Sample QuestionsMaths (Standard) - 2024 (30-3-1) 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, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of $70^{\circ}$ with MN . The measure of $\angle MON$ is :
- A
$120^{\circ}$
- ✓
$140^{\circ}$
- C
$70^{\circ}$
- D
$90^{\circ}$
Answer: B.
View full solution →Perimeter of a sector of a circle whose central angle is $90^{\circ}$ and radius 7 cm is :
Answer: D.
View full solution →The mean of five observations is 15 . If the mean of first three observations is 14 and that of the last three observations is 17 , then the third observation is
Answer: C.
View full solution →If a digit is chosen at random from the digits $1,2,3,4,5,6,7,8,9$; then the probability that this digit is an odd prime number is :
- ✓
$\frac{1}{3}$
- B
$\frac{2}{3}$
- C
$\frac{4}{9}$
- D
$\frac{5}{9}$
Answer: A.
View full solution →A pair of irrational numbers whose product is a rational number is :
- A
$(\sqrt{16}, \sqrt{4})$
- B
$(\sqrt{5}, \sqrt{2})$
- ✓
$(\sqrt{3}, \sqrt{27})$
- D
$(\sqrt{36}, \sqrt{2})$
Answer: C.
View full solution →Assertion (A) : In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is $\frac{4}{5}$.
Reason (R) : P(E) $+P($ not $E)=1$
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C
Assertion (A) is true, but Reason (R) is false.
- D
Assertion (A) is false, but Reason (R) is true.
Answer: A.
View full solution →Assertion (A) : The point which divides the line segment joining the points $A (1,2)$ and $B (-1,1)$ internally in the ratio $1: 2$ is $\left(\frac{-1}{3}, \frac{5}{3}\right)$
Reason (R) : The coordinates of the point which divides the line segment joining the points $A \left(x_1, y_1\right)$ and $B \left(x_2, y_2\right)$ in the ratio $m _1: m _2$ are
$
\left(\frac{m_1 x_2+m_2 x_1}{m_1+m_2}, \frac{m_1 y_2+m_2 y_1}{m_1+m_2}\right)
$
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C
Assertion (A) is true, but Reason (R) is false.
- ✓
Assertion (A) is false, but Reason (R) is true.
Answer: D.
View full solution →Evaluate $: \frac{\cos 45^{\circ}+\sin 60^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}}$
View full solution →In the given figure, $\frac{ EA }{ EC }=\frac{ EB }{ ED }$, prove that $\triangle EAB \sim \triangle ECD$
View full solution →Points $A (-1, y)$ and $B (5,7)$ lie on a circle with centre $O (2,-3 y)$ such that $AB$ is a diameter of the circle. Find the value of $y$. Also, find the radius of the circle.
View full solution →Find a relation between $x$ and $y$ such that the point $P (x, y )$ is equidistant from the points $A (7,1)$ and $B (3,5)$.
View full solution →Sum of two numbers is $105$ and their difference is $45$ . Find the numbers.
View full solution →Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord.
Prove that $\frac{\sin \theta-2 \sin ^3 \theta}{2 \cos ^3 \theta-\cos \theta}=\tan \theta$.
View full solution →$P (-2,5)$ and $Q (3,2)$ are two points. Find the coordinates of the point $R$ on line segment $PQ$ such that $PR=2QR$.
View full solution →Find the ratio in which the line segment joining the points $(5,3)$ and $(-1,6)$ is divided by Y -axis.
View full solution →Solve the following system of linear equations graphically :
$x-y+1=0$
$x+y=5$
View full solution →A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is $14 \ mm$ and the diameter of the capsule is $4 \ mm$ , find its surface area. Also, find its volume.
View full solution →A solid iron pole consists of a solid cylinder of height $200 \ cm$ and base diameter $28 \ cm$ , which is surmounted by another cylinder of height $50 \ cm$ and radius $7 \ cm$ . Find the mass of the pole, given that $1 \ cm^3$ of iron has approximately $8 g$ mass.
View full solution →From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20 m$ high building are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower.
View full solution →State and prove Basic Proportionality theorem.
The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is $2 \frac{16}{21}$, find the fraction.
View full solution →Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250.
Now. Mukta asked some questions as given below to the students:
(i) What is the least prime number used by students?
(ii) (a) How many students are in the class ?
OR
(b) What is the highest prime number used by students?
(iii) Which prime number has been used maximum times?
A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.
Based on the above, answer the following questions:
(i) Find the area of the square shaped grass field.
(ii) (a) Find the area of the total field in which these horses can graze.
OR
(b) If the length of the rope of each horse is increased from 7 m to 10 m , find the area grazed by one horse. (Use $\pi=3.14$ )
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm ? View full solution →