CBSE Class 10 Maths Basic 2026 Question Paper 430/5/3 with Solutions

The graph of a polynomial $p(x)$ is shown here. The number of zeroes of the polynomial $p(x)$ is

1. (A)5
2. (B)1
3. (C)0
4. (D)4

Three coins are tossed together. The probability of getting exactly two tails is

1. (A)$\frac{2}{8}$
2. (B)$\frac{1}{2}$
3. (C)$\frac{3}{8}$
4. (D)1

A bag contains some red and some white balls. A ball is drawn at random from the bag. If the probability of getting a red ball is $\frac{2}{7}$, then the probability of getting a white ball is

1. (A)$\frac{1}{14}$
2. (B)$\frac{5}{7}$
3. (C)$\frac{1}{7}$
4. (D)$\frac{2}{7}$

The total surface area of a solid cone of radius 7 cm and slant height 25 cm, is

1. (A)724 cm${}^2$
2. (B)704 cm${}^2$
3. (C)550 cm${}^2$
4. (D)616 cm${}^2$

The length of a pendulum is 70 cm and it describes an arc of length 88 cm when swings. The angle subtended by the arc at the centre is

1. (A)$36^{\circ }$
2. (B)$70^{\circ }$
3. (C)$72^{\circ }$
4. (D)$80^{\circ }$

The distance between the points $(-2,5)$ and $(5,-2)$ is

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

$17\times 11\times 13+11$ is

1. (A)a prime number.
2. (B)multiple of 17.
3. (C)a composite number.
4. (D)an odd number.

PQ is tangent to a circle at a point P on the circle. The number of tangents which can be drawn to the circle parallel to PQ, is

1. (A)2
2. (B)1
3. (C)many
4. (D)zero

If $-26,x,2$ are in A.P., then the value of $x$ is

1. (A)14
2. (B)$-13$
3. (C)$-12$
4. (D)$-14$

The roots of the quadratic equation $x^2+9=0$ are

1. (A)real and equal
2. (B)not real
3. (C)real and negative of each other
4. (D)rational numbers

PQ is tangent to the circle with centre O such that OP = 2OQ. $m\angle OPQ$ is

1. (A)$15^{\circ }$
2. (B)$60^{\circ }$
3. (C)$45^{\circ }$
4. (D)$30^{\circ }$

If value of $\cot \theta$ is $\sqrt{5}$, then $\sin \theta$ equals

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

A card is drawn from a well-shuffled deck of 52 playing cards. The probability of getting a queen of spade is

1. (A)$\frac{1}{26}$
2. (B)$\frac{1}{52}$
3. (C)0
4. (D)$\frac{1}{4}$

In the given figure, DE $\parallel$ BC.
If AD : AB = 1 : 3 and AE = 2.5 cm, then AC equals

1. (A)7.5 cm
2. (B)5 cm
3. (C)10 cm
4. (D)2.5 cm

If $14^{th}$ term of an A.P. is 4 and its $15^{th}$ term is zero, then its first term is

1. (A)$-48$
2. (B)$-56$
3. (C)56
4. (D)48

A cylinder of radius $r$ is surmounted on a hemisphere of same radius. If total height of the object is 13 cm, then its inner surface area is

1. (A)$2\pi r(r+13)$
2. (B)$13\pi r$
3. (C)$2\pi (13+r{)}^2$
4. (D)$26\pi r$

The value of k for which sum of the zeroes of the polynomial $p(x)=3x^2-kx+6$ is 2, is

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

Which of the following statements is not always true ?

1. (A)Two circles are similar.
2. (B)Two isosceles right triangles are similar.
3. (C)Two rectangles are similar.
4. (D)Two equilateral triangles are similar.

Assertion (A) : For an acute angle $\theta$, $\cos \theta$ is always less than 1.
Reason (R) : In a right-angled triangle, hypotenuse is the longest side and $\cos \theta =\frac{\text{Base}}{\text{Hypotenuse}}$.

1. (A)Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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) : Median of a data is the value of $\frac{N}{2}$, where N represents sum of all frequencies.
Reason (R) : Median divides the whole distribution in two equal parts.

1. (A)Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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 probability that a number selected at random from the numbers 30, 31, 32, 33, ....., 60 is (i) a prime number (ii) a multiple of 6.

Slips of letters of the word ‘BACKGROUND’ are put in a bowl and thoroughly mixed. One slip is picked up at random. Find the probability that picked up slip’s letter is (i) a vowel (ii) present in the word ‘BALL’.

In the given figure, two triangles ABC and PQR are shown such that $\angle A=\angle P$ and $\angle C=\angle R$. If AD $\perp$ BC and PS $\perp$ QR, then prove that (i) $△ADB\sim △PSQ$ (ii) AD $\times$ QS = BD $\times$ PS.

Find the H.C.F. and L.C.M. of 408 and 312.

If $\sec A=\sqrt{2}$ and $\tan B=\sqrt{3}$, then find the value of $2\sin A\cos B$.

Evaluate : $\frac{4{\cos }^{3}60^{\circ }+\text{cosec}30^{\circ }}{{\tan }^{2}30^{\circ }}$

In the given figure, PQ is a tangent to a circle with centre O(−5, 3). If coordinates of P and Q are (3, 1) and (0, 6) respectively, then using distance formula, show that PQ $\perp$ OQ.

If $\alpha ,\beta$ are zeroes of the polynomial $p(x)=5x^2-7x-3$, then form a quadratic polynomial whose zeroes are $\frac{2}{\alpha }$ and $\frac{2}{\beta }$.

Find the zeroes of the polynomial $p(x)=3x^2+7x-20$ and verify the relationship between its zeroes and the coefficients.

The $4^{th}$ and $10^{th}$ term of an A.P. are 13 and 25 respectively. Find its $24^{th}$ term.

From 232 to 540, find the number of multiples of 3.

Chord AB of a circle subtends an angle of $120^{\circ }$ at the centre O of the circle. Find the length of arc AB, if radius of the circle is 21 cm.

Determine the ratio in which the line $2x+y=6$ divides the line segment joining the points (1, 3) and (2, 5).

Prove that $\sqrt{2}$ is an irrational number.

Prove that : $\sqrt{\frac{1-\cos A}{1+\cos A}}=\frac{\tan A}{\sec A+1}$.

Find the missing frequencies p and q in the following frequency distribution, when sum of frequencies is 40 and mean is 19 :

ABCD is a rectangle of dimensions 80 cm $\times$ 60 cm. Another rectangle PQRS is drawn inside ABCD leaving space of equal width $x$ cm along the edges of ABCD. If area PQRS is half of the area ABCD, then find the value of $x$.

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/h more, it would have taken 30 minutes less for the same journey. Find the original speed of the train.

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ }$ and $30^{\circ }$ respectively. Find the height of the poles and the distance of the point from the poles.

In the given figure, $△ABC$ is right angled triangle with $\angle A=90^{\circ }$. AD is perpendicular to BC.
Prove that :
(i) $△DBA\sim △DAC$
(ii) $D{A}^2=DB\times DC$
(iii) Find the area of $△ABC$ when DB = 9 cm and DC = 16 cm.

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.

There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylinderical).
The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm. Considering mushroom a solid object, answer the following questions :
(i) What is the total height of a mushroom ?
(ii) Find the volume of the stem.
(iii) (a) Determine the volume of 7 such mushrooms.
OR (b) Find the total surface area of 7 such mushrooms.

In a circular museum hall of radius 14 m, some statues are displayed. Statues are kept inside the inner concentric circle of radius 7 m. One such statue lying in sector OAB, is fenced along line segments OA, AP, PB and BO where P is a point on outer circle.
Based on above information, answer the following questions :
(i) Find $m\angle AOP$. (1)
(ii) Prove that $△OAP\cong △OBP$. (1)
(iii) (a) Find the length of fencing required to protect the statue. (Take $\sqrt{3}$ = 1.73) (2)
OR (b) Find area of quadrilateral OAPB. (Take $\sqrt{3}$ = 1.73)

Seema daily goes to a park to exercise on machines available there. When Seema spent 15 minutes on exercise bicycle and 30 minutes on double cross walker, she received a message of burning 435 calories on her fitness watch. When she spent 30 minutes on exercise bicycle and 40 minutes on double cross walker, she received a message of burning 690 calories.
To find the number of calories burned per minute on each machine, answer the following :
(i) Represent the above situation in terms of a pair of linear equations in two variables.
(ii) Show that the equations have unique solution.
(iii) (a) Solve both equations to find the values of the variables using elimination method.
OR (b) Solve both equations to find the values of the variables using substitution method.