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Mathematics — Algebra & Equations MCQs
Practice Mathematics — Algebra & Equations multiple-choice questions for Islamabad Police competitive exams. Each question includes the correct answer and a short explanation, and past-paper questions are marked so you can revise both repeated and fresh material in one place.
Despite the lack of necessary funds, the FIA successfully conducted the investigation into the financial irregularities, which earned praise from senior officials.
Despite of the lack of necessary funds, the FIA successfully conducted the investigation into the financial irregularities, earning praise from senior officials.
Despite the lack of necessary funds, the FIA successfully conducted the investigation into the financial irregularities, earning praise from senior officials.
Despite of the lack of necessary funds, the FIA successfully conducted the investigation into the financial irregularities, and it earned praise from senior officials.
ExplanationThe correct prepositional usage is 'Despite' or 'In spite of,' not 'Despite of.' Option B fixes the prepositional error while retaining the grammatical integrity of the concluding participle phrase.
If the police had implemented stricter protocols, traffic congestion in major urban centers would have been reduced significantly and improved the daily lives of commuters.
If the police had implemented stricter protocols, traffic congestion in major urban centers would have been reduced significantly, thereby improving the daily lives of commuters.
If the police had implemented stricter protocols, traffic congestion in major urban centers would have been reduced significantly, improving the daily lives of commuters.
If the police had implemented stricter protocols, traffic congestion in major urban centers would have been significantly reduced and improved the daily lives of commuters.
ExplanationThe use of 'thereby improving' (Option B) correctly establishes a causal relationship (reduction leads to improvement) and resolves the parallelism issue present in the other options, making the consequence explicit.
The officer was advised to follow the procedure, filing a complaint, and submit necessary documents.
The officer was advised to follow the procedure, file a complaint, and submit necessary documents.
The officer was advised to follow the procedure, file a complaint, and to submit necessary documents.
The officer was advised, to follow the procedure, filing a complaint, and submitting necessary documents.
ExplanationTo maintain parallelism, all elements following 'advised to' must be in the infinitive form (to + verb). The correct structure requires listing three parallel verbs: to follow, file, and submit. Option A achieves this by making all verbs base forms, ensuring grammatical consistency.
approved
approves
would approve
will approve
ExplanationThe clause 'If the Director General were present' establishes a hypothetical condition (Second Conditional), requiring 'would + base verb' in the main clause.
the chances of her giving a presentation are significantly higher
the chances of her giving a presentation would be significantly higher
the chances of her giving a presentation were significantly higher
the chances of her giving a presentation would be significantly higher
ExplanationThe clause 'If she were to attend...' establishes a hypothetical situation (Second Conditional). Therefore, the main clause must use the resulting conditional tense ('would be') to maintain consistency.
will be expected to undergo
is expected to undergo
are expected to undergo
have been expected to undergo
ExplanationThe subject of the sentence is 'the entire security department,' which is treated as a singular unit (a collective noun). Phrases starting with 'along with' do not change the singular nature of the main subject.
mandatory attendance sheets, timely filing of expense claims, and supervisor signs off on all reports.
mandatory attendance sheets, the timely filing of expense claims, and supervisor's sign-off on all reports.
mandatory attendance sheets, timely filing of expense claims, and supervisor signature on all reports.
mandatory attendance sheets, timely filing of expense claims, and the supervisor signing off on all reports.
ExplanationParallelism requires all items in the list to share the same grammatical structure. The best option uses noun phrases for all three items: 'sheets' (NP), 'filing' (NP/GP), and 'supervisor's sign-off' (NP).
submit
submission
to submit
submitting
ExplanationThe modal verb 'must' is followed by the bare infinitive form of the verb (submitting -> submit).
The committee members were greatly divided on which plan to adopt, making it difficult for them to reach any unanimous decision.
The committee members were greatly divided on which plan to adopt, which made it difficult for them to reach any unanimous decision.
The committee members were greatly divided on which plan to adopt, making it difficult for them to reach a unanimous decision.
The committee members were greatly divided on which plan to adopt, making it difficult for them to reach a unanimous decision.
ExplanationWhen referring to a specific, singular outcome like a unanimous decision, the definite article 'a' is required instead of 'any'. Option A provides the most grammatically sound structure.
If the new guidelines had been properly disseminated, the employees would not have misinterpreted the policy's crucial directives and thus could not avoid a significant overhaul of the departmental protocol.
If the new guidelines had been properly disseminated, the employees would not have misinterpreted the policy's crucial directives and thus could avoid a significant overhaul of the departmental protocol.
If the new guidelines had been properly disseminated, the employees would not have misinterpreted the policy's crucial directives and thus could avoid avoiding a significant overhaul of the departmental protocol.
If the new guidelines had been properly disseminated, the employees would not have misinterpreted the policy's crucial directives and thus could have avoided a significant overhaul of the departmental protocol.
ExplanationThis is a Third Conditional structure (hypothetical past). The result clause must use the perfect conditional modal ('could have avoided') to maintain tense parallelism with the initial 'If' clause ('had been disseminated').
The officers among us found that the evidence was insufficient.
We advised them that they should look into the matter themselves.
The new regulations apply to all departments in the entire organization.
Between you and me, I think they overreacted to the criticism.
ExplanationOption C is grammatically flawless, demonstrating correct subject-verb agreement ('regulations' is plural, requiring 'apply') and appropriate prepositional use. Option B is grammatically flawed; it should use an infinitive clause (e.g., 'We advised them to look into...'). While Options A and D are also grammatically sound, Option C presents the clearest and most textbook-perfect example of Subject-Verb Agreement and prepositional construction.
Neither the Chief Inspector, nor the accompanying officers, was aware of the security vulnerability that had been exploiting the system for weeks.
Neither the Chief Inspector nor the accompanying officers was aware of the security vulnerability that had been exploiting the system for weeks.
Neither the Chief Inspector nor the accompanying officers were aware of the security vulnerability that had been exploiting the system for weeks.
Neither the Chief Inspector nor the accompanying officers were aware of the security vulnerability which had exploited the system for weeks.
ExplanationThe correlative conjunction 'neither... nor' requires subject-verb agreement to follow the rule of proximity. When the second subject ('officers') is plural, the verb must be plural ('were').
He spoke to the chairman and advised him to submit his full proposal by the end of the week.
He spoke to the chairman, and he advised him to submit his full proposal by the end of the week.
He spoke to the chairman, advising him that he should submit his full proposal by the end of the week.
He spoke to the chairman advising him to submit his full proposal by the end of the week.
ExplanationThe use of the non-restrictive clause structure ('advising him that...') in Option D is the most grammatically sophisticated and fluid choice.
Despite the initial difficulty of the new system, the trainees were impressed by how quickly the staff adapted, making the training process remarkably effective.
Despite the initial difficulty of the new system, the trainees were impressed by the staff's quick adaptation, making the training process remarkably effective.
Despite the initial difficulty of the new system, the trainees were impressed by how quickly the staff adapted, which made the training process remarkably effective.
Despite the initial difficulty of the new system, the trainees were impressed by the staff's quick adaptation, thus making the training process remarkably effective.
ExplanationThe structure is corrected by focusing on the 'staff's quick adaptation' as the direct cause. Option D is the most concise and natural way to use a participial phrase to signal the resulting outcome.
Despite
Though
In spite of
Despite of
ExplanationThe phrase 'Despite of' is grammatically incorrect. The options 'Despite' (B) and 'In spite of' (C) are both correct prepositions. However, since the options are given to replace the error, 'Despite' is grammatically sufficient and correctly removes the superfluous 'of'.
should be given regular exercises, and advanced modules.
should be given regular exercises and advanced modules.
should be given regular exercises as well as, advanced modules.
should be given regular exercises as well as advanced modules.
ExplanationThe phrase 'as well as' connects two items that function as a unit and correctly mandates the use of 'and' to maintain parallelism and flow.
The more effort we put in, the greater the success we will achieve.
Putting more effort in, more success we will achieve.
The more effort we put in, the success we achieve will be greater.
More effort we put in, more successful we will be.
ExplanationThe construction 'The more... the more...' requires parallel grammatical structure. Option B maintains this structure correctly ('the greater the success').
Neither John nor his friends was aware of the changes.
Every candidate must bring its own CNIC.
Despite of the rain, the match continued.
The committee has decided to postpone the meeting until further notice.
ExplanationThe rule of proximity for 'neither...nor' dictates that the verb must agree with the subject closest to it. Since 'friends' is plural, the correct verb form is 'were', not 'was'. (Note: Options A, B, and D are all grammatically incorrect, but D tests a specific subject-verb agreement rule.)
Having completed the mandatory training, the staff were informed that they could now operate the sensitive machinery.
The staff, having completed the mandatory training, was informed that it could now operate the sensitive machinery.
Having completed the mandatory training, the staff was informed that they could now operate the sensitive machinery.
The staff was informed, having completed the mandatory training, that they could now operate the sensitive machinery.
ExplanationThe initial participial phrase 'Having completed...' must be grammatically linked to the subject. Furthermore, 'staff' is a collective noun, making it singular ('was informed') and requiring the singular pronoun 'it' for machine operation in the corrected clause.
After reviewing the archaeological findings, the museum displayed the ancient artifacts with pride.
The ancient artifacts were displayed with pride after reviewing the archaeological findings by the museum.
The museum displayed the ancient artifacts with pride, after reviewing the archaeological findings.
After reviewing the archaeological findings, the museum proudly displayed the ancient artifacts.
ExplanationOption A is the most concise and grammatically superior choice. It improves flow by replacing the adjectival phrase 'with pride' with the adverb 'proudly,' while maintaining the correct subject-verb relationship (the museum reviewed and displayed).
Having analyzed the data carefully, it was determined that the suspect was apprehended near the Lahore railway station.
The suspect, having analyzed the data carefully, was apprehended near the Lahore railway station.
Having analyzed the data carefully, the suspect was apprehended near the Lahore railway station.
The suspect was apprehended near the Lahore railway station, having analyzed the data carefully.
ExplanationThe dangling participle in Option A suggests the suspect (the one apprehended) was doing the analyzing, which is unlikely. Option D uses the passive structure 'it was determined' to correct this ambiguity.
Although the report was meticulously reviewed, several fundamental errors were found that required immediate correction before submission.
Although the report was meticulously reviewed, yet several fundamental errors were found that required immediate correction before submission.
Although the report was meticulously reviewed, however, several fundamental errors were found that required immediate correction before submission.
Although the report was meticulously reviewed, therefore several fundamental errors were found that required immediate correction before submission.
ExplanationThe use of 'Although' already establishes a subordinate clause and signals contrast; therefore, using the conjunction 'yet' is redundant. Option A removes this faulty conjunction, resulting in clear grammar.
The report suggested that the committee should consider implementing changes, and this would benefit
The report suggested that the committee should consider implementing changes, thereby benefiting
The report suggested that the committee should consider implementing changes, which are benefiting
The report suggested that the committee should consider implementing changes, that would benefit
ExplanationUsing 'thereby benefiting' correctly converts the clause into a precise participial phrase, effectively showing a clear cause-and-effect relationship, which is superior to the original structure.
Every one of the students has submitted their assignment by the deadline.
Neither the manager nor the employees were aware of the policy change.
She is more wise than her colleagues regarding this issue.
The committee submits its final report on Friday.
ExplanationWhen acting as a single unit, a collective noun like 'committee' takes a singular verb and pronoun ('submits', 'its'). Option A fails on singular/plural agreement (Every one needs 'his/her'). Option B is grammatically correct based on the rule of proximity (the verb agrees with the nearest subject, 'employees', requiring 'were'). However, 'C' provides the most standard and least ambiguous usage of the collective noun. Option D uses an incorrect comparative form; it should be 'wiser'.
Assistant Sub-Inspector believe
officers believes
officers believed
officers believe
ExplanationWith 'neither...nor,' the verb agrees with the noun closest to it ('officers'), which is plural, requiring the plural verb 'believe'.
findings; it was later recommended that a follow-up study be commissioned.
findings—it was later recommended that a follow-up study be commissioned.
findings, and it was later recommended that a follow-up study be commissioned.
findings, it was later recommended that a follow-up study be commissioned.
ExplanationThe original sentence contains a comma splice. Using the coordinating conjunction 'and' correctly joins the two independent clauses, showing the sequential relationship between the findings and the recommendation.
The shipment contain various items, which needs careful checking.
Each students must submit their assignment before the deadline.
She is more taller than her sister, which is obvious.
Between you and me, this policy is extremely questionable.
ExplanationSentence A is correct; 'between' is used idiomatically and grammatically for two entities, and 'me' is the proper object pronoun. Options B, C, and D contain definite errors: B has S-V agreement issues (should be contains/need); C uses a double comparative (should be taller); and D has plural and pronoun agreement issues (should be Each student... his/her).
submit time sheets daily, attend all required training sessions, and discuss operational improvements.
submit time sheets daily, to attend all required training sessions, and discussing operational improvements.
submitting time sheets daily, attending all required training sessions, and discussing operational improvements.
submitting time sheets daily, attending all required training sessions, and to discuss operational improvements.
ExplanationParallel structure requires that all list items maintain the same grammatical form. Since the initial verbs (submit and attend) are in the base form (imperative/infinitive complement), the final verb must also be in the base form: discuss.
The success of the project depends on many factors, including funding, teamwork, and the commitment of every single employee.
The success of the project depends on many factors, including funding, teamwork, and the commitment every single employee.
The success of the project depends on many factors, including funding, teamwork, and the commitment of every single employee.
The success of the project depends on many factors, including funding, teamwork, and commitment to every single employee.
ExplanationOption C maintains the clearest parallel structure by listing 'funding,' 'teamwork,' and 'the commitment of every single employee.'
Having checked the credentials thoroughly, the suspect admitted
The supervisor, having checked the credentials thoroughly, admitted
Having checked the credentials thoroughly, the supervisor admitted
The supervisor admitted, having checked the credentials thoroughly
ExplanationThe introductory phrase 'Having checked the credentials thoroughly' must be followed by the person who performed the action (the subject). Since the suspect performed the checking, Option C is the correct structure.
The committee was unable to reach a decision until the necessary background data were compiling and reviewing.
The committee was unable to reach a decision until the necessary background data were compiled and reviewed.
The committee was unable to reach a decision until the necessary background data was compiled and reviewed.
The committee was unable to reach a decision until necessary background data were to be compiled and reviewed.
ExplanationWhen 'data' is treated as a singular mass noun (which is often required in formal/official writing), it takes the singular verb 'was' and maintains parallel structure 'was compiled and reviewed'.
The report detailed the necessity for the government to allocate resources to modernizing the educational infrastructure, which includes schools and universities across the province.
The report detailed the necessity for the government to allocate resources to modernizing the educational infrastructure, including schools and universities across the province.
The report detailed the necessity for the government to allocate resources for modernizing the educational infrastructure, including schools and universities across the province.
The report detailed the necessity for the government to allocate resources in modernizing the educational infrastructure, including schools and universities across the province.
ExplanationAlthough 'necessity' is preferred, the primary error is the relative clause ('which'). Replacing it with the participle phrase ('including') smooths the flow and corrects the structure.
must
would be able to
will have to
should
ExplanationWhen conveying advice or recommendation regarding a required action, 'should' is the most appropriate modal verb. 'Must' expresses absolute necessity, while 'would be able to' is grammatically incorrect in this structure.
Frequently Asked Questions
Are these Mathematics — Algebra & Equations MCQs free?
Yes. Every Mathematics — Algebra & Equations MCQ on this page is free to practice, including the correct answer and explanation.
Do these include past-paper questions?
Yes — questions sourced from past papers are clearly marked with a "Past Paper" badge, alongside fresh practice questions.
Which exams do these Mathematics — Algebra & Equations MCQs help with?
They are aimed at Islamabad Police and related Pakistani competitive exams that test Mathematics — Algebra & Equations.
How should I practice subject-wise MCQs?
Attempt each question first, then reveal the answer and read the explanation. Short, focused sessions on one subject work better than long unstructured reading.