratio $1: 3$ internally.
(iii) What are the coordinates of the point D ?
View full solution →Based on the above, answer the following questions:
(i) Find the mid-point of the segment joining F and G .
(ii) (a) What is the distance between the points A and C ?
OR
(b) Find the coordinates of the point which divides the line segment joining the points A and B in the ratio $1: 3$ internally.
(iii) What are the coordinates of the point D ?
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