Read and download PDF of CBSE Class 10 Mathematics Sample Paper Set X designed as per the latest curriculum and examination pattern for Class 10 issued by CBSE, NCERT and KVS. The latest Class 10 Mathematics Sample Papers have been provided with solutions so that the students can solve these practice papers and then compare their answers. This will help them to identify mistakes and improvement areas in Mathematics Standard 10 which they need to study more to get better marks in Grade 10 exams. After solving these guess papers also refer to solved Class 10 Mathematics Question Papers available on our website to build strong understanding of the subject
Mathematics Sample Paper Class 10
Students can refer to the below Class 10 Mathematics Sample Paper designed to help students understand the pattern of questions that will be asked in Grade 10 exams. Please download CBSE Class 10 Mathematics Sample Paper Set X
Mathematics Class 10 Sample Paper
SECTION – A
Question : If the numbers 2n – 1, 3n + 2 and 6n – 1 are in A.P., then find n and hence find the numbers.
Answer : Let 2n – 1, 3n + 2 and 6n – 1 are in A.P.
∴ (3n + 2) – (2n – 1) = (6n – 1) – (3n + 2)
⇒ n + 3 = 3n – 3 ⇒ 6 = 2n ⇒ n = 3
∴ Numbers are : 2(3) –1 = 5, 3(3) +2 = 11 and 6(3) –1 = 17.
Question : A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is recast into a hollow cylinder of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
OR
If the diameter of cross-section of a wire is decreased by 5%, how much percent will the length be increased so that volume remains the same?
Answer : Volume of iron = (440 × 260 × 100) cm3
Internal radius of the pipe = 30 cm
External radius of the pipe = (30 + 5)cm = 35 cm
Let the length of the pipe be h cm.
Volume of iron in the pipe = (External volume) – (Internal volume)
OR
If the diameter of cross-section of a wire is decreased by 5%, how much percent will the length be increased so that volume remains the same?
Answer :
Question : Find k so that the quadratic equation (k + 1)x2 − 2(k + 1)x + 1 = 0 has equal roots.
OR
If one root of the quadratic equation 3x2 + px + 4 = 0is 2/3, then find the value of p and the other root of the equation.
Answer : We have (k + 1)x2 – 2(k + 1)x + 1 = 0
Comparing with Ax2 + Bx + C = 0 we get A = (k + 1),B,= -2(k+ 1), C= 1
If roots are equal, then D = 0, i.e. B2 – 4AC = 0
⇒ B2 = 4AC
⇒ 4(k+ 1)2 = 4(k+ 1)
⇒ k2 + 2k + 1 = k + 1
⇒ k2 + k = 0
⇒ k(k + 1) = 0
⇒ k = 0, - 1Since k = - 1 does not satisfy the equation, thus k = 0
OR
If one root of the quadratic equation 3x2 + px + 4 = 0is 2/3, then find the value of p and the other root of the equation.
Answer :
Question : The difference of mother’s age and her daughter’s age is 21 years and the twelfth part of the product of their ages is less than the mother’s age by 18 years. Find their ages.
Answer :
Question : In figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120⁰, then prove that OR = PR + RQ.
Question : Calculate the mean for the following frequency distribution:
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