CBSE Class 10 Maths Basic 2023 Question Paper 430/1/1 with Solutions

The prime factorisation of natural number 288 is

1. (A)$2^4\times 3^3$
2. (B)$2^4\times 3^2$
3. (C)$2^5\times 3^2$
4. (D)$2^5\times 3^1$

If $2\cos \theta =1$, then the value of $\theta$ is

1. (A)$45^{\circ }$
2. (B)$60^{\circ }$
3. (C)$30^{\circ }$
4. (D)$90^{\circ }$

A card is drawn at random from a well-shuffled deck of 52 cards. The probability of getting a red card is :

1. (A)$\frac{1}{26}$
2. (B)$\frac{1}{13}$
3. (C)$\frac{1}{4}$
4. (D)$\frac{1}{2}$

The discriminant of the quadratic equation $2x^2-5x-3=0$ is

1. (A)1
2. (B)49
3. (C)7
4. (D)19

The distance between the points $(3,0)$ and $(0,-3)$ is

1. (A)$2\sqrt{3}$ units
2. (B)6 units
3. (C)3 units
4. (D)$3\sqrt{2}$ units

The seventh term of an A.P. whose first term is 28 and common difference $-4$, is

1. (A)0
2. (B)4
3. (C)52
4. (D)56

The graph of $y=p(x)$ is shown in the figure for some polynomial $p(x)$. The number of zeroes of $p(x)$ is/are :

1. (A)0
2. (B)1
3. (C)2
4. (D)3

The sides of two similar triangles are in the ratio 4 : 7. The ratio of their perimeters is

1. (A)4 : 7
2. (B)12 : 21
3. (C)16 : 49
4. (D)7 : 4

In the given figure, AB $\parallel$ CD. If AB = 5 cm, CD = 2 cm and OB = 3 cm, then the length of OC is

1. (A)$\frac{15}{2}$ cm
2. (B)$\frac{10}{3}$ cm
3. (C)$\frac{6}{5}$ cm
4. (D)$\frac{3}{5}$ cm

The sum and the product of zeroes of the polynomial $p(x)=x^2+5x+6$ are respectively

1. (A)$5,-6$
2. (B)$-5,6$
3. (C)2, 3
4. (D)$-2,-3$

A die is thrown once. Find the probability of getting a number less than 7.

1. (A)$\frac{5}{6}$
2. (B)1
3. (C)$\frac{1}{6}$
4. (D)0

The angle subtended by a vertical pole of height 100 m at a point on the ground $100\sqrt{3}$ m from the base is, has measure of

1. (A)$90^{\circ }$
2. (B)$60^{\circ }$
3. (C)$45^{\circ }$
4. (D)$30^{\circ }$

The volume of a cone of radius ‘r’ and height ‘3r’ is :

1. (A)$\frac{1}{3}\pi r^3$
2. (B)$3\pi r^3$
3. (C)$9\pi r^3$
4. (D)$\pi r^3$

The distance between two parallel tangents of a circle of diameter 7 cm is :

1. (A)7 cm
2. (B)14 cm
3. (C)$\frac{7}{2}$ cm
4. (D)28 cm

In the above figure, the criterion of similarity by which $△ABC\sim △PQR$ is :

1. (A)SSA (Side – Side – Angle) Similarity
2. (B)ASA (Angle – Side – Angle) Similarity
3. (C)SAS (Side – Angle – Side) Similarity
4. (D)AA (Angle – Angle) Similarity

The larger of two supplementary angles exceeds the smaller by 18 degrees. What is the measure of larger angle ?

1. (A)$81^{\circ }$
2. (B)$99^{\circ }$
3. (C)$36^{\circ }$
4. (D)$54^{\circ }$

In the given figure, the perimeter of $△ABC$ is :

1. (A)30 cm
2. (B)15 cm
3. (C)45 cm
4. (D)60 cm

In the given figure, BC and BD are tangents to the circle with centre O and radius 9 cm. If OB = 15 cm, then the length (BC + BD) is :

1. (A)18 cm
2. (B)12 cm
3. (C)24 cm
4. (D)36 cm

Assertion (A) : A tangent to a circle is perpendicular to the radius through the point of contact.
Reason (R) : The lengths of tangents drawn from the external point to a circle are equal.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Assertion (A) : The system of linear equations $3x+5y-4=0$ and $15x+25y-25=0$ is inconsistent.
Reason (R) : The pair of linear equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ is inconsistent if $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Find the coordinates of the point which divides the line segment joining the points $(7,-1)$ and $(-3,4)$ internally in the ratio 2 : 3.

Find the value(s) of y for which the distance between the points A(3, $-1$) and B(11, y) is 10 units.

Evaluate : ${\tan }^{2}60^{\circ }-2{\mathrm{cosec}}^{2}30^{\circ }-2{\tan }^{2}30^{\circ }$.

Find the LCM and HCF of 92 and 510, using prime factorisation.

Solve for $x$ and $y$ : $x+y=6$, $2x-3y=4$.

Find out whether the following pair of linear equations are consistent or inconsistent :
$5x-3y=11$, $-10x+6y=22$

In the given figure, ABC and AMP are two right triangles, right angled at B and M, respectively. Prove that $△ABC\sim △AMP$.

Prove that
$\sec \theta (1-\sin \theta )(\sec \theta +\tan \theta )=1$

Prove that
$\frac{1+\sec \theta }{\sec \theta }=\frac{{\sin }^2\theta }{1-\cos \theta }$

Show that the points $A(1,7)$, $B(4,2)$ $C(-1,-1)$ and $D(-4,4)$ are vertices of the square ABCD.

Prove that the tangents drawn from an external point to a circle are equal in length.

If $\alpha$, $\beta$ are zeroes of the quadratic polynomial $x^2+3x+2$, find a quadratic polynomial whose zeroes are $\alpha +1$, $\beta +1$.

Prove that $3+7\sqrt{2}$ is an irrational number, given that $\sqrt{2}$ is an irrational number.

In the given figure, DE $\parallel$ AC and DF $\parallel$ AE
Prove that
$\frac{BF}{FE}=\frac{BE}{EC}$

The diagonals of a quadrilateral ABCD intersect each other at the point O such that $\frac{AO}{BO}=\frac{CO}{OD}$
Show that quadrilateral ABCD is a trapezium.

The diagonal of a rectangular field is 60 m more than the shorter side. If the longer side is 80 m more than the shorter side, find the length of the sides of the field.

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present age.

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. Also, find the volume of the vessel.

The table given below shows the daily expenditure on food of 25 households in a locality :
Daily expenditure (₹): 100 – 150, 150 – 200, 200 – 250, 250 – 300, 300 – 350
Number of household: 4, 5, 12, 2, 2
Find the mean daily expenditure on food. Also, find the mode of the data.

A TV tower stands vertically on the bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ }$. From another point 20 m away from the point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ }$. Find the height of the tower.

An aeroplane when flying at a height of 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are $60^{\circ }$ and $45^{\circ }$ respectively. Find the vertical distance between the aeroplanes at that instant. (Use $\sqrt{3}=1.73$)

Aahana being a plant lover decides to convert her balcony into beautiful garden full of plants. She bought few plants with pots for her balcony. She placed the pots in such a way that number of pots in the first row is 2, second row is 5, third row is 8 and so on.
Based on the above information, answer the following questions :
(i) Find the number of pots placed in the 10th row. (1)
(ii) Find the difference in the number of pots placed in 5th row and 2nd row. (1)
(iii) If Aahana wants to place 100 pots in total, then find the total number of rows formed in the arrangement. (2)
OR (iii) If Aahana has sufficient space for 12 rows, then how many total number of pots are placed by her with the same arrangement ? (2)

Interschool Rangoli Competition was organized by one of the reputed schools of Odissa. The theme of the Rangoli Competition was Diwali celebrations where students were supposed to make mathematical designs. Students from various schools participated and made beautiful Rangoli designs. One such design is given below.
Rangoli is in the shape of square marked as ABCD, side of square being 40 cm. At each corner of a square, a quadrant of circle of radius 10 cm is drawn (in which diyas are kept). Also a circle of diameter 20 cm is drawn inside the square.
(i) What is the area of square ABCD ? (1)
(ii) Find the area of the circle. (1)
(iii) If the circle and the four quadrants are cut off from the square ABCD and removed, then find the area of remaining portion of square ABCD. (2)
OR (iii) Find the combined area of 4 quadrants and the circle, removed. (2)

Blood group describes the type of blood a person has. It is a classification of blood based on the presence or absence of inherited antigenic substances on the surface of red blood cells. Blood types predict whether a serious reaction will occur in a blood transfusion.
In a sample of 50 people, 21 had type O blood, 22 had type A, 5 had type B and rest had type AB blood group.
Based on the above, answer the following questions :
(i) What is the probability that a person chosen at random had type O blood ? (1)
(ii) What is the probability that a person chosen at random had type AB blood group ? (1)
(iii) What is the probability that a person chosen at random had neither type A nor type B blood group ? (2)
OR (iii) What is the probability that person chosen at random had either type A or type B or type O blood group ? (2)