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ICSE Class 10 Algebra: Equations, Inequations & Matrices — practice questions — page 4

Explore 212 free Algebra: Equations, Inequations & Matrices questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra: Equations, Inequations & Matrices questions and exercises with answers

Showing questions 91–120 of 212.

Three scores are 66, 72, 81. A fourth is an integer from 0 to 100. How many give 75 ≤ mean < 78?Read the answer and worked solution →Count integer solutions common to (2x+1)/3 > (x-2)/2 and (5-x)/4 ≥ 1.Read the answer and worked solution →Mix x L of 30% juice with 10 L of 10% juice. For a final concentration strictly between 20% and 25%, x is:Read the answer and worked solution →Pens cost ₹8 each plus ₹30 delivery. Spending must be at least ₹100 but under ₹150. How many pen counts work?Read the answer and worked solution →For A=[[5,-2],[7,4]], which entry is in row 2, column 1?Read the answer and worked solution →Adding two 2×2 matrices gives a matrix of what order?Read the answer and worked solution →What role does a same-order null matrix play in matrix addition?Read the answer and worked solution →Multiplying [[2,-1],[3,4]] on the right by [[1,0],[0,1]] givesRead the answer and worked solution →What is [[2,-1],[3,4]] × [[0,0],[0,0]]?Read the answer and worked solution →Which matrix must be added to A to obtain a null matrix?Read the answer and worked solution →Subtracting A from B gives [[1,2],[3,4]]. Compute A minus B.Read the answer and worked solution →Which pair always has equal values for real 2×2 matrices?Read the answer and worked solution →For real 2×2 matrices, A-B=B-A holds precisely whenRead the answer and worked solution →Regrouping a sum of three same-order matrices is justified by which law?Read the answer and worked solution →Expand 3(A+B), where A and B are 2×2 matrices.Read the answer and worked solution →For any 2×2 matrix A, simplify (1/2)A+(3/2)A.Read the answer and worked solution →A matrix entry is -4. What is the corresponding entry of (-3/2)A?Read the answer and worked solution →If k is a non-zero rational number and kA=O, what must A be?Read the answer and worked solution →The top-left entry of (-1/2)A is 3. What is A's top-left entry?Read the answer and worked solution →I is the 2×2 identity matrix. If A+I=[[3,-1],[4,6]], find A.Read the answer and worked solution →For A=[[2,-3],[4,0]] and identity matrix I, find I-A.Read the answer and worked solution →Solve 2X+[[1,0],[-1,2]]=[[5,6],[3,0]].Read the answer and worked solution →If [[x+y,x-y],[0,1]]=[[7,1],[0,1]], find xy.Read the answer and worked solution →Calculate c₁₂ when C=[[1,2],[0,1]]×[[2,0],[1,3]].Read the answer and worked solution →A=[[1,2],[0,1]], B=[[2,0],[1,3]]. What are the top-left entries of AB and BA?Read the answer and worked solution →Square [[2,1],[0,2]]. Which number occupies the upper-right position?Read the answer and worked solution →For N=[[0,3],[0,0]], find N².Read the answer and worked solution →Left-multiply B=[[1,2],[3,4]] by [[2,0],[0,3]]. Find the lower-left entry.Read the answer and worked solution →P=[[0,1],[1,0]], A=[[2,3],[5,7]]. What is the first row of PA?Read the answer and worked solution →Find the bottom-right entry of [[2,0],[0,-1]] × [[3,0],[0,4]].Read the answer and worked solution →

Worked practice questions

Three scores are 66, 72, 81. A fourth is an integer from 0 to 100. How many give 75 ≤ mean < 78?

  1. 11 scores
  2. 12 scores
  3. 13 scores
  4. 14 scores
Show answer and solution

Correct answer: B. 12 scores

The first scores total 219, so 300 ≤ 219 + x < 312 gives the twelve integers from 81 through 92.

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Count integer solutions common to (2x+1)/3 > (x-2)/2 and (5-x)/4 ≥ 1.

  1. 8
  2. 10
  3. 9
  4. 7
Show answer and solution

Correct answer: C. 9

Clearing denominators gives x > -8 and x ≤ 1, leaving nine integers from -7 to 1.

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Mix x L of 30% juice with 10 L of 10% juice. For a final concentration strictly between 20% and 25%, x is:

  1. 10 ≤ x ≤ 30
  2. 5 < x < 15
  3. 20 < x < 30
  4. 10 < x < 30
Show answer and solution

Correct answer: D. 10 < x < 30

The bounds on (1 + 0.30x)/(10 + x) give x > 10 and x < 30.

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